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3 years ago

Make t the subject 2(t-5)=y

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

5 0

Answer:

t = (y + 10)/2

Step-by-step explanation:

Make t the subject in

2(t - 5) = y

Step 1

Expand the bracket by multiplying each term in the bracket by 2

2Xt - 2X5 = 2t - 10

2t - 10 = y

Step 2

To move 10 to the other side of the right hand side (RHS) of the equation, we add 10 to both sides of the equation.

2t - 10 + 10 = y + 10

2t = y + 10

Step 3

Make t the subject by dividing both sides of the equation by its coefficient, 2

2t/2 = (y + 10)/2

t = y+10 / 2

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2 years ago

What is the equation of the line

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Hello there!

The answer is B. $\frac{2}{7}$
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Explanation and Work:

We first must identify if the line goes through the origin or not.

The origin is (0, 0)

The line does go through the origin. This means that there is no y-intercept

The specific equation we would you use would be:

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We find this by finding the slope.

Slope is found by:

$\frac{y2 - y1}{x2 - x1}$

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Now, let's plug in these numbers.

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So, now let's plug he slope into our formula.

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3 years ago

[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 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.

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3 years ago

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