The first row are input, x the second row is output, y .

Find the number b such that the line y = b divides the region bounded by the curves y = x2 and y = 4 into two regions with equal

densk [106]

Answer:

b = ∛16 ≈ 2.520

Step-by-step explanation:

The area bounded by y=x^2 and y=b is given by the integral ...

$\displaystyle A(b)=\int\limits^{\sqrt{b}}_{-\sqrt{b}} {(b-x^2)} \, dx=2b\sqrt{b}-\frac{2}{3}b\sqrt{b}=\frac{4}{3}b^{\frac{3}{2}}$

For b = 4,

A(4) = (4/3)4^(3/2) = 32/3

We want to find b such that the area is half that, or ...

A(b) = (1/2)(32/3) = 16/3

So, we're solving the equation ...

16/3 = 4/3b^(3/2)

4 = b^(3/2) . . . . . . . . . . . . . . multiply by 3/4

4^(2/3) = b = ∛16 . . . . . . . . raise to the 3/2 power

6 0

4 years ago

If you walk 420 minutes how much calories do you burn?

iren2701 [21]

27 caloires yeahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

3 0

3 years ago

Read 2 more answers

Latanya leaves her house at 12:30 p.M. And bikes at 12 mi/h to Marta's house. She stays at Marta's house for 90 minute. Both gir

Llana [10]

Answer:

Marta's house is 3.10 miles from Latanya's house

Step-by-step explanation:

* Lets explain how to solve the problem

- Latanya leaves her house at 12:30 p.M.

- She bikes at 12 mi/hr to Marta's house

- She stays at Marta's house for 90 minute

- Both girls walk back to latanya's house at 2.5 mi/h

- They arrive at latanya's house at 3:30 p.M.

- We need to know how far is Marta's house from latanya's house

∵ Latanya starts her trip at 12:30 p.M.

∵ She returns her home at 3:30 p.M.

∴ The time of her trip is → 3:30 - 12:30 = 3 hours

- But she stays at at Marta's house for 90 minutes

∵ 1 hour = 60 minutes

∴ 90 minutes = 90 ÷ 60 = 1.5 hours

∴ The time from her house to Marta's house and from Marta's house

to her house is → 3 - 1.5 = 1.5 hours

- Assume that the distance from her house to Marta's house is d

and the time from her house to Marta's house is $t_{1}$ ,

the time from Marta's house to her house is $t_{2}$

∵ Latanya bikes at 12 mi/h to Marta's house

∵ Distance = speed × time

∴ d = 12 × $t_{1}$

∵ Both girls walk back to latanya's house at 2.5 mi/h

∴ d = 2.5 × $t_{2}$

- Equate the two expressions of d

∴ 12 $t_{1}$ = 2.5 $t_{2}$ ⇒ (1)

∵ $t_{1}$ + $t_{2}$ = 1.5

- Subtract $t_{1}$ from both sides

∴ $t_{2}$ = 1.5 - $t_{1}$ ⇒ (2)

- Substitute equation (2) in equation (1)

∴ 12 $t_{1}$ = 2.5(1.5 - $t_{1}$ )

∴ 12 $t_{1}$ = 3.75 - 2.5 $t_{1}$

- Add 2.5 $t_{1}$ to both sides

∴ 14.5 $t_{1}$ = 3.75

- Divide both sides by 14.5

∴ $t_{1}$ = $\frac{15}{58}$ hour

∴ She spends 15/58 hour to bike to Marta's house

- Lets find d

∵ d = 12 $t_{1}$

∴ d = $12*\frac{15}{58}=3.10$ miles

* <em>Marta's house is 3.10 miles from Latanya's house</em>

6 0

4 years ago

Meaghan and Lily are dividing 43.61 by 7. Meaghan says that the first digit of the quotient is in the ones place. Lily says it i

Ivahew [28]

Answer: Meaghan is right.

Step-by-step explanation:

For a number like:

123.45

the tens place would be the "2" (second number at the left of the decimal point)

The ones place would be the "3" (first number at the left of the decimal point)

Let's suppose that Lily is correct.

Then the quotient of:

43.61/7

Will be a number with two digits in the left of the decimal point.

The smallest number that meets this condition, is the number 10.

Then let's see:

7*10 = 70

then:

70/7 = 10

and:

43.61 < 70

(70 is larger than 43.61)

then:

43.61/7 < 70/7 = 10

Then:

(43.61/7) < 10

This means that our quotient is smaller than 10, then the first digit of the quotient can not be on the tens place.

Then Meaghan is the correct one.

We also could perform the quotient to find:

43.61/7 = 6.23

So yes, Meaghan is correct.

5 0

3 years ago

A right isosceles triangle has an angle with measure of 45°. If x represents the measure of the third angle of the triangle, wha

katrin2010 [14]

Answer:

x = 45°

Step-by-step explanation:

"Isosceles" means the base angles are congruent: they both have the same measure, 45°. (The hypotenuse is the "base" for this isosceles triangle.)

The acute angles of a right triangle are complementary, so the third angle can also be found as 90° -45° = 45°.

7 0

4 years ago