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2 years ago

Find the distance between the two points . (5,-3) , (-4,7)

Mathematics

1 answer:

emmasim [6.3K]2 years ago

7 0

Answer:

sqrt(181)

Step-by-step explanation:

sqrt (9^2 + 10^2)

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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

ANSWER QUICK AND WILL GIVE 1000 POITS PLEASE!!!!!!!A truck drove 229.77 miles on 11.1 gallons of gas. How far could the truck dr

Archy [21]

Answer:

347.76 miles

Step-by-step explanation:

A truck drove 229.77 miles on 11.1 gallons of gas.

<u>Find the mileage per gallon:</u>

229.77 / 11.1 = 20.7 mpg

<u>Find the distance can be driven on full tank:</u>

20.7 * 16.8 = 347.76 miles

4 0

2 years ago

Read 2 more answers

Sarah has a 22 ounce lemonade. She drinks 9 ounces. Enter the percentage of ounces Sarah has left of her lemonade. Round your an

blagie [28]

Answer:

40.91 percent

7 0

2 years ago

Read 2 more answers

How do you use the product rule to find the derivative of y=x√⋅cos(x)y=sqrt(x)*cos(x) ?

Ipatiy [6.2K]

$y=\sqrt x\cos x\\
y'=(\sqrt x)'\cos x+\sqrt x (\cos x)'\\
y'=\frac{1}{2\sqrt x}\cos x+\sqrt x\cdot(-\sin x)\\
y'=\frac{1}{2\sqrt x}\cos x-\sqrt x\sin x\\
$

7 0

2 years ago

to raise money for her school field trip, Jane is selling candles. She has a large cancel for $8, and a small candle for $5. If

Fed [463]

Answer:

45 large candles
53 small candles

Step-by-step explanation:

Let c represent the number of large candles Jane sold. Then 98-c is the number of small candles. Her revenue is ...

8c +5(98-c) = 625

3c + 490 = 625 . . . . . . eliminate parentheses, collect terms

3c = 135 . . . . . . . . . . . . subtract 490

c = 45 . . . . . . . . . . . . . . divide by 3

Jane sold 45 large candles and 98-45 = 53 small candles.

7 0

2 years ago