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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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Rotate ΔABC with vertices A(-1, 4), B(2, 1), and C(3, -3) about the origin by 90°.
MAXImum [283]
You got this you can do it I don’t know the answer but I hope you find someone who does(:
4 0
3 years ago
Ares of a rectangular floor of your house is Ax+5x-2. if the length is x+2 units, find A​
Snezhnost [94]

Answer:

A=4.

Step-by-step explanation:

Note: In the expression of area the first term should be Ax^2.

It is given that area of a rectangular floor of your house is Ax^2+5x-2 and the length is (x+2) units.

We know that, area of a rectangle is

Area=length\times width

Since length of the rectangle is (x+2), therefore (x+2) is a factor of Ax^2+5x-2 and the value of Ax^2+5x-2 is 0 at x=-2.

A(-2)^2+5(-2)-2=0

4A-10-2=0

4A-12=0

4A=12

Divide both sides by 4.

A=4

Therefore, the value of A is 4.

7 0
3 years ago
Solve the pair of simultaneous equations and leave the answer as a fraction in
Elena-2011 [213]

Answer:

x = 11/3 = 3 2/3

y = 13/3 = 4 1/3

Step-by-step explanation:

Here, we want to solve the system of equations simultaneously

x + y = 8

2x -3 = y

From the second equation, we have an equation for y

we can simply proceed to substitute this into the first equation

x + 2x - 3 = 8

3x - 3 = 8

3x = 8 + 3

3x = 11

x = 11/3

Recall;

y = 2x - 3

y = 2(11/3) - 3

y = 22/3 - 3

y = (22-3(3))/3

y = (22-9)/3 = 13/3

6 0
2 years ago
Find the sum of the following infinite geometric series.
Crazy boy [7]

Answer:

Final answer is \frac{80}{3}.

Step-by-step explanation:

We have been given an infinite geometric series.

Now we need to find it's sum.

common ratio r=-\frac{1}{5}.

plug n=1 to get the first term

a_n=32\left(-\frac{1}{5}\right)^{\left(n-1\right)}

a_1=32\left(-\frac{1}{5}\right)^{\left(1-1\right)}

a_1=32\left(-\frac{1}{5}\right)^{\left(0\right)}

a_1=32\left(1\right)

a_1=32

Now plug these values into infinite sum formula

S_{\infty}=\frac{a_1}{1-r}=\frac{32}{1-\left(-\frac{1}{5}\right)}=\frac{32}{1.2}=\frac{320}{12}=\frac{80}{3}

Hence final answer is \frac{80}{3}.

8 0
3 years ago
What is 13 hours after 4:00 am.
kupik [55]
I believe it would be 5:00 pm, because 12 hours after 4:00 am is 4:00 pm, plus one hour is 5:00pm.
8 0
3 years ago
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