A thorny chain rule problem and the fundamental theorem of calculus MC
question.
A thorny chain rule problem and the fundamental theorem of calculus MC question.
The document discusses graphing simple quadratic functions by hand without a calculator or table of values. It provides examples of graphing quadratic equations like y = x^2, y = 1/2x^2 + 2, and y = 5x^2 - 8, explaining how to identify the vertex and determine if the graph has roots by setting it equal to 0. It then gives a real world example of graphing the function d=-16t^2 +30 that models the height of a stick dropped from a flying eagle over time, noting that the domain is non-negative to only measure time positively and the range does not exceed 30 feet since that was the starting height.
CNC Mazar will provide internet service to ELIET TRALLER TOUR for one month according to the agreement sheet. CNC will charge 3000af per month for the service, with payment required in advance on the first date of each month. The agreement was signed by the managing director of CNC Mazar and includes their contact information.
The document summarizes the author's experiences visiting various locations in Havana, Cuba. It describes the Malecon coastal promenade, long lines at the popular state-run Coppelia ice cream parlor, better home-cooked meals from private restaurants compared to state-owned restaurants, patriotic symbols and billboards supporting Fidel Castro and the revolution, and a plaza honoring Jose Marti, a poet and leader of Cuba's independence movement.
Fallon strategic planners Aki Spicer (Aki Octagon) and Avin Narasimhan (Desi Stoneage) have come back from the future to offer their POV about Virtuality and it’s implications for brands.
One of the hottest debates in marketing circles today is the viability of virtual worlds like Second Life. What are they? What do people do there Why? What’s in it for me—if anything? We’ve seen companies flooding these worlds, and some are finding it difficult to translate their virtual world presence into real world gains.
The truth is, we traverse virtual dimensions every day without even thinking about it. From financial transactions, to games, to our daily Facebook interactions with friends, Virtuality is a new normal and it impacts many facets of our lives. It is through this lens that we explore what Virtuality means now and in the future, and what our agency needs to know to extract the most from it.
*Brainfood is an monthly digest of Fallon Planner’s strategic intelligence and bridges the gap between trends, business issues, and actionable opportunities for the agency and clients.
Behind Their Eyes - making thinking visible is not enough
Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
“If you really want to understand something, try changing it.” - Kurt Lewin
As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore inquiry as a pedagogical stance and the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants will leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
The document discusses graphing simple quadratic functions by hand without a calculator or table of values. It provides examples of graphing quadratic equations like y = x^2, y = 1/2x^2 + 2, and y = 5x^2 - 8, explaining how to identify the vertex and determine if the graph has roots by setting it equal to 0. It then gives a real world example of graphing the function d=-16t^2 +30 that models the height of a stick dropped from a flying eagle over time, noting that the domain is non-negative to only measure time positively and the range does not exceed 30 feet since that was the starting height.
CNC Mazar will provide internet service to ELIET TRALLER TOUR for one month according to the agreement sheet. CNC will charge 3000af per month for the service, with payment required in advance on the first date of each month. The agreement was signed by the managing director of CNC Mazar and includes their contact information.
The document summarizes the author's experiences visiting various locations in Havana, Cuba. It describes the Malecon coastal promenade, long lines at the popular state-run Coppelia ice cream parlor, better home-cooked meals from private restaurants compared to state-owned restaurants, patriotic symbols and billboards supporting Fidel Castro and the revolution, and a plaza honoring Jose Marti, a poet and leader of Cuba's independence movement.
Fallon strategic planners Aki Spicer (Aki Octagon) and Avin Narasimhan (Desi Stoneage) have come back from the future to offer their POV about Virtuality and it’s implications for brands.
One of the hottest debates in marketing circles today is the viability of virtual worlds like Second Life. What are they? What do people do there Why? What’s in it for me—if anything? We’ve seen companies flooding these worlds, and some are finding it difficult to translate their virtual world presence into real world gains.
The truth is, we traverse virtual dimensions every day without even thinking about it. From financial transactions, to games, to our daily Facebook interactions with friends, Virtuality is a new normal and it impacts many facets of our lives. It is through this lens that we explore what Virtuality means now and in the future, and what our agency needs to know to extract the most from it.
*Brainfood is an monthly digest of Fallon Planner’s strategic intelligence and bridges the gap between trends, business issues, and actionable opportunities for the agency and clients.
Behind Their Eyes - making thinking visible is not enough
Walk into any classroom and watch the breakneck pace at which teachers are working hard to help students learn. Mind you, if we don’t uncover what students are thinking while learning, they may be running down the wrong path. OK, so we need ways to make student thinking visible. Seeing their thinking is important, but we also need to create the time and space for teachers to absorb, reflect, and act on what their students thinking reveals. This workshop shares strategies both for making student thinking visible and for creating time and space for teachers to meaningfully act on what they learn about what’s going on behind their eyes.
“If you really want to understand something, try changing it.” - Kurt Lewin
As the Director of Learning for a school division made up of 18 schools, my job is to help lead the largest change initiative ever undertaken in our school community. One of the most important, difficult, messy things any school leader does is lead change. While we can learn from the change leadership of others, copying their work most often leads to failure. Success is more likely to come from adapting others work to our own context. In this workshop I share the journey we’ve undertaken collectively in our schools; how we developed a shared vision, cultivated collaborative cultures, maintained a focus on deep learning, and wrestle with the nuances of accountability. Informed by the latest research on change management in education, we also model strategies for fostering deep learning conversations in your schools. We’ll engage in some deeper learning conversations together and take back a wealth of ideas you can adapt to your own context. Developing collaborative cultures is careful and precise work that has profound impact when carried out well. So how do you do that? Come, let’s learn together. Good people are important, but good cultures are moreso.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore inquiry as a pedagogical stance and the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants will leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
The document is a presentation about digital citizenship given by Darren Kuropatwa at the Building Learning Communities Conference in Boston, MA in July 2017. It discusses the importance of digital citizenship and responding to adversity with persistent kindness. It provides examples of digital citizenship issues and scenarios for discussion. It encourages participants to think about their own digital footprint and how to be good digital citizens.
Presented at the Riding the Wave Conference in Gimli, Manitoba. May 2017.
In two words, you remember the whole story: glass slipper, sour grapes, cold porridge. You remember more than facts, you recall relationships & deeper connections between characters. Some of the powerful ways we leverage digital for deeper learning includes challenging sources of information (fake news), exploring bias (developing empathy through multiple perspectives), and creating powerful feedback loops that foster deeper learning.
Powerful narratives, in a word or two, bring to mind a wealth of ideas & relationships; more than just facts. How can we find stories that make our teaching sticky and help kids find, and more importantly tell, stories that make learning stick? This workshop will equip teachers with the skills & knowledge to foster deeper learning across the curriculum by intentionally leveraging digital tools to foster deeper learning.
Tales of Learning and the Gifts of Footprints v4.2Darren Kuropatwa
This document appears to be a presentation about digital learning and storytelling. It discusses shifting from compliance to care, private to public learning, and consumer to participatory models. It addresses what digital storytellers look like and principles of learning including starting where students are, learning being done by and for students, students talking about learning, having learning targets, and feedback. It encourages generosity, sharing tales of learning, and giving the gifts of footprints.
Presented at the Richmond District Conference, Feb 2017.
A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning. Held at the BYTE Conference 2017 in Portage la Prairie, Manitoba.
A group of educators from the BYTE Conference 2017 (Build Your Teaching Experience) share their ideas about learning as a series of visual metaphors they found on their phones.
The document discusses storytelling and how it can be used as a tool for learning. It suggests that storytelling allows students to think in metaphors and learn through stories. It provides examples of how digital tools like QR codes and apps can be used to incorporate storytelling into the classroom. It also outlines some rules of thumb for using storytelling, such as personalizing tasks to students' experiences, collaborating on group projects, and getting feedback from both inside and outside the classroom.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
This document contains multiple sections on topics related to technology and its impact on society, including how the internet allows information to be easily shared but also persist indefinitely, issues around online privacy and bullying, and ways for parents to support their children's safe and responsible internet use. The document advocates for empowering youth and promoting kindness both online and off.
Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning.
A group of educators from the Anderson Union High School & Redding School Districts and share their ideas about learning as a series of visual metaphors.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
This document contains a collection of images, quotes, and short passages on topics related to online communities, sharing, and empowerment through technology. The snippets discuss how the internet allows information to be easily shared, encourages learning, and can help empower victims of bullying. The overarching theme is about the positive impact community and connection through online platforms can provide.
Slides to support a master class at the Building Learning Communities Conference in Boston, MA. 18 July 2016.
How can we make learning sticky using powerful storytelling frameworks that tap into peoples' emotions? How do we involve all students in creating digital content that doesn't also create hours of content for teachers to assess? This interactive session will showcase Digital Storytelling activities teachers can use in class tomorrow! Document student learning & foster reflective ways for students to share their learning. 1st: we play! Then we'll discuss how to practically adapt these ideas, make them your own, and figure out what sort of infrastructure needs to be in place to support these kinds of powerful learning experiences. We’ll learn how to exercise your students' & your own creativity muscles and share simple strategies for collecting & publishing student work.
Slides in support of a professional learning day for administrators in Hanover School Division focused on developing a common language & understanding of Deep Learning Design.
Slides in support of a professional learning day for administrators in Hanover School Division focused on answering the question: What is Inquiry Learning?
Slides to facilitate a conversation with school leaders & administrators around emerging issues related to Digital Citizenship. Both to raise awareness of the multifaceted nature of the subject and identify action items for schools moving forward.
The material here is taken from Mike Ribble's "Nine Elements of Digital Citizenship".
http://digitalcitizenship.net
The document is a presentation about digital citizenship given by Darren Kuropatwa at the Building Learning Communities Conference in Boston, MA in July 2017. It discusses the importance of digital citizenship and responding to adversity with persistent kindness. It provides examples of digital citizenship issues and scenarios for discussion. It encourages participants to think about their own digital footprint and how to be good digital citizens.
Presented at the Riding the Wave Conference in Gimli, Manitoba. May 2017.
In two words, you remember the whole story: glass slipper, sour grapes, cold porridge. You remember more than facts, you recall relationships & deeper connections between characters. Some of the powerful ways we leverage digital for deeper learning includes challenging sources of information (fake news), exploring bias (developing empathy through multiple perspectives), and creating powerful feedback loops that foster deeper learning.
Powerful narratives, in a word or two, bring to mind a wealth of ideas & relationships; more than just facts. How can we find stories that make our teaching sticky and help kids find, and more importantly tell, stories that make learning stick? This workshop will equip teachers with the skills & knowledge to foster deeper learning across the curriculum by intentionally leveraging digital tools to foster deeper learning.
Tales of Learning and the Gifts of Footprints v4.2Darren Kuropatwa
This document appears to be a presentation about digital learning and storytelling. It discusses shifting from compliance to care, private to public learning, and consumer to participatory models. It addresses what digital storytellers look like and principles of learning including starting where students are, learning being done by and for students, students talking about learning, having learning targets, and feedback. It encourages generosity, sharing tales of learning, and giving the gifts of footprints.
Presented at the Richmond District Conference, Feb 2017.
A series of stories woven together to start a conversation with middle and high school students, teachers, and parents about living our lives on and offline (on The Fourth Screen) more thoughtfully.
This talk focuses primarily on the ideas of Empathy, Empowerment & Persistent Kindness and shares resources teachers can use to lead these sorts of conversations with their own students.
Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning. Held at the BYTE Conference 2017 in Portage la Prairie, Manitoba.
A group of educators from the BYTE Conference 2017 (Build Your Teaching Experience) share their ideas about learning as a series of visual metaphors they found on their phones.
The document discusses storytelling and how it can be used as a tool for learning. It suggests that storytelling allows students to think in metaphors and learn through stories. It provides examples of how digital tools like QR codes and apps can be used to incorporate storytelling into the classroom. It also outlines some rules of thumb for using storytelling, such as personalizing tasks to students' experiences, collaborating on group projects, and getting feedback from both inside and outside the classroom.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
This document contains multiple sections on topics related to technology and its impact on society, including how the internet allows information to be easily shared but also persist indefinitely, issues around online privacy and bullying, and ways for parents to support their children's safe and responsible internet use. The document advocates for empowering youth and promoting kindness both online and off.
Slides to support a master class on making student thinking visible through practical hands-on activities and structured around Dylan Wiliam's work on formative assessment and active learning.
A group of educators from the Anderson Union High School & Redding School Districts and share their ideas about learning as a series of visual metaphors.
In a world where knowledge is more a verb than a noun how do we foster deep learning in our students? Good questions cause thinking. Unfortunately, many of the questions regularly asked in classrooms focus on knowledge as a noun. This presentation will explore the effective use of thinking and learning tools in the classroom. We will work together to model teaching practices that lead to students co-constructing a networked (real world) rather than hierarchical (artificial) understanding of their world regardless of grade level or discipline.
Participants leave this workshop with a toolkit of research based questioning and thinking strategies they can begin using with their students tomorrow.
This document contains a collection of images, quotes, and short passages on topics related to online communities, sharing, and empowerment through technology. The snippets discuss how the internet allows information to be easily shared, encourages learning, and can help empower victims of bullying. The overarching theme is about the positive impact community and connection through online platforms can provide.
Slides to support a master class at the Building Learning Communities Conference in Boston, MA. 18 July 2016.
How can we make learning sticky using powerful storytelling frameworks that tap into peoples' emotions? How do we involve all students in creating digital content that doesn't also create hours of content for teachers to assess? This interactive session will showcase Digital Storytelling activities teachers can use in class tomorrow! Document student learning & foster reflective ways for students to share their learning. 1st: we play! Then we'll discuss how to practically adapt these ideas, make them your own, and figure out what sort of infrastructure needs to be in place to support these kinds of powerful learning experiences. We’ll learn how to exercise your students' & your own creativity muscles and share simple strategies for collecting & publishing student work.
Slides in support of a professional learning day for administrators in Hanover School Division focused on developing a common language & understanding of Deep Learning Design.
Slides in support of a professional learning day for administrators in Hanover School Division focused on answering the question: What is Inquiry Learning?
Slides to facilitate a conversation with school leaders & administrators around emerging issues related to Digital Citizenship. Both to raise awareness of the multifaceted nature of the subject and identify action items for schools moving forward.
The material here is taken from Mike Ribble's "Nine Elements of Digital Citizenship".
http://digitalcitizenship.net
AI Transformation Playbook: Thinking AI-First for Your BusinessArijit Dutta
I dive into how businesses can stay competitive by integrating AI into their core processes. From identifying the right approach to building collaborative teams and recognizing common pitfalls, this guide has got you covered. AI transformation is a journey, and this playbook is here to help you navigate it successfully.
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Unlocking WhatsApp Marketing with HubSpot: Integrating Messaging into Your Ma...Niswey
50 million companies worldwide leverage WhatsApp as a key marketing channel. You may have considered adding it to your marketing mix, or probably already driving impressive conversions with WhatsApp.
But wait. What happens when you fully integrate your WhatsApp campaigns with HubSpot?
That's exactly what we explored in this session.
We take a look at everything that you need to know in order to deploy effective WhatsApp marketing strategies, and integrate it with your buyer journey in HubSpot. From technical requirements to innovative campaign strategies, to advanced campaign reporting - we discuss all that and more, to leverage WhatsApp for maximum impact. Check out more details about the event here https://events.hubspot.com/events/details/hubspot-new-delhi-presents-unlocking-whatsapp-marketing-with-hubspot-integrating-messaging-into-your-marketing-strategy/
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Discover the Beauty and Functionality of The Expert Remodeling Serviceobriengroupinc04
Unlock your kitchen's true potential with expert remodeling services from O'Brien Group Inc. Transform your space into a functional, modern, and luxurious haven with their experienced professionals. From layout reconfiguration to high-end upgrades, they deliver stunning results tailored to your style and needs. Visit obriengroupinc.com to elevate your kitchen's beauty and functionality today.
NewBase 20 June 2024 Energy News issue - 1731 by Khaled Al Awadi_compressed.pdfKhaled Al Awadi
Greetings,
Hawk Energy is pleased to present you with the latest energy news
NewBase 20 June 2024 Energy News issue - 1731 by Khaled Al Awadi
Regards.
Founder & S.Editor - NewBase Energy
Khaled M Al Awadi, Energy Consultant
MS & BS Mechanical Engineering (HON), USAGreetings,
Hawk Energy is pleased to present you with the latest energy news
NewBase 20 June 2024 Energy News issue - 1731 by Khaled Al Awadi
Regards.
Founder & S.Editor - NewBase Energy
Khaled M Al Awadi, Energy Consultant
MS & BS Mechanical Engineering (HON), USAGreetings,
Hawk Energy is pleased to present you with the latest energy news
NewBase 20 June 2024 Energy News issue - 1731 by Khaled Al Awadi
Regards.
Founder & S.Editor - NewBase Energy
Khaled M Al Awadi, Energy Consultant
MS & BS Mechanical Engineering (HON), USAGreetings,
Hawk Energy is pleased to present you with the latest energy news
NewBase 20 June 2024 Energy News issue - 1731 by Khaled Al Awadi
Regards.
Founder & S.Editor - NewBase Energy
Khaled M Al Awadi, Energy Consultant
MS & BS Mechanical Engineering (HON), USAGreetings,
Hawk Energy is pleased to present you with the latest energy news
NewBase 20 June 2024 Energy News issue - 1731 by Khaled Al Awadi
Regards.
Founder & S.Editor - NewBase Energy
Khaled M Al Awadi, Energy Consultant
MS & BS Mechanical Engineering (HON), USAGreetings,
Hawk Energy is pleased to present you with the latest energy news
NewBase 20 June 2024 Energy News issue - 1731 by Khaled Al Awadi
Regards.
Founder & S.Editor - NewBase Energy
Khaled M Al Awadi, Energy Consultant
MS & BS Mechanical Engineering (HON), USA
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japanese language course in delhi near meheyfairies7
Next is the Nihon Language Academy in East Delhi, renowned for its comprehensive curriculum and interactive teaching methods. They boast a faculty of experienced educators with a blend of both Indian and Japanese nationals. The academy provides extensive support for JLPT exam preparation along with personalized tutoring sessions if needed. Nihon Language Academy also arranges exchange programs with partner institutes in Japan, which provides students an opportunity to experience Japanese culture and language first-hand.
The Enigmatic Gemini: Unveiling the Dual Personalitiesmy Pandit
Explore the fascinating world of the Gemini Zodiac Sign, where duality reigns supreme. Discover the personality traits, important dates, and horoscope insights that define the ever-curious and communicative Gemini.
[To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
Unlock the full potential of the MECE (Mutually Exclusive, Collectively Exhaustive) Principle with this comprehensive PowerPoint deck. Designed to enhance your analytical skills and strategic decision-making, this presentation guides you through the fundamental concepts, advanced techniques, and practical applications of the MECE framework, ensuring you can apply it effectively in various business contexts.
The MECE Principle, developed by Barbara Minto, an ex-consultant at McKinsey, is a foundational tool for structured thinking. Minto is also renowned for the Minto Pyramid Principle, which emphasizes the importance of logical structuring in writing and presenting ideas. This presentation includes a clear explanation of the MECE principle and its significance. It offers a detailed exploration of MECE concepts and categories, highlighting how to create mutually exclusive and collectively exhaustive segments. You will learn to combine MECE with other powerful business frameworks like SWOT, Porter's Five Forces, and BCG Matrix. Discover sophisticated methods for applying MECE in complex scenarios and enhancing your problem-solving abilities. The deck also provides a step-by-step guide to performing thorough and structured MECE analyses, ensuring no aspect is overlooked. Insider tips are included to help you avoid common mistakes and optimize your MECE applications.
The presentation features illustrative examples from various industries to show MECE in action, providing practical insights and inspiration. It includes engaging group activities designed for the practice of the MECE principle, fostering collaborative learning and application. Key takeaways and success factors for mastering the MECE principle and applying it in your professional work are also covered.
The MECE Principle presentation is meticulously designed to provide you with all the tools and knowledge you need to master the MECE principle. Whether you're a business analyst, manager, or strategist, this presentation will empower you to deliver insightful and actionable analysis, drive better decision-making, and achieve outstanding results.
LEARNING OBJECTIVES:
1. Understand the MECE Principle
2. Improve Analytical Skills
3. Apply MECE Framework
4. Enhance Decision-Making
5. Optimize Resource Allocation
6. Facilitate Strategic Planning
Revolutionizing Surface Protection Xlcoatings Nano Based SolutionsExcel coatings
Excelcoating Transforming surface protection with their cutting-edge, eco-friendly nano-based coatings. This presentation delves into their innovative product lineup, including Excel CoolCoat for roof cooling, Excel NanoSeal for cement surfaces, Excel StayCool for UV-filtering glass, Excel StayClean for solar panels, Excel CoolTile for heat-reflective tiles, and Excel InsulX for film insulation.
2. 1. The annual interest rate on mortgages (loans for home purchases) during the
1980’s varied according to the function r(t) = 0.07 + 0.03cos (0.53t - 1.60),
where t represents the number of years since January 1, 1980. (So, for example,
r(3) ≈ 0.10 indicates a 10% mortgage interest rate on January 1, 1983.)
Bank data from the same years reveal that the number N of home mortgages
issued per year depended on the mortgage interest rate r, according to the
formula N(r) = (40 000)(0.5)r. (So, for example, N(0.05) ≈ 38 637 tells us that
when the mortgage rate was 5%, the banks issued 38 637 mortgages per year.)
(a) What was the mortgage interest rate on January 1, 1985.
(b) How many mortgages per year were issued when the interest rate was 9%?
(c) Since r (the interest rate) depends on t (time) and N (the number of
mortgages) depends on r, then N must be a function of t. Determine the rate at
which the number of mortgages was changing (with respect to time) 5 years
after January 1, 1980.
3. (c) Since r (the interest rate) depends on t (time) and N (the number of
mortgages) depends on r, then N must be a function of t. Determine the rate at
which the number of mortgages was changing (with respect to time) 5 years
after January 1, 1980.