Question

MAT 132 TEST 2 Review (Jan 2025 ) 1. If a ball is to thrown verically upwards, the ball reaches a height of 10 fl a) \( y=-4 t^{2}+6 t+13 \) b) \( y=-7 t^{2}+2(+23 \) feet after \( t \) seconds. i) find max height ii) when ball reach Gack to ground iii) when does ball reaches \( 12 \mathrm{ft}, 5 \mathrm{ft} \)

Ask by Davies Sanders. in Malaysia
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

For equation (a): - Maximum height: 15.25 feet - Time to reach the ground: 2.70 seconds - Time to reach 12 ft: 1.65 seconds - Time to reach 5 ft: 2.35 seconds For equation (b): - Maximum height: \( \frac{1}{7} \) seconds - Time to reach the ground: - Time to reach 12 ft: - Time to reach 5 ft:

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Bonus Knowledge

For the quadratic equation \( y = -4t^2 + 6t + 13 \), the maximum height can be found using the vertex formula \( t = -\frac{b}{2a} \). Here, \( a = -4 \) and \( b = 6 \). Plugging in these values gives \( t = \frac{6}{8} = 0.75 \) seconds. Substitute \( t = 0.75 \) back into the equation to find the maximum height, which is approximately \( 15.5 \) feet. To find when the ball hits the ground, we need to set \( y = 0 \). Solving the equation \( -4t^2 + 6t + 13 = 0 \) using the quadratic formula will yield the time when it returns to the ground. You will find two values for \( t \): one when it is thrown up and another when it falls back down. For \( 12 \) ft and \( 5 \) ft, set the equation equal to these heights and solve for \( t \) in both cases, which will give you the moments when the ball reaches these heights. Now, let's not forget that while working through these calculations, sketching a graph could really put things in perspective! Seeing the arc of the ball's flight visually illustrates when it reaches its peak height and when it splashes back down—it can make the math much more engaging! Also, while attempting to solve for various heights of \( 12 \) ft and \( 5 \) ft, be cautious of potential errors in calculation, such as misapplying the quadratic formula or overlooking negative roots that could also represent the ball's return trajectory. Double-check your work and ensure each step is accounted for, especially when substituting back into the height function!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy