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Mathematics

2 answers:

Ahat [919]2 years ago

8 0

Answer is B : 3x*3x + 2(3x*8y) + 8y*8y

Sever21 [200]2 years ago

5 0

Answer is B long answer=(3x+8y)^2

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Multiple-Choice Integration, Picture Included, Please Include Work

ValentinkaMS [17]

$\displaystyle\int_0^2\sqrt{4-x^2}\,\mathrm dx$

Recall that a circle of radius 2 centered at the origin has equation

$x^2+y^2=4\implies y=\pm\sqrt{4-x^2}$

where the positive root gives the top half of the circle in the x-y plane. The definite integral corresponds to the area of the right half of this top half. Since the area of a circle with radius $r$ is $\pi r^2$ , it follows that the area of a quarter-circle would be $\dfrac{\pi r^2}4$ .

You have $r=2$ , so the definite integral is equal to $\dfrac{2^2\pi}4=\pi$ .

Another way to verify this is to actually compute the integral. Let $x=2\sin u$ , so that $\mathrm dx=2\cos u\,\mathrm du$ . Now

$\displaystyle\int_0^2\sqrt{4-x^2}\,\mathrm dx=\int_0^{\pi/2}\sqrt{4-(2\sin u)^2}(2\cos u)\,\mathrm du=4\int_0^{\pi/2}\cos^2u\,\mathrm du$

Recall the half-angle identity for cosine:

$\cos^2u=\dfrac{1+\cos2u}2$

This means the integral is equivalent to

$\displaystyle2\int_0^{\pi/2}(1+\cos 2u)\,\mathrm du=2u+\sin2u\bigg|_{u=0}^{u=\pi/2}=\pi$

4 0

3 years ago

You currently have a balance of $712.35 in your bank account. To avoid paying a monthly fee, you must maintain a minimum balance

vampirchik [111]

Answer:

hi i will help you with this

Step-by-step explanation:

6 0

3 years ago

Find the points of intersection of the line x = 3 + 2t, y = 5 + 8t, z = −6 + t, that is, l(t) = (3 + 2t, 5 + 8t, −6 + t), with t

blsea [12.9K]

See, please, suggested decision:
When the line intersects the xy-plane, then parameter z=0, when does the xz - y=0 and when does yz, x=0. All the details are in attachment.
If it's possible, check arithmetic part.