Find product mentally using distributive property 12×(2 2/3)

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 v(t) 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 t = 11, t = 16, and t = 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 x-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

Shirts with the a school's mascot were printed, and the table shows the number of people who bought them the first, second, thir

goldenfox [79]

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

The graph could represent the data shown in the table is the graph goes perfectly diagonal starting from zero, up to the other corner of the graph

6 0

3 years ago

What is 9x + 20y = −18

mojhsa [17]

Y = 1/10
Alternate form

- 1
y=-0.1, y=-10

3 0

3 years ago

2 - 4x = 3x - 12 Solve for x

vova2212 [387]

Answer:

x = 2

Step-by-step explanation:

Step 1: Write out equation

2 - 4x = 3x - 12

Step 2: Add 4x on both sides

2 - 4x + 4x = 3x + 4x - 12

2 = 7x - 12

Step 3: Add 12 on both sides

2 + 12 = 7x - 12 + 12

14 = 7x

Step 4: Divide both sides by 7

14/7 = 7x/7

2 = x

Step 5: Rewrite

x = 2

6 0

3 years ago

Read 2 more answers

55 POINTS!!!!!!

vladimir1956 [14]

A
c
d
b
c
a
hope it helped!

5 0

3 years ago