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3 years ago

Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.

1 answer:

6 0

Length of circular track is:

L = 2*r*pi

He run 3/4 of it so length is:
L' = 3*2/4*r*pi = 3/2*r*pi

To calculate speed of his movement we use formula:
v = s/t where s = L' and t = 1 minute 45 seconds = 105 seconds

v = L'/t = $\frac{3*r*pi}{2*105}$

v = r* pi/70

If we take that r = 1 answer is $\pi /70$

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The Garden Task

Igoryamba

If the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

the perimeter = 24 ft
the area = 36 sq. ft
if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Recall:

A square has equal side lengths
Perimeter of a square = 4(side length)
Area of a square = $(side $ length)^2$

Given:

Perimeter of square (P) = $(14x - 32) $ ft$

Side length (s) = $(x + 2) $ ft$

First, let's find the value of x by creating an equation using the perimeter formula:

Perimeter of a square = 4(side length)

Plug in the values

$(14x - 32) = 4(x + 2)$

Solve for x

$14x - 32 = 4x + 8\\\\14x - 4x = 32 + 8\\\\10x = 40\\\\x = 4$

Find how much fencing would be needed (Perimeter of the fence):

Perimeter of the fence = $(14x - 32) $ ft$

Plug in the value of x

Perimeter of the fence = $14(4) - 32 = 24 $ ft$

Find the area of the garden:

Area of the garden = $(side $ length)^2$

Area = $(x + 2)^2$

Plug in the value of x

Area = $(4 + 2)^2 = 6^2 = 36 $ ft^2$

Find the perimeter if the garden size is doubled:

Perimeter of the new garden = 2 x 24 = 48 ft

Find the area if the garden size is doubled:

Perimeter of the new garden = 2 x 36 = 72 sq. ft

In summary, if the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

the perimeter = 24 ft
the area = 36 sq. ft
if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Learn more here:

brainly.com/question/13511952

4 0

2 years ago

Can someone help please

maw [93]

Answer:

A, B, C, D, and F are all solutions.

Step-by-step explanation:

All of the possible answers are correct except for E. Answer E is 0.001 less than -4 which would not make the equation true. Hope this helps!!

6 0

3 years ago

The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. Wha

valkas [14]

The answer is 0.3413 because Explanation:

z=x−uσ, where u=6 0andσ=10.

Therefore the probability student finish the test between 50 to 60 minutes is,

P(50≤x≤60)=P(50−6010≤z≤60−6010)

P(−1≤z≤0)=P(z≤0)−P(z≤−1)

=0.5000−0.1587=0.3413

3 0

3 years ago

Each bag of pattern blocks contains 50 blocks. To make a class pattern, the teacher combines 4 bags of blocks. How many pattern

iVinArrow [24]

Each bag contains 50 pattern blocks so 4 bags is

50 x 4 = 200 pattern blocks

hope this helps

4 0

3 years ago

he commercial division of a real estate firm is conducting a regression analysis of the relationship between , annual gross rent

blondinia [14]

Answer:

Number of apartment = 9

Step-by-step explanation:

Given the ANOVA result :

ANOVA ____ df ____ SS

Regression __ 1 ___ 41587.1

Residual ____ 7 ___

Total _______ 8 __ 51984.5

Number of apartment building in sample (n) :

Degree of freedom (df) = n - 1

The degree of freedom = total = 8

Hence,

8 = n - 1

8 + 1 = n - 1 + 1

9 = n

Hence, number of apartment building in sample = 9

4 0

3 years ago