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2 years ago

1. Function or Not? Function Not

Mathematics

1 answer:

Licemer1 [7]2 years ago

6 0

Answer:

function

Step-by-step explanation:

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Find the numbers b such that the average value of f(x) = 7 + 10x − 9x2 on the interval [0, b] is equal to 8.

barxatty [35]

Answer:

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

Step-by-step explanation:

The mean value of function within a given interval is given by the following integral:

$\bar f = \frac{1}{b-a}\cdot \int\limits^b_a {f(x)} \, dx$

If $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ , $a = 0$ , $b = b$ and $\bar f = 8$ , then:

$\frac{1}{b}\cdot \int\limits^b_0 {7+10\cdot x -9\cdot x^{2}} \, dx = 8$

$\frac{7}{b}\int\limits^b_0 \, dx + \frac{10}{b} \int\limits^b_0 {x}\, dx - \frac{9}{b} \int\limits^b_0 {x^{2}}\, dx = 8$

$\left(\frac{7}{b} \right)\cdot b + \left(\frac{10}{b} \right)\cdot \left(\frac{b^{2}}{2} \right)-\left(\frac{9}{b} \right)\cdot \left(\frac{b^{3}}{3} \right) = 8$

$7 + 5\cdot b - 3\cdot b^{2} = 8$

$3\cdot b^{2}-5\cdot b +1 = 0$

The roots of this polynomial are determined by the Quadratic Formula:

$b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

The numbers $b$ such that the average value of $f(x) = 7 +10\cdot x - 9\cdot x^{2}$ on the interval [0, b] is equal to 8 are $b_{1} \approx 1.434$ and $b_{2} \approx 0.232$ .

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3 years ago

Find a 95% confidence interval for the difference in proportions, pt-po, two ways, using StatKey or other technology and percent

beks73 [17]

A bit confusing for me to be able to answer this for you… any way you can simplify your question?

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2 years ago

Find the quotient show work please

Papessa [141]

5/68 5 can go into 68 13 times with a remainder of 3 So we add a decimal point and a zero. Carry the 3 and zero down making 30 5 can go into 30 6 times making the answer 13.6

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3 years ago

Expanded form of 680,705

denis23 [38]

$\huge\boxed{600,000 + 80,000 + 700 + 5}$

To find expanded form, we need to split up the digits. When you do that, you take one digit and cut off everything to the left of it, then make everything to the right zeros.

$600,000 + 80,000 + 0 + 700 + 0 + 5$