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dezoksy [38]
2 years ago
7

Find the gradient of the curve y=-x^-3-5x^2+7x at x=2​

Mathematics
1 answer:
Harman [31]2 years ago
5 0

-8

Step-by-step explanation:

The gradient or slope of a curve y is simply the derivative of the curve at a point x. So we can proceed as follows

\dfrac{dy}{dx} = \dfrac{d}{dx}(x^3 -5x^2 +7) = 3x^2 -10x

Evaluated at x = 2, the gradient of the slope is

\left.\dfrac{dy}{dx}\right|_{x=2} = 3(2)^2 - 10(2) = -8

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4vir4ik [10]

Answer:

Last option: increasing: -2 < x < 0 and x> 3/2;

decreasing: x < -2 and 0 < x < 3/2

Step-by-step explanation:

The function given is an absolute cubic function. (Pictured below).

We can determine from the graph that the equation increases over the interval:

increasing: -2 < x < 0 and x> 3/2;

decreasing: x < -2 and 0 < x < 3/2

6 0
3 years ago
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There are 20 students on the school's student council. A special homecoming dance committee is to be formed by randomly selectin
AysviL [449]

You can choose from 20 students for the first student, 19 for the second, 18 for the third, ..., 14 for the seventh student.

That gives you 20 * 19 * 18 * 17 * 16 * 15 * 14.

That number would allow you to write the students in different order. Since order here does not matter, any group with the same students in any order is the same group, you need to divide by the number of way you can order 7 items. Divide by 7 * 6 * 5 * 4 * 3 * 2 * 1

(20 * 19 * 18 * 17 * 16 * 15 * 14)/(7 * 6 * 5 * 4 * 3 * 2 * 1) = 77,520

Answer: 77,520

8 0
4 years ago
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Increase 120 centimetres by 24%
Eva8 [605]
It is a simple problem where 120 centimeters need to be increased by 24%. The increased length can be found by:
120 * (24/100)
= 12 * (24/10)
= 288/10
= 28.8 centimeters
Then the total length of increase = 28.8 cm
Then the increased length = (120 + 28.8) cm
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So the length becomes 148.8 cm after it is increased by 24%.
3 0
4 years ago
A new car depreciates at a rate of 15% per year. What is the expected value of a $25,000 car after 5 years (rounded to nearest w
geniusboy [140]
The answer to the question above is letter B. The new car depreciates at the rate of 15% per year. The expected value of the car after 5 years is $11,093. to explain the calculation of the answer :
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3 years ago
a worker A finishes a project on his own in 12 days. the worker completes the same work alone in 16 days. the two workers starte
ankoles [38]

Answer:

<em>Worker B needs 9 days to finish the rest of the work</em>

Step-by-step explanation:

<u>Proportions</u>

Worker A finishes a project on his own in 12 days and worker B does the same in 16 days.

Worker A does 1/12 of the project in one day and worker B does 1/16 of the project in one day. When working together, they do

\frac{1}{12}+\frac{1}{16}=\frac{7}{48}

After 3 days they have completed:

3*\frac{7}{48}=\frac{7}{16}

parts of the project, this means it still remains:

1-\frac{7}{16}=\frac{9}{16}

parts of the project and it is done by B alone. Since B does \frac{1}{16} per day, he now takes

\displaystyle \frac{\frac{9}{16}}{\frac{1}{16}}=9

days to complete the project.

Worker B needs 9 days to finish the rest of the work

4 0
3 years ago
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