A cylinder with<br> a radius of 2<br> inches and height<br> of 8 inches

One more question on this test guys. please answer as fast as possible. If you do,

GaryK [48]

1. The given rectangular equation is $x=2$ .

We substitute $x=r\cos \theta$ .

$r\cos \theta=2$

Divide through by $\cos \theta$

$r=\frac{2}{\cos \theta}$

$r=2}\sec \theta$

$\boxed{x=2\to r=2\sec \theta}$

2. The given rectangular equation is:

$x^2+y^2=36$

This is the same as:

$x^2+y^2=6^2$

We use the relation $r^2=x^2+y^2$

This implies that:

$r^2=6^2$

$\therefore r=6$

$\boxed{x^2+y^2=36\to r=6}$

3. The given rectangular equation is:

$x^2+y^2=2y$

This is the same as:

We use the relation $r^2=x^2+y^2$ and $y=r\sin \theta$

This implies that:

$r^2=2r\sin \theta$

Divide through by r

$r=2\sin \theta$

$\boxed{x^2+y^2=2y\to r=2\sin \theta}$

4. We have $x=\sqrt{3}y$

We substitute $y=r\sin \theta$ and $x=r\cos \theta$

$r\cos \theta=r\sin \theta\sqrt{3}$

This implies that;

$\tan \theta=\frac{\sqrt{3}}{3}$

$\theta=\frac{\pi}{6}$

$\boxed{x=\sqrt{3}y\to \theta=\frac{\pi}{6}}$

5. We have $x=y$

We substitute $y=r\sin \theta$ and $x=r\cos \theta$

$r\cos \theta=r\sin \theta$

This implies that;

$\tan \theta=1$

$\theta=\frac{\pi}{4}$

$\boxed{x=y\to \theta=\frac{\pi}{4}}$

6 0

3 years ago

Find the measure of angle A.<br> 75°<br> x + 53<br> +68

sleet_krkn [62]

Answer:

Step-by-step explanaton:

6 0

3 years ago

The swimming pool at lifetime city health and fitness club measures 20 meters in length and 15 meters in width wat is the are of

8_murik_8 [283]

20*15 is 300 meters which is the area

8 0

3 years ago

Read 2 more answers

Find the domain of the function (f/g)(x) given f (x)=x^2-4x-5 and g(x)=x^2-25

stealth61 [152]

Answer:

all real numbers except ±5.

Step-by-step explanation:

Each function (f(x), g(x)) has a domain that is all real numbers. Their quotient (f(x)/g(x)) must exclude values that make g(x) = 0. The quotient is undefined when the denominator is zero. Those excluded values are x = ±5.

The domain of (f/g)(x) is all real numbers except ±5.

___

Of course you recognize x^2 -25 = 0 has solutions x = ±√25 = ±5. You can get there two ways:

add 25 and take the square root: x^2=25; x=±√25.
factor the difference of squares and set the factors to zero: (x-5)(x+5)=0 has solutions x-5=0 and x+5=0, that is, x = ±5.

5 0

3 years ago

Help asap

ZanzabumX [31]

Your fruit punch recipe can be composed of 4 juice containers of lemonade, 2 juice containers of orange juice, 2 juice containers of grape juice, 2 juice containers of apple juice, 2 juice containers of cranberry juice, and 2 juice containers of pineapple juice.

<h3>Unit conversion</h3>

Unit conversion is a tool very useful to solve some questions. For this exercise, you should know that 1 liter (l) = 1000 milliliters (ml).

The question asks you a design your own fruit punch recipe with exactly 5 liters of punch and includes at least three of the juice.

You have several options, an alternative is to use all juices.

Step 1 - Convert the units for each given juice containers

250 milliliters of lemonade = 0.250 l of lemonade juice

500 milliliters of orange juice = 0.500 l of orange juice

250 milliliters of grape juice = 0.250 l of grape juice

250 milliliters of apple juice= 0.250 l of apple juice

500 milliliters of cranberry juice = 0.500 l of cranberry juice

500 milliliter’s of pineapple juice = 0.500 l of pineapple juice

Step 2 -Design your own fruit punch recipe with exactly 5 liters

4 juice containers of lemonade = 4* 0.250 l = 1 l of lemonade

2 juice containers of orange juice= 2* 0.500 l = 1 l of orange juice

2 juice containers of grape juice= 2* 0.250 l = 0.500 l of grape juice

2 juice containers of apple juice= 2* 0.250 l = 0.500 l of apple juice

2 juice containers of cranberry juice= 2* 0.500 l = 1 l of cranberry juice

2 juice containers of pineapple juice= 2* 0.500 l = 1 l pineapple juice

Thus, your own fruit punch recipe is composed of: 4 juice containers of lemonade, 2 juice containers of orange juice, 2 juice containers of grape juice, 2 juice containers of apple juice, 2 juice containers of cranberry juice, and 2 juice containers of pineapple juice.

Read more about the unit conversion for capacity here:

brainly.com/question/14965845

4 0

2 years ago

A cylinder with a radius of 2 inches and height of 8 inches