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ElenaW [278]
3 years ago
13

Question 1: Imagine that we are measuring rain fall with a rain gauge. It is raining

Mathematics
1 answer:
sdas [7]3 years ago
7 0

Answer:

13.5 inches

Step-by-step explanation:

after 5 hours = 6 inches

11 - 5 = 6 hours to go

1.25 x 6 = 7.5 inches

7.5 + 6 = 13.5 inches

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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
Which student correctly wrote the algebraic expression for the following statement?
Leno4ka [110]
Haileys work is correct so B should be the right answer
3 0
3 years ago
Read 2 more answers
Select all the true statements about the number 3,600−−−−−√.
Paul [167]

Answer:

3,600−−−−−√ is a rational number.I guess

6 0
3 years ago
Read 2 more answers
The median is the same as the ______________.
Ilia_Sergeevich [38]

Answer: Option A

The median is the same as the _ Second quartile_.

Step-by-step explanation:

Given a series of data ordered from least to greatest, the median is the value that is in the center.

That is, the median represents the value that divides 50% of the data.

In the same way, the first quartile Q_1 is the value that divides 25% of the data and the third quartile Q_3 is the value that divides 75% of the data.

The second quartile Q_2 is the number that divides 50% of the data.

Then notice that the second quartile is equal to the median

Then te answer is the option A.

7 0
4 years ago
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Ten gallons of paint were poured into two containers of different sizes. Use one variable to express the amount poured into each
wolverine [178]
X ≥ 10 gallons of paint
3 0
3 years ago
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