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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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swat32

A rotation is a transformation that preserves figure shape, figure sizes, angles and lengths.

Therefore,

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Answer: option C and D.

6 0
3 years ago
A rectangular prism is 3 units high 2 units wide and 5 units long what is its surface area in square units
Luba_88 [7]

Answer:

62 square units

Step-by-step explanation:

The area of a rectangular prism is the sum of the areas of its six faces. Opposite faces have the same area, so it is the sum of 3 pairs of faces. The area of one face of each pair is the product of the dimensions of that face. Those three areas are ...

• L·W

• W·H

• H·L

so the total surface area is ...

A = 2(LW +WH +HL)

For hand calculation, this can be simplified a bit to ...

A = 2(LW +H(L+W)) . . . . . requires one less multiplication

For your prism, the area is ...

A = 2(5·2 + 3(5+2)) = 2(10 +21) = 62 . . . square units

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3 years ago
What factor is missing? 24 + 12= ____(8+4)
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(2/3)^x-1=27/8, Find x. Please, a step-by-step explanation.​
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Answer:

x=-2

Step-by-step explanation:

(2/3)^x-1=27/8

Rewriting the right hand side

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1 - 1/4 - 1/3

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=12/12 - 7/12

=5/12

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3 years ago
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