Ask question

Ask question

All categories

3 years ago

8

100 POINTS TO ANYONE WHO ANSWER THISS!!! An oil slick is expanding as a circle. The radius of the circle is increasing at the ra

te of 20 meters per day. Express the area of the circle as a function of d, the number of days elapsed.

1 answer:

Dima020 [189]3 years ago

3 0

Answer:

circle area = 400*d^2

Step-by-step explanation:

You might be interested in

[need math help] Study buddies part #2

rosijanka [135]

Answer:

Part A) The distance between Whitney's house and Anh's house is 6.5 miles.

Part B) The total distance traveled by Whitney during the trip was 9.5 miles.

Step-by-step explanation:

Part A)

Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.

So, instead, we can calculate Whitney's total displacement. Total displacement is given by:

$\displaystyle \text{Displacement}=\int_a^bv(t)\, dt$

Where <em>v(t)</em> is the velocity function.

So, the displacement of Whitney when she traveled from her house to Anh's house will be:

$\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt$

To calculate the integral, we can split it off at <em>t</em> = 11, <em>t</em> = 16, and <em>t</em> = 24.

The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:

$\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt$

Now, we can calculate the area of each figure.

The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:

$\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}$

The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:

$\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}$

Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:

$\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}$

However, notice that the second figure is below the <em>x</em>-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.

Then the displacement will be:

$\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}$

So, the distance between Whitney's house and Anh's house is 6.5 miles.

Part B)

The total distance differs from displacement in that it includes all the distances in both directions. It is given by:

$\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt$

In other words, all of our values are now positive. We will utilize the same strategy:

$\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt$

Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:

$\displaystyle \text{Distance} =5.6+1.5+2.4=9.5$

Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.

6 0

3 years ago

The numbers of bags of crisps sold per day in a general shop was recorded over 13 days.

Alona [7]

I just figured it out so I’ll answer it on this account lol.

Q1 = 32, Q2 = 45, Q3 = 52

Interquartile range = 52 - 32 = 20

Range = 68 - 21 = 47

6 0

3 years ago

The sum of a number x and 5 equals 14.

Fudgin [204]

Sum means addition so the equation is x+5=14

To get the answer, just do 14-5 and the answer is 9

4 0

3 years ago

Larry is making custom signs to sell at his shop. The cost of making each sign is $50 plus $4.50 per sign, he will sell them for

Valentin [98]

The best way to answer this would be making a graph

For 1 sign it costs 54.50 and he makes 15

For 2 signs it costs 59 and he makes 30

For 3 signs it costs 63.50 and he makes 45

For 4 signs it costs 68 and he makes 60

For 5 signs it costs 72.50 and he makes 75

This means that after 5 signs Larry will be making profit

8 0

3 years ago

At a birthday party, there are 2 gift boxes that are red, 7 gift boxes that are green, 4 gift boxes that are blue, and 11 gift b

Monica [59]

2 Red — 7 Green — 4 Blue — 11 Random
2 + 7 + 4 + 11 = 24
Probability of Green falling.
7/24

Hope this helps

5 0

3 years ago