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Greeley [361]
3 years ago
14

Use the graph of f to calculate

ormula1" title="\int\limits^4_0 {f(t)} \, dt" alt="\int\limits^4_0 {f(t)} \, dt" align="absmiddle" class="latex-formula">. PLEASE HELP!

Mathematics
1 answer:
frozen [14]3 years ago
3 0

You should already be aware that the definite integral of f(t) is equivalent to the signed area under the curve of

\displaystyle\int_0^1f(t)\,\mathrm dt

corresponds the area of the triangle on the left, and

\displaystyle\int_1^4f(t)\,\mathrm dt

is the area of the trapezoid in the middle. You should know how to compute the area of these shapes.

We end up with

\displaystyle\int_0^4f(t)\,\mathrm dt=-\frac{1\times2}2+\frac{(1+3)\times2}2=3

since the triangle has height 2 and base 1, and the trapezoid has height 2 with two base lengths 1 and 3.

Edit: The area under the curve is highlighted red in the attachment below. It's the area between the curve and the horizontal axis, but it's also signed, meaning the area <em>below</em> the axis is negative, and the area <em>above</em> the axis is positive.

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Which number is greatest?​
user100 [1]

Answer:

6.23 \times 10 {}^{12}

Step-by-step explanation:

6 .23\times 10 {}^{12}

6.23 \times 1000000000000 \\ 6230000000000

7 0
3 years ago
Read 2 more answers
Which of the following companies offers the greatest total employment compensation? Company A Company B Company C Company D Gros
san4es73 [151]

we know that

To find the company with the greatest total employee compensation package, adds each company's gross pay, paid insurance, and paid time off, then subtract the job expenses on the sum

So

Find the total employee compensation package for each company

Step 1

Find the total employee compensation package for company A

total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses

total\ employee\ compensation=37,600+2,800+3,100-1,200\\ total\ employee\ compensation=42,300\ dollars

Step 2

Find the total employee compensation package for company B

total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses

total\ employee\ compensation=36,800+2,400+3,600-600\\ total\ employee\ compensation=42,200\ dollars

Step 3

Find the total employee compensation package for company C

total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses

total\ employee\ compensation=38,100+2,100+2,900-300\\ total\ employee\ compensation=42,800\ dollars

Step 4

Find the total employee compensation package for company D

total\ employee\ compensation=gross\ pay\ +\ paid\ insurance\ +\ paid\ time\ -\ job\ expenses

total\ employee\ compensation=39,000+1,800+2,500-800\\ total\ employee\ compensation=42,500\ dollars

therefore

the answer is

the company with the greatest total employee compensation package is the company C

8 0
3 years ago
Read 2 more answers
Suppose that y varies directly as the square of x, and that y=567 when x=9. What is y when x=4
Gwar [14]

Answer:

y  = 112

Step-by-step explanation:

If  y varies directly as the square of x

mathematically;

y ∝ x²

y = kx² where 'k' is the constant of proportionality

let u know the value of k for this equation by making k the subject of the formular from y = kx²

divide both sides by x²

k = y / x²

given that  y = 567 x = 9

k = 567/(9)²

k = 567/81

k = 7

now to get the value of  y when x = 4

from the equation conneting x, y,

y = kx²

y = 7 × (4)²

y = 7 × 16

y  = 112

6 0
3 years ago
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
mixer [17]

Answer:

B

Step-by-step explanation:

To solve for x, we have to get x by itself. To do this, perform the opposite of what is being done to the equation.

5x+14=k

First, subtract 14 from both sides, because 14 is being added on to 5x. Subtraction is the opposite of addition.

5x+14-14=k-14

5x=k-14

Now, divide both sides by 5, because 5 and x are being multiplied. Division is the opposite of multiplication.

5x/5=k-14/5

x=k-14/5

So, the correct answer is choice B

6 0
3 years ago
Simplify the radical completely.
Sonja [21]

Answer:

D

Step-by-step explanation:

But basically, one by one you try moving the terms out of the radical.

75 is also 25 * 3 and since 25 has a perfect square root of 5 that goes out and 3 stays inside the radical.

x^3 is also x^2 * x and since x^2 has a perfect square root which is just x that goes outside while the remaining x stays inside.

y^9 is also y^8 * y and since we move variables out the radical in twos y^ goes outside the radical and y stays inside alone.

Finally, z is just z it can't be taken out so it stays inside the radical.

Hope that helps!

8 0
2 years ago
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