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3 years ago

In the interval 0º < x < 360°, find the values of x for which tan x= -0.6745

1 answer:

7 0

Tan(θ) = 3 tan(θ), 0° ≤ θ ≤ 360°

Solve for θ to the nearest degree.

tan(θ) = 3 tan(θ)

Subtract tan(θ) from both sides:

0 = 2 tan(θ)

Divide by 2 both sides:

tan(θ) = 0

If (x,y) is a point on the terminal ray of θ,

then tan(θ) = y/x = 0, and y = 0.

y = 0 ==> θ = 0°, 180°, or 360° in the interval 0° ≤ θ ≤ 360°.

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A sphere of radius r is cut by a plane h units above the equator, where

Anika [276]

Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$

5 0

3 years ago

PLEASE HELP! WILL GIVE BRAINLIEST!!!!!

Sophie [7]

The 8 percent commission must be at least $1000.

8% = $1000

1% = $125

100% = $12500

Hence, Jim needs to sell $12500 dollars worth of widgets.

6 0

3 years ago

How to write numbers in standard form?

Rama09 [41]

Standard form is just another way of saying "how to write a number in a regular form".

Ex. Standard form is any number.

4
65
234
1,865
234,908
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6 0

3 years ago

Find the equation of the line shown

Alenkinab [10]

Answer:

y = -x + 9.

Step-by-step explanation:

The slope = rise run

= 9 /-9

= -1.

The y intercept is at y = 9 so the equation is:

y = -x + 9.

7 0

2 years ago

What is 2.3w-7+8.1-3w

stepan [7]

2.0 w-1.1
2.3 w -3w = 2.0 w , -7+8.1 =1.1

8 0

3 years ago