A circle has a circumference of 16 pi inches. What is the radius of the circle?

Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hy

vladimir1956 [14]

Answer:

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

we know that

In the right triangle XYZ

$cos(Y)=\frac{ZY}{XY}$ ---> adjacent side divided by the hypotenuse

substitute the values

$cos(30\°)=\frac{ZY}{4}$

Remember that

$cos(30\°)=\frac{\sqrt{3}}{2}$

so

substitute

$\frac{\sqrt{3}}{2}=\frac{ZY}{4}$

$ZY=(4)\frac{\sqrt{3}}{2}$

$ZY=2\sqrt{3}\ units$

step 2

$sin(Y)=\frac{XZ}{XY}$ --> opposite side divided by the hypotenuse

substitute the values

$sin(30\°)=\frac{XZ}{4}$

Remember that

$sin(30\°)=\frac{1}{2}$

so

$\frac{1}{2}=\frac{XZ}{4}$

$XZ=2\ units$

step 3

$tan(Y)=\frac{XZ}{ZY}$ --> opposite side divided by adjacent side

substitute the values

$tan(Y)=\frac{2}{2\sqrt{3}}$

$tan(Y)=\frac{1}{\sqrt{3}}$

Simplify

$tan(Y)=\frac{\sqrt{3}}{3}$

so

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

7 0

2 years ago

Read 2 more answers

2/3x - 1/6 > 1/2 <br><br> Please sole and add equation in response if possible thanks :

Shkiper50 [21]

The solution would be x > 1 sorry if its wrong but hope it helps

8 0

1 year ago

Read 2 more answers

Suppose your car has hhh liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more

Igoryamba

Answer:

g = (h+a) - l

None of them

Step-by-step explanation:

Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them

Let

h = liters of oil in the morning

l= liters that has leaked

a= liters that were added during the day

g= amount of liters at the end of the evening

Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked

Substituting each variable into the formula, we have

g = (h+a) - l

3 0

2 years ago

Sasha is cutting a cake into 42 equal-sized pieces. If 14 people want cake, then they can each have 3 slices. And if 21 people w

kupik [55]

Answer:

k = 42

the constant of proportionality in this inverse variation is 42.

Step-by-step explanation:

Let x represent the number of people that want cake

And y the number of slices each can have;

Since x is inversely proportional to y;

x = k/y .....1

Where k is the proportionality constant;

To solve for k, we will substitute any of the case scenario given into equation 1.

If 14 people want cake, then they can each have 3 slices;

x = 14 , y = 3

substituting;

14 = k/3

k = 14 × 3 = 42

k = 42

the constant of proportionality in this inverse variation is 42.

Therefore,

x = 42/y

4 0

2 years ago

Announcements for 84 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean len

Marina86 [1]

Answer:

Step-by-step explanation:

Hello!

You need to construct a 95% CI for the population mean of the length of engineering conferences.

The variable has a normal distribution.

The information given is:

n= 84

x[bar]= 3.94

δ= 1.28

The formula for the Confidence interval is:

x[bar]± $Z_{1-\alpha/2}$ *(δ/n)

Lower bound(Lb): 3.698

Upper bound(Ub): 4.182

Error bound: (Ub - Lb)/2 = (4.182-3.698)/2 = 0.242

I hope it helps!

6 0

3 years ago