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3 years ago

Let f(x)=x^2+5x-8. What is the average rate of change from x = 2 to x = 6? Enter the answer in the box ___

Mathematics

1 answer:

koban [17]3 years ago

5 0

Answer:

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [2, 6 ]

f(b) = f(6) = 6² + 5(6) - 8 = 36 + 30 - 8 = 58

f(a) = f(2) = 2² + 5(2) - 8 = 4 + 10 - 8 = 6

Hence

average rate of change = $\frac{58-6}{6-2}$ = $\frac{52}{4}$ = 13

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there is 60% chance it is blue and 50% its a fantasy one.

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2 years ago

a manufacturer has determined that if his company sells x items per day then their profit is given by P=-x^2+ 700 x-10000 euros.

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Answer:

Step-by-step explanation:

To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula

$x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x= \frac{-b-\sqrt{b^{2}-4ac } }{2a}$

$x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}$

$x= \frac{-700+\sqrt{530000} }{2}; x= \frac{-700-\sqrt{530000} }{2}$

$x=\frac{-700+100\sqrt{53} }{2}; x=\frac{-700-100\sqrt{53} }{2};$

$x=-350 + 50\sqrt53 = 14.005; x = -350 - 50\sqrt53 = -714.005$

In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.

$(-714.005)^2+700(-714.005)-10000=-0.360$

Furthermore, we must round to the nearest whole number, as you cannot make part of an item.

Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:

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2 years ago

Micah is preparing for a piano recital. He practices for 50 minutes on Monday and 90 minutes on Wensday

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Answer:

She increased 80% the practise time

Step-by-step explanation:

The question is incomplete, the following is missing:

<em>by how much did she increase the time she practised each day? </em>

From Monday to Wednesday she increased 90 - 50 = 40 minutes the practise time.

To compute the increment as a percentage use: increment/reference *100

In this case, that is: 40/50*100 = 80%, where 50 minutes is taken as a reference.

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