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3 years ago

What is the definition of csc θ ?

1 answer:

7 0

The trigonometric function cosecant is written as csc θ. For acute angles, csc θ can be found by the SOHCAHTOA definition, shown below on the left. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. f(x) = csc x is a periodic function with period 2π.

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The length of a rectangular prism is 12 inches, and its width is 8 inches. The height of the prism is 16 inches. What is the sur

finlep [7]

Answer:

The answer to your question is letter B

Step-by-step explanation:

Data

length = 12 in

width = 8 in

height = 16 in

surface area = ?

Formula

Surface area = 2( length x width) + 2(length x height) + 2((width x height)

Substitution

Surface area = 2(12 x 8) + 2(12 x 16) + 2(8 x 16)

Simplification

Surface area = 256 + 384 + 102

Result

Surface area = 832 in²

7 0

3 years ago

Marsha is buying a new cell phone. She has a 45% off coupon from the store. She pays $275 for the cell phone. What is the price

jekas [21]

Answer:

The price of the cell phone without the coupon= $500

Step-by-step explanation:

Step 1: Express discounted amount

The discounted amount can be expressed as a function of the original cost of the phone as follows;

D=r×A

where;

D=discounted amount

r=coupon rate

A=original price of the cell phone before the coupon

In our case;

r=45%=45/100=0.45

A=a

replacing;

Discounted amount=(0.45×a)=0.45 a

Step 2: Amount she pays up

Amount she pays=Original cost of cell phone-discounted amount

where;

Amount she pays= $275

original cost of cell phone=a

discounted amount=0.45 a

replacing;

$275=a-0.45 a

0.55 a=275

a=275/0.55

a=500

The price of the cell phone without the coupon= $500

7 0

3 years ago

An integer is 5 more than 4 times another. If the product of the two integers is 51, then find the integers.

Yakvenalex [24]

Answer:

3 and 17 are required integers

Step-by-step explanation:

Let one integer be x
And other integer be y

x = 4y + 5

xy = 51

According to question :

➞ (4y + 5)y = 51

➞ 4y² + 5y = 51

➞ 4y² + 5y - 51 = 0

➞ 4y² + 17y - 12y - 51 = 0

➞ y (4y + 17) - 3(4y + 17) = 0

➞ (y - 3)(4y - 17) = 0

➞ y - 3 = 0

➞ y = 3

Hence,

➞ y = 3

➞ x = 4y + 5

➞ x = 4 (3) + 5

➞ x = 12 + 5

➞ x = 17

∴ The required integers are 3 and 17

7 0

3 years ago

-2xt+y =4 what’s the slope and y intercept

Elina [12.6K]

Answer:

y interecept 4

slope 2

Step-by-step explanation:

4 0

3 years ago

The volumes of two spheres are in a ratio of 1:8 what is the eatio rafi

Agata [3.3K]

Remark
I take it that you want to know the ratio of the radii. If this is not correct, leave a comment below my answer.

You could do this by giving the spheres a definite volume, like 1 and 8 and then solve for r for one of them and then use the other sphere to find it's radius. It is not exactly the best way, and if you are going to to a physics class you want to be doing this using cancellation.

Step One
Set up the Ratio for the volumes.

$\frac{V_1}{V_2} = \frac{1}{8}$

Step Two
Setup the equation for V1/V2 using the definition for a sphere. V = 4/3 pi r^3

$\dfrac{1}{8} = \frac{ \frac{4}{3} \pi( r_1)^3 }{ \frac{4}{3} \pi( r_2)^3 }$

Step Three
Cancel the 4/3 and pi on the top and bottom of the fractions on the right.

You are left with 1/8 = (r1)^3/ (r2)^3

Step Four
Take the cube root of both sides.
cube root 1/8 = 1/2

Cube root of (r1)^3 = r1
Cube root of (r2)^3 = r2

Step Five
Answer
$\frac{r_1}{r_2} = \frac{1}{2}$ Answer <<<<<<<

8 0

3 years ago