The length of a rectangle is increasing at a rate of 6cm/s and its width is increasing at a rate of 3cm/s. When the length is 20cm and the width is 15cm, how fast is the area of the rectangle increasing?

150 cm/s

Step-by-step explanation:

We have that the area of a rectangle is as follows:

a = l * w

they ask us to change the increase in area with respect to time, therefore, if we derive with respect to t we are left with:

da / dt = w * (dl / d) t + l * (dw / dt)

From the statement we know that:

l = 20 cm

w = 15 cm

dl / dt = 6 cm / s

dw / dt = 3 cm / s

replacing each value we have:

da / dt = 15 * 6 + 20 * 3

da / dt = 150

Which means that 150 cm / s increases the area of the rectangle in relation to time

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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