Destiny’s bank account has a balance of $612.75 before she starts spending money. She makes the following transactions: (See tab
le below.) Destiny is considering splitting the cost of a new TV with her roommate. Her share would be $110.35. Can she afford this? *
No, she is overdrawn already.
No, making that purchase will overdraw her account.
Yes, but doing so will clear out her account.
Yes, she can make the purchase and have money left over.
No, she is overdrawn already.
No, making that purchase will overdraw her account.
Yes, but doing so will clear out her account.
Yes, she can make the purchase and have money left over.
1 answer:
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General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as .
Comparing the function f(x)=ax^{2} +bx+c with the given function , we get
,
and
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds
The maximum height is found by substituting in the function as below:
Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts.