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mr Goodwill [35]
2 years ago
11

Heda ate 1/12 box of ceral now the box is 3/4 full

Mathematics
1 answer:
ale4655 [162]2 years ago
5 0
The answer would be 5/4
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[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
Determine if the following statement is sometimes, always, or never true. The central angle of a minor arc is an acute angle.
zavuch27 [327]
It is sometimes true
5 0
3 years ago
What’s the answer(s) ?
yulyashka [42]
Im sorry im trying to get some points ): i hope u find ur answer!
7 0
3 years ago
You have to pick 5 members of the student council to go to meeting. If there are 10 members total, how many 5 member teams can y
rodikova [14]
2 becuae......................................................................................................you have 5/10
7 0
3 years ago
find two consecutive odd integers that 7 times the smaller integer is 61 more than 2 times the larger integer.
Aleks04 [339]

Answer:

x = 13     smaller integer

x + 2 = 15  the other integer

Step-by-step explanation:

x = the smaller integer

x + 2 = the next integer          

7(x) = 61 + 2(x + 2)

7x = 61 + 2x +4

5x = 61 + 4

5x  = 65

x = 13     smaller integer

x + 2 = 15  the other integer

8 0
3 years ago
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