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2 years ago

If 4 + 6 = 10, does (4 + 6) X 3= 10 X 3? Why or why not?

Mathematics

1 answer:

spayn [35]2 years ago

3 0

Answer: Yes, they equal

Explanation: (4 + 6) x 3 = 30 ; 10 x 3 = 30, 30 = 30

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pantera1 [17]

Answer:

V ≈ 226.72 cm³

Step-by-step explanation:

Use the formula for volume of a cone using slant height and radius.

V = 1/3 π r² √ l² - r²

Then, plug in dimensions and solve.

V = 1/3 π (10)² √ 10² - 5²

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G verify that the divergence theorem is true for the vector field f on the region

Alenkasestr [34]

$\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1$

Converting to spherical coordinates, we have

$\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi$

On the other hand, we can parameterize the boundary of $E$ by

$\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle$

with $0\le u\le2\pi$ and $0\le v\le\pi$ . Now, consider the surface element

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv$
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So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

$\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv$
$=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi$

as required.

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3 years ago

PLEASE HURRY WILL GIVE BRAINLIEST What is the solution of

ANTONII [103]

Answer:

Option A

Step-by-step explanation:

Find zeros first:

x² + x - 6 = x² + 3x - 2x - 6 = x(x + 3) - 2(x + 3) = (x - 2)(x + 3)
x = 2, x = -3, x = 7 (but x ≠ 7 as no division by zero)

We have 4 intervals:

x ≤ - 3, three negatives, the result is negative or zero
-3 ≤ x ≤ 2, two negatives and one positive, the result is positive or zero
2 ≤ x < 7, two positives and one negative, the result is negative or zero
x > 7, three positives, the result is positive or zero

The solution is:

x ≤ - 3 or 2 ≤ x < 7

Correct choice is A

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2 years ago

Mary went to the store and spent $4.32 on candy Jessie went to the store and spent $7.32 on snacks. How much more did Jessie spe

Liula [17]

We do 7.32-4.32 to get a $3 difference

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3 years ago

Read 2 more answers

If 4 + 6 = 10, does (4 + 6) X 3= 10 X 3? Why or why not?​

If 4 + 6 = 10, does (4 + 6) X 3= 10 X 3? Why or why not?