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3 years ago

Annie bought 55.56 cubic yards of

Mathematics

2 answers:

faltersainse [42]3 years ago

6 0

B. Annie paid $97.23 for the topsoil.

Arturiano [62]3 years ago

4 0

She paid $97.23 for the top soil. You just have to multiply 1.75 by 55.56. However, if you wanted to do this without actually solving the problem, it’s a rather easy guess. Since you know 55 times 1 is 55, choose the closest answer to it. Sometimes when it comes to math you don’t actually have to solve the problem, just take an educated guess. :)

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Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with

skad [1K]

Parameterize S by the vector function

$\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle$

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

$\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle$

The integral of the field over S is then

$\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv$

$\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv$

$\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}$

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2 years ago

What are both of the ranges

MArishka [77]

Answer:

0.8 < x < 16.8

Step-by-step explanation:

The third side of the triangle is always less than the other two sides combined. I think of it like if it was greater than the other two sides added, there would be no triangle- it'd be a line.

The other rule is that it has to be greater than the difference between the two lines.

I hope this helped!

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