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2 years ago

Find the area of the rectangle.

Mathematics

1 answer:

aev [14]2 years ago

3 0

Answer:

$69y+23$

Step-by-step explanation:

The area of a rectangle will always be length times width or width times length, doesn't matter which way.

In this case, the width is $3y+1$ miles and the length is $23$ miles. So, the area is $23(3y+1)=23*3*y+23*1=69*y+23$ .

So, the area is $\boxed{69y+23}$ and we're done.

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lara31 [8.8K]

$\dfrac{3}{4}a+\dfrac{1}{2}b-\dfrac{1}{2}a=\left(\dfrac{3}{4}a-\dfrac{1}{2}a\right)+\dfrac{1}{2}b\\\\\text{Find the common denominator:}\ it's\ 4\\\\\dfrac{1}{2}=\dfrac{1\cdot2}{2\cdot2}=\dfrac{2}{4}\\\\=\left(\dfrac{3}{4}a-\dfrac{2}{4}a\right)+\dfrac{1}{2}b=\boxed{\dfrac{1}{4}a+\dfrac{1}{2}b}\to\boxed{A)}$

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3 years ago

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MArishka [77]

Answer: i dont understand

Step-by-step explanation:

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3 years ago

What is the antiderivative of sin^2(x)cos^2(x)?

marin [14]

Answer:

$\frac{x}{8}-\frac{\sin(4x)}{32}+C$

Step-by-step explanation:

[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]

Recall that we can express the squared trig functions in terms of cos(2x). That is,

$\cos(2x)=2\cos^2x-1 \\ \cos(2x)=1 - 2\sin^2x.$

And so inverting these,

$\cos^2x=\frac{1}{2} (1+\cos2x) \\ \sin^2x=\frac{1}{2} (1-\cos2x)$ .

Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

$\sin^2x \cdot \cos^2x =\frac{1}{2} (1-\cos2x) \cdot \frac{1}{2} (1+\cos2x) = \frac{1}{4}(1-\cos^2(2x)).$

Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).

$\cos(2x)=2\cos^2x-1 \Rightarrow \cos(4x)=2\cos^2(2x)-1 \Rightarrow \cos^2(2x) = \frac{1}{2}(1+\cos(4x))$

So then,

$\sin^2x \cdot \cos^2x = \frac{1}{4}(1-\cos^2(2x)) = \frac{1}{4}(1-\frac{1}{2}(1+\cos(4x))) = \frac{1}{4}(1-\frac{1}{2}-\frac{1}{2}\cos(4x))=\frac{1}{8}(1-\cos(4x)).$

This is now integrable (phew),

$\int \sin^2x\cos^2x \ dx = \int \frac{1}{8}(1-\cos(4x)) \ dx = \frac{1}{8} \int (1-\cos(4x)) \ dx = \frac{1}{8}(x-\frac{1}{4}\sin(4x))+C.$

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3 years ago

Please help <br> solve for y<br> 5x-4y=10

a_sh-v [17]

x is -2 and y is -5/2 hope this helps

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3 years ago

Monique Fournier deposited $12,500 into a savings account paying 6.5% annual interest compounded monthly. What amount will she h

nikklg [1K]

6.5%=.065
.065/12=0.00541666666666666666666666666667/month
3 years = 36 months
(1+0.00541666666666666666666666666667)^36=1.2146716269797335689295444127607
1.2146716269797335689295444127607 x 12500=$15183.40 in the account after 3 years
15183.40-12500=$2683.40 in interest earned
☺☺☺☺

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3 years ago