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disa [49]
2 years ago
8

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.

7 0
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?
4 0
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
3 0
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

We don't need to keep the zeros.

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

We can check this by adding the numbers back up to get 680,705.

680,000 + 700 + 5

680,700 + 5

680,705

6 0
3 years ago
What is 15 to the 5 power
inna [77]
15^5 is 759,375
..........................
6 0
3 years ago
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