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3 years ago

4. Michelle sets up tables for her art class student. Each square table can seat two people 20 points

Mathematics

1 answer:

egoroff_w [7]3 years ago

3 0

Answer:

Hate to say it but if there is 2 people per square table and there are 8 tables in a row it would seat 16 people

Step-by-step explanation:

8 x 2 = 16

SRY :(

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What 9 intergers are between -3.5 and 5.5

laila [671]

3.5 3.4 3.3 3.2 3.1 3 -5.5 -1 -2

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3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

3 years ago

Find the volume of the cylinder.

Georgia [21]

<h3>Answer:</h3><h3>Exact volume = 32pi</h3><h3>Approximate volume = 100.48</h3>

The approximate volume only applies when pi = 3.14

Use either answer, but not both of course.

===============================================

Work Shown:

V = volume of cylinder

V = pi*r^2*h

V = pi*2^2*8

V = pi*32

V = 32pi .... exact volume in terms of pi

V = 32*3.14

V = 100.48 .... approximate volume when we use pi = 3.14

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3 years ago

Can anyone help me figure out the answer to this

Alex17521 [72]

3x-11=17-4x add 4x to both sides

7x-11=17 add 11 to both sides

7x=28 divide both sides by 7

x=4

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4 years ago

Item 19 A cylindrical container of four rubber balls has a height of 20 centimeters and a diameter of 5 centimeters. Each ball i

Lady_Fox [76]

First you need to find the volume of the cylinder. Then find the volume of all 4 rubber balls (spheres). Subtract the cylinder's volume by the spheres' volumes.

Volume of cylinder: πr²h
π2.5²(20) = 392.7 cm³

Volume of sphere: 4/3πr³
4/3π2.5³ = 65.45 cm³

392.7 - 65.45 = 327.25

The amount of space in the container unoccupied by the rubber balls is 327 cm³.

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4 years ago