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3 years ago

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Evaluate each function. 1) f(x) = x2 + 4x; Find f(-7)

1 answer:

katrin [286]3 years ago

5 0

Answer:

The answer is -77

Step-by-step explanation:

Ok, so assuming by x2 you mean x squared, I will solve this. So basically when you have a function, f(-7) would mean that you would have to replace all the x's in the equation with -7. So let's write that out. that would be f(-7) = -7^2 + (-7*4). So now according to PEMDAS, you would solve the exponent first, and -7^2 is equal to -49, because when you solve it you would do -(7^2), which is -(49), which is then -49. So now you have f(-7)= -49+ (4*-7). Solving for (4*-7), you get -28. This leaves you with -49 + (-28), which is -49 - 28. Simplifying that, you get the answer, which is -77.

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A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t

Vlad1618 [11]

Answer:

$185553.7\text{ feet}^3$

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is $84\text{ feet}$ , and the total height of the building up to the top of the dome is $91\text{ feet}$ .

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be $h\text{ feet}$

As the dome hemispherical.

circumference of a hemisphere $=\frac{1}{2}\times2\pi\times radius$

$=\pi\times radius$

$\frac{22}{7}\times radius=84$

$radius=26.75\text{ feet}$

total height of the building up to the top of the dome $=\text{radius of hemisphere}+\text{height of mountaintop}$

$=26.75+h=91$

$h=64.25\text{ feet}$

Volume of building $=\text{volume of cylindrical mountaintop}+\text{volume of dome}$

$=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3$

as radius of mountain top is same as dome

putting values

$=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3$

$=145484.6+40069.1$

$185553.7\text{ feet}^3$

Hence the total volume of the building is $185553.7\text{ feet}^3$

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puteri [66]

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Step-by-step explanation:

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Find the absolute maximum and absolute minimum values of f on the given interval. (If an answer does not exist, enter DNE.)

vodka [1.7K]

Answer:

absolute max is 120 and absolute min is -8

Step-by-step explanation:

Find critical numbers

f'(x) = 3x^2 - 12x + 9 = 0

= 3(x^2 - 4x + 3) = 0

3(x-3)(x-1) = 0

(x-3) = 0 or (x-1)=0

x = 1,3

Test them!

x<1 Sign of f' on this interval is positive

1<x<3 Sign of f' on this interval is negative

x>3 Sign of f' on this interval is positive

f(x) changes from positive to negative at x = 1 which means there is a relative maximum here.

f(x) changes from negative to positive at x = 3 which means there is a relative minimum here.

Test the endpoints to find the absolute max and min.

f(-1) = -8

f(1) = 12

f(3) = 8

f(7) = 120

The absolute maximum value of f is 120 and the absolute minimum value of f is -8.

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