There are many cylinders with a height of 9inches. Let r represent the radius in inches and v represent the volume in cubic inches what belongs in cell A

Answers

Answer 1

Answer:

Complete question :

There are many cylinders with a height of 9 inches. Let r represent the radius in inches and V represent the volume in cubic inches.

a. Complete the table relating the radius and volume of cylinders with height 9 inches. Write each volume as a multiple of , or round to the nearest cubic inch.

Answer:

A = 9π in³

B = 36π in³

C = 81π in³

Step-by-step explanation:

Radius, r = 1, 2, 3

Height of cylinder = 9

Volume, V of cylinder : πr²h

For, r = 1

V = π(1)²9 = 9π in³

For, r = 2

V = π(2)²9 = 4*9π in³ = 36π in³

For r = 3

V = π(3)²9 = 9*9π in³ = 81π in³

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Three families shared the cost of purchasing a $5,000 generator. The martins paid 1/3 of the cost and the millers paid 40% and the browns paid the rest how much did the brown pay

Answers

Answer:

The amount Paid by Brown for generator =$ 2000

Step-by-step explanation:

Given as ,

The total cost of generator purchasing = $5,000

Millers paid 40% of the total cost of generator,

i.e 40% of $5,000

Or, 0.4 × 5,000

Or, $2,000

So, Millers paid amount = $2,000

So,. rest amount is now = $5,000 - $2,000 = $3,000

Again, Martins paid $(1)/(3)$ of $ 3,000

Or Martin paid amount = $1,000

Now, Again rest amount = $3,000 - $1,000 = $2,000

Now as per question, Brown paid the rest amount,

Hence Brown paid the rest amount for generator = $2,000 Answer

One of diagonals of a parallelogram is its altitude. What is the length of this altitude, if its perimeter is 50 cm, and the length of one side is 1 cm longer than the length of the other?

Answers

The length of that altitude is 5 cm.

Explanation

According to the below diagram, $ABCD$ is a parallelogram with diagonal $\overline{AC}$ as its altitude.

Suppose, the length of side $\overline{AB}$ is $x$ cm.

As the length of one side is 1 cm longer than the length of the other, so the length of side $\overline{BC}$ will be: $(x+1) cm$

Given that, the perimeter of the parallelogram is 50 cm. So, the equation will be.....

$2[x+(x+1)]=50\n \n 2(2x+1)=50\n \n 4x+2=50\n \n 4x=48\n \n x= 12$

So, the length of $\overline{AB}$ is 12 cm and the length of $\overline{BC}$ is (12+1)= 13 cm.

Suppose, the length of the altitude( $\overline{AC}$ ) is $h$ cm.

Now, in right angle triangle $ABC$ , using Pythagorean theorem....

$(AC)^2+(AB)^2= (BC)^2\n \n h^2+(12)^2= (13)^2\n \n h^2+144= 169\n \n h^2= 25\n \n h= √(25)= 5$

So, the length of that altitude is 5 cm.

How would you write out 'x is not equal to 2 and x is not equal to 7' Algebraically and in Interval Notation?

Answers

Algebraically:
x ≠ 2, 7
Interval Notation:
2 ≠ x ≠ 7

Final answer:

Algebraically, 'x is not equal to 2 and x is not equal to 7' is written as x≠2 and x≠7. In Interval Notation, it is written as (-∞, 2) U (2, 7) U (7, ∞). The given conditions exclude the numbers 2 and 7 from the entire real number line.

Explanation:

In the field of Mathematics, if you want to express the condition 'x is not equal to 2 and x is not equal to 7' algebraically, you write it as x≠2 and x≠7. In Interval Notation, you'd denote this as (-∞, 2) U (2, 7) U (7, ∞). This is read as 'x is all real numbers except 2 and 7' because we have excluded these two numbers from the entire real number line.