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2 years ago

The area of a small pond is 78.5 yds. What is the diameter of the pond?

Mathematics

1 answer:

Zolol [24]2 years ago

7 0

Answer:

Diameter of pound = 10 yd

Step-by-step explanation:

Given area of circular pond = 78.5 square yd

To find the diameter of the pond.

Solution:

The pond being circular in shape, the area of pond can be given as:

⇒ $\pi\ r^2$

where $r$ represents radius of the pond.

Thus, we have:

⇒ $\pi\ r^2=78.5$

Using $\pi=3.14$

⇒ $3.14r^2=78.5$

Solving for $r$

Dividing both sides by 3.14

⇒ $\frac{3.14r^2}{3.14}=\frac{78.5}{3.14}$

⇒ $r^2=25$

Taking square root both sides.

⇒ $\sqrt{r^2}=\sqrt{25}$

⇒ $r=\pm5$

So, radius = 5 yd, as distances are always positive.

Diameter = $2\times radius=2\times 5\ yd= 10\ yd$

Thus, diameter of pound = 10 yd

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Mr. mole left his burrow that lies 7 meters below the ground and started digging his way deeper into the ground, descending at a

Keith_Richards [23]

Answer:

A(t)=−1.8t−4.5

Step-by-step explanation:

Mr. Mole is descending at a constant rate, so we are dealing with a linear relationship.

We know that Mr. Mole descended at a rate of 1.81.81, point, 8 meters per minute, so the slope \green mmstart color green, m, end color green is \green{-1.8}−1.8start color green, minus, 1, point, 8, end color green, and our function looks like A(t)=\green{-1.8}t+\pink bA(t)=−1.8t+bA, left parenthesis, t, right parenthesis, equals, start color green, minus, 1, point, 8, end color green, t, plus, start color pink, b, end color pink.

We also know that after 555 minutes, Mr. Mole was 13.513.513, point, 5 meters below the ground, which means that A(5)=-13.5A(5)=−13.5A, left parenthesis, 5, right parenthesis, equals, minus, 13, point, 5. We can substitute this into the formula of the function to find \pink bbstart color pink, b, end color pink:

\qquad\begin{aligned}A(5)&=-13.5\\ \green{-1.8}\cdot5+\pink b&=-13.5\\ -9+\pink b&=-13.5\\ \pink b&=\pink{-4.5}\end{aligned}

A(5)

−1.8⋅5+b

−9+b

=−13.5

=−4.5

This means that Mr. Mole's initial altitude is 4.54.54, point, 5 meters below the ground.

AKA the answer is A(t)=−1.8t−4.5

3 0

2 years ago

A stone is dropped into a barrel of water and sinks to the bottom. The ball is completely covered by water. By how much does the

Rom4ik [11]

Answer:

Answer: 5/12 or approx. 0.42

Step-by-step explanation:

The ball will displace as much water as its volume.

Meaning, the volume of the ball and the volume of the increase in water in the barrel will be equal.

Volume of a sphere:

$V_s=\frac{4}{3} \pi r^3$

The radius is half the diameter. The diameter of the sphere is 10, thus:

$r = d/2 = 10/2 = 5$

5^3 = 5*5*5 = 25*5 = 125

$V_s=\frac{4}{3} \pi * 5^3=\frac{4}{3} \pi * 125$

The volume of a cylinder, which will be the shape of the increase in water, is the following:

$V_c=\pi r^2 h$

We know the radius r, as we know the diameter.

$r=d/2=40/2=20$

$V_c=\pi r^2 h=\pi h * 20^2 = \pi h * 400$

We are looking for the height of the cylinder, h, as that will be the height of the water rise.

Since we know these 2 volumes are the same, we'll set them equal to each other and solve the equation:

$V_s = V_c$

$\frac{4}{3} * 125 * \pi = 400 * h * \pi$

We can get rid of pi by dividing both sides by pi:

$\frac{4}{3} * 125 = 400 * h$

And now divide both sides by 400:

$\frac{4}{3} * \frac{125}{400}= h$

Just reversing it and putting h to the left:

$h = \frac{4}{3} * \frac{125}{400} = \frac{4 * 125}{3 * 400}$

I see that I can divide both the numerator and the denominator by 4:

$h =\frac{125}{3 * 100}= \frac{125}{300}$

I'll now divide both the numerator and the denominator by 25 to simplify the expression:

$h=\frac{125}{300} =\frac{125 / 25}{300 / 25} = \frac{5}{12}$

Answer: The water rises by 5/12 (five twelfths).

If I want an approximate decimal answer, I can simply run this expression in a calculator:

$\frac{5}{12}$ ≈ $0.416666667$ ≈ $0.42$

7 0

2 years ago

Omar and Caleb each had a repair made on their cars. The initial cost of each repair is $1,000. Omar and Caleb each have two cou

scoundrel [369]

Answer:

854

Step-by-step explanation:

1000/15=66

1000-66-80=854

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2 years ago

Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a \$7.50$7.50dollar sig

BigorU [14]

Answer:

Step-by-step explanation:

Delivery fee = $7.50

Price per pizza = $14

Planned amount = $60

7.50 + 14p < 60

Subtract 7.50 from both sides

14p < 60 - 7.50

14p < 52.50

Divide both sides by 14

p < 52.50 / 14

p < 3.75

Each pizza is cut into 8 slices

Total slices she can afford = 3.75 × 8

= 30 slices

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2 years ago

First, she needs to find her resting heart rate by counting her pulse for one minute immediately after she wakes up for 5 days i

andreyandreev [35.5K]

Answer:

Step-by-step explanation:

She finds her average resting heart rate to be 62 after 5 days.

That means, average of the 5 heart rate pulse=62

If the last day was 58 and all the other days were the same.

Let x be her pulse on the other days,

Then,

$Average, 62=\dfrac{58+4x}{5}\\\text{Cross Multiply}\\58+4x=62 X 5\\\text{Suntract 58 from both sides}\\4x=(62X5)-58\\4x=310-58\\4x=252\\\text{Divide both sides by 4}\\x=63$

Her pulse on all the other days is 63.

4 0

2 years ago