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Daniel [21]
3 years ago
7

Why is the answer C?

Mathematics
1 answer:
baherus [9]3 years ago
6 0

Step-by-step explanation:

∫₋₂² (f(x) + 6) dx

Split the integral:

∫₋₂² f(x) dx + ∫₋₂² 6 dx

Graphically, if f(-x) = -f(x), then ∫₋₂² f(x) dx = 0.  But we can also show this algebraically.

Split the first integral:

∫₋₂⁰ f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Using substitution, write the first integral in terms of -x.

∫₂⁰ f(-x) d(-x) + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₂⁰ f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Flip the limits and multiply by -1.

∫₀² f(-x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

Rewrite f(-x) as -f(x).

∫₀² -f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

-∫₀² f(x) dx + ∫₀² f(x) dx + ∫₋₂² 6 dx

The integrals cancel out:

∫₋₂² 6 dx

Evaluating:

6x |₋₂²

6 (2 − (-2))

24

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This soda can is going to be made from aluminum. How many square centimeters of aluminum are needed if the radius r = 3.5 cm and
kari74 [83]

208.81 square centimeters of aluminium are needed

<em><u>Solution:</u></em>

Given that,

Radius = 3.5 cm

Height = 6 cm

We have to find the square centimeters of aluminum needed

So we have to find the surface area of cylinder

<em><u>The surface area of cylinder is given by formula:</u></em>

A = 2 \pi r(h+r)

Where "r" is the radius and "h" is the height of cylinder

<em><u>Substituting the values we get,</u></em>

A  = 2 \times 3.14 \times 3.5 \times (6+3.5)\\\\A = 21.98 \times 9.5\\\\A = 208.81

Thus 208.81 square centimeters of aluminium are needed

8 0
3 years ago
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE
Viktor [21]

Answer:

<h2> (2, -1)</h2>

Step-by-step explanation:

Given the function f(x) = 8x³ − 12x² − 48x, <em>the critical point of the function occurs at its turning point i,e at f'(x) = 0</em>

First we have to differentiate the function as shown;

f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\  \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\

Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1

Hence the critical numbers of the function are (2, -1)

8 0
3 years ago
I have one hundred eighty two figures and sevendy five figures how many do i have in total
Andrei [34K]
You would have two hundred and fifty seven figures.
4 0
3 years ago
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52% of what number equals 39
OverLord2011 [107]
To figure this equation out, you'll have to divide 39 by 52% (0,52)

39 / 0.52 = 75

39 is 52% of 75 is your answer.

Hope this helps!
8 0
3 years ago
Read 2 more answers
Please help &lt;3 Thanks!!
iVinArrow [24]

what dou you need?????????

7 0
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