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2 years ago

If vector A⃗ has components Ax and Ay and makes an angle θ with the +x axis, then...

1 answer:

7 0

If vector A⃗ has components Ax and Ay and makes an angle θ with the +x axis, then tanθ = Ay/Ax to get the angle of the vector components. Since the trigonometric function of tanθ is sinθ over cosθ, and since sinθ = y/r and cosθ = x/r.

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How to write a fraction as a mixed number?

Anna [14]

On the computer? You write mixed fractions like: 1 2/4

Obviously, 1 2/4 is an example.

3 0

2 years ago

Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an

Natasha_Volkova [10]

Answer:

The volume of the solid is 243 $\sqrt{2} \ \pi$

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0 ≤ ρ² ≤ 81

0 ≤ ρ ≤ 9

The intersection that takes place in the sphere and the cone is:

$x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81$

$2(x^2 + y^2) =81$

$x^2 +y^2 = \dfrac{81}{2}$

Thus; the region bounded is: 0 ≤ θ ≤ 2π

This implies that:

$z = \sqrt{x^2+y^2}$

ρcosФ = ρsinФ

tanФ = 1

Ф = π/4

Similarly; in the X-Y plane;

z = 0

ρcosФ = 0

cosФ = 0

Ф = π/2

So here; $\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}$

Thus, volume: $V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi$

$V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho$

$V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}$

$V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]$

V = 243 $\sqrt{2} \ \pi$

4 0

2 years ago

Which and which and plz help

Stella [2.4K]

The 4th one, since both values have less than .5 after the decimal

6 0

2 years ago

if the area of polygon P is 20 units² and the ratio of similarity of polygon P to polygon G is 7/3, what is the area of polygon

kipiarov [429]

Hope this helped and I’ve shown my work and the answer! :)

5 0

2 years ago

An insurance agent receives 16% commission on every premium paid. how much commission is paid on a policy with a premium of $497

a_sh-v [17]

Answer:

$79.63

Step-by-step explanation:

You can figure this by estimating. 16% is a little less than 20%, which is 1/5. $497.69 is almost $500. So, 1/5 of that is almost $100, and a little less than that is about $80. The closest answer choice is $79.63.

If you want to figure it exactly, you can do the multiplication ...

16% of $497.69 = 0.16 × $497.69 = $79.6304 ≈ $79.63

5 0

2 years ago