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IceJOKER [234]
3 years ago
14

Consider the function f(x) = x² – 3x – 4 and complete parts (a) through (C). (a) Find f(a+h); f(a+h)-f(a) (b) Find (c) Find the

instantaneous rate of change of f when a = 7. (a) f(a+h) = (Simplify your answer. Do not factor.)
Mathematics
1 answer:
Artist 52 [7]3 years ago
7 0

Answer:

(a)

f(a+h)=a^{2} +2ah+h^{2} -3a-3h-4

(b)

f(a+h)-f(a)=2ah+h^{2} -3h

(c)

\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2h+11

Step-by-step explanation:

(a)

Simply evaluate (a+h) in the function:

f(a+h)=(a+h)^{2} -3(a+h)-4=a^{2} +2ah+h^{2} -3a-3h-4

(b)

Evaluate (a) in the function:

f(a)=a^{2} -3a-4

Using the previous answers lets calculate f(a+h)-f(a)

f(a+h)-f(a)=a^{2} +2ah+h^{2} -3a-3h-4-(a^{2} -3a-4)=2ah+h^{2} -3h

(c) To find the rate of change of f(a+1) when a=7 we need to calculate its derivate at that point:

\frac{df(a+h)}{dx} \left \{ { \atop {a=7}} \right. =2a+2h-3=2(7)+2h-3=2h+14-3=2h+11

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Umnica [9.8K]

Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture, the amount of steel Kassidy will need is mathematically given as

SA=16.094711 ft^2

<h3>What is the amount of steel Kassidy will need to create the sculpture if the base of the sculpture is 4-feet tall and has a 2-foot diameter.?</h3>

Generally, the equation for the surface area of a cone is mathematically given as

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Therefore

SA=πr(rπ+√(h^2+r^2))

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8 0
2 years ago
Solve h = −16t2 + 36t + 4.
kvasek [131]
I can do each of the things I asked above.
So, let's change this into vertex form:
h=-16t^2+36t+4
h=(-16t^2+36t)+4
h=-16(t^2-2.25t)+4
h=-16(t^2-2.25t+1.27-1.27)+4
h=-16(t^2-2.25t+1.27)+20.32+4
h=-16(t-1.125)^2+24.32
The vertex is at (1.125,24.32)
<span>Answers may vary due to rounding

</span>Factored Form:
h = -16t^2 + 36t + 4
h = -4\left(4t^2-9t-1\right)

Quadratic Formula:
x =  \frac{-b +/- \sqrt{b^2-4(a)(c)}}{2a}
<span>h = -16t^2 + 36t + 4
</span>a = -16 b = 36 c = 4
h = \frac{-(36) +/- \sqrt{(36)^2-4(-16)(4)}}{2(-16)}
h = \frac{-36 +/- \sqrt{1552}}{-32}
h = ≈-0.11
h = ≈2.36

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