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2 years ago

WHICH OF THE FOLLOWING IS EQUIVILENT TO 60^1/2

Mathematics

1 answer:

son4ous [18]2 years ago

8 0

I can’t see any choices, can you tell me what the choices r

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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

PLEASE HELP!!!!!!

Montano1993 [528]

Answer:

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

What’s 8x8 <br> This is to test how the app works not serious

lisov135 [29]

Answer:

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

3) Ashley uses the two points on the coordinate plane to represent the location of her house and the public library. Each unit o

Aleonysh [2.5K]

By counting grid squares, we see the library is 5 miles north and 6 miles east of Ashley's house. Using the Pythagorean theorem, we can find the straight-line distance to be
.. d = √(5^2 +6^2)
.. = √(25 +36)
.. = √61 . . . . . miles
.. ≈ 7.81 . . . . miles

4 0

2 years ago

While setting up a fireworks display, you have a tool at the top of the

atroni [7]

Answer:

0.79 sec

Step-by-step explanation:

Given there is a tool at the top of the building which is dropped by a worker and it follows the following equation at every instant of time .

$h(t)=-16t^{2} +h_{0}$

where $h_{0} =10 feet$

We know that this height is measured from the base of the building which means that when the tool reaches the bottom of the building it has h = 0 feet.

Let this be done at time t

h(t) = 0

$-16t^{2} +10=0$

$t^{2} =\frac{10}{16}$

$t=\frac{\sqrt{10} }{4}$

t = 0.79 sec

Therefore the total time taken by the tool to reach the bottom of the building is 0.79 sec.

8 0

3 years ago