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3 years ago

Will 3 liter bottle of water fit in two half-gallon jugs

Mathematics

1 answer:

Studentka2010 [4]3 years ago

3 0

Yes it can hold up to a little over 4 liters

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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

Mr. Dunford will give 6 pencils to each of his 30 students in his class. There are 12 pencils in each box he will order. He has

horsena [70]

Answer:

The answer to this problem is 4

Step-by-step explanation:

6 0

3 years ago

-7 2/3 + (-5 1/2) + 8 3/4

Dennis_Churaev [7]

Answer:

-4.41666666667

Step-by-step explanation:

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3 years ago

What is the solution set to the inequality 5(x – 2)(x + 4) > 0

Fittoniya [83]

<span>5(x – 2)(x + 4) > 0
(5x-10)(x+4)>0
6x -6 > 0
+6 +6
6x >
</span>x<-4 or x>2

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2 years ago

Christian was 145 cm tall when he was 12 years old. And 3 years later, he became 168.2 cm tall. By what percent did Christian's

Sav [38]

Answer: 16%

Step-by-step explanation:

168.2 - 145 = 23.2

23.2/145 = 0.16

0.16 as a percent is 16%

6 0

3 years ago