MATHEMATICS HIGH SCHOOL

Two similar pyramids have corresponding dimensions in the ratio 3:5 Find the ratio of their volumes

Answers

Answer 1
Answer:

Answer:27:125

Step-by-step explanation:

Given

Ratio of corresponding dimensions is in the ratio of 3:5

If the two pyramids are similar then the ratio of their volumes is proportional to the cube of their side ratio

i.e.

\Rightarrow (V_1)/(V_2)=((l_1)/(l_2))^3

\Rightarrow (V_1)/(V_2)=((3)/(5))^3

\Rightarrow (V_1)/(V_2)=(27)/(125)

Thus the ratio of their volumes is 27:125

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Prove that 1+cosA/sinA + sinA/1+cosA=2cosecA

Answers

(1+cos\alpha)/(sin\alpha)+(sin\alpha)/(1+cos\alpha)=2cosec\alpha\n\nL=((1+cos\alpha)(1+cos\alpha)+sin\alpha\cdot sin\alpha)/(sin\alpha(1+cos\alpha))=(1+2cos\alpha+cos^2\alpha+sin^2\alpha)/(sin\alpha(1+cos\alpha))\n\n=(1+2cos\alpha+1)/(sin\alpha(1+cos\alpha))=(2+2cos\alpha)/(sin\alpha(1+cos\alpha))=(2(1+cos\alpha))/(sin\alpha(1+cos\alpha))\n\n=(2)/(sin\alpha)=2\cdot(1)/(sin\alpha)=2cosec\alpha=R

Juan earns 52 dollars per weekworking part-time at a book store.
He makes one dollar more for each
book that he sells. The amount, A
(in dollars), that Juan
earns in a week if he sells b books
is given by the following.

A=52 + b

How much does Juan earn in a
week if he sells 37 books?

Answers

Answer:

the answer is 89

Step-by-step explanation:

52 plus 37 = 89

Answer:

89 books

Step-by-step explanation:

he sells 37 books so we do 52+37 and get 89

Write "252 miles per 8 gallons " as a rate in simplest form

Answers

Hi there! 252 miles per gallon would be 252 miles/8 gallons. The GCF of 252 and 8 is 4 so we are going to divide by 4. 252÷4=63 and 8÷4=2. In this case, we have a fraction of 63/2.

Answer:

Rate per gallon in simplest form is, (63)/(2)

Step-by-step explanation:

Unit rates defined as the rates are expressed as a quantity of 1, such as 5 feet per second or 6 miles per hour, they are called unit rates.

Given the statement: 252 miles per 8 gallons.

⇒ Number of miles = 252

and number of gallons = 8

Unit rate per gallons = \frac{\text{Number of miles}}{\text{Number of gallons}}=(252)/(8)

Divide numerator and denominator both by 4 we get;

Unit rate per gallons = ((252)/(4) )/((8)/(4)) = (63)/(2)

Therefore,  "252 miles per 8 gallons " as a rate in simplest form is, (63)/(2)

A monster truck tire will travel will travel 12.56 ft in one revolution. What is the radius of the tire?

Answers

If it travels 12.56 ft in one revolution, then the circumference of the tire is 12.56 ft.
Circumference = 2 x π x radius
12.56=2 x 3.14 x radius
radius x 6.28=12.56

Radius= 2 ft

Hope this helps :)
1 revolution
the part that touches the ground makes 1 full circle
therefor 12.56 is the cirvmerncere
circumfrence=2pir
12.56=circumfrence
12.56=2pir
divide both sides by 2
6.28=pir
aprox pi to 3.14 and divide both sides by 3.14
2=r

radius=2 feet

Triangle inequality Theorem

Answers

states that the sum of any 2 sides of a triangle must be greater than the measure of the third.

The manual for your boat engine calls 91 octane gas. The gas stations by your house only sell 87 and 93 octane. If the boat's tank holds 30 gallons, how many gallons of each should you buy for a 91 octane mix?

Answers

I not exactly sure if this is right but with the numbers that you are given, you can do a simple division problem of 91/30=3.0999 because you don't want decimals, you need a solid number of gallons you must buy you would have to buy 4 gallons for that 91 octane mix, leaving you with some gas.

Hope I helped you!
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