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2 years ago

Use a unit rate to find the unknown value 16/32= /14

1 answer:

7 0

Okay. So this is already set up as a proportion. Cross multiply the values in order to get 224 = 32x. Now, divide each side by 32 to isolate the variable. 224/32 is 7. x = 7. There. The unknown value is 7.

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1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

$x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1$

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

7 0

2 years ago

Which of the following(s) is true of a rectangle?

arsen [322]

<h2>Explanation:</h2>

Let's take a look at all of our options.

A. it is also a square

A rectangle is NOT <em>always </em>a square because a square has congruent sides, so that means all four of its sides are <em>always </em>equal.
A rectangle <em>can </em>be a square but it can also not be a square, so therefore A cannot be an option because it is not always true about a rectangle.

B. the sum of its angle measures is 360

This is true because every quadrilateral's angle measures will add up to 360 degrees, no matter what. This is like how a triangle's angle measures always add up to 180 degrees.
B is an option because it is an ALWAYS true statement.

C. it has four congruent angles

A rectangle always has 90 degree angles, giving it its shape.
Since a rectangle always has the same-degree angles, that means that it DOES have four congruent angles.
C is also an option because it is always true.

D. it has four congruent sides

A rectangle does not ALWAYS have four congruent sides. Say for example a rectangle has a longer length than its width.
A square has four congruent sides, but a rectangle is not always a square, therefore this option is not applicable for a rectangle since it is not always true.

<h2>Answers:</h2>

B and C are always true of a rectangle.

7 0

3 years ago

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a film canister in the shape of a cylinder has a height of 8 centimeters and a volume of the film canister. write an equation fo

uranmaximum [27]

Answer:

Part a) The equation for the volume of the film canister is

$32\pi=\pi r^{2}(8)$

Part b) The radius of the film canister is $2\ cm$

Step-by-step explanation:

<u><em>The complete question is</em></u>

A film canister in the shape of a cylinder has a height of 8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

$V=\pi r^{2} h$

where

r is the radius of the circular base

h is the height of the cylinder

we have

$V=32\pi\ cm^3$

$h=8\ cm$

substitute

$32\pi=\pi r^{2}(8)$ ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

$32\pi=\pi r^{2}(8)$

$32\pi=8\pi r^{2}$

Simplify

Divide by 8π both sides

$4=r^{2}$

square root both sides

$r=2\ cm$

8 0

2 years ago

Use a common denominator to write an equivalent fraction for each fraction 1/6 , 1/9

Contact [7]

Answer:

1/6 = 3/18

1/9 = 2/18

Step-by-step explanation:

The common denominator for 6 and 9 is the smallest number that they both go into, which is 18. We need to multiply 6 by 3 to get 18 and multiply 9 by 2 to get 18

1/6 *3/3 = 3/18

1/9 *2/2 = 2/18

3 0

2 years ago

Why does one of the ratios in a percent proportion always have a denominator of 100?

zzz [600]

Answer:

Ratios in a percent proportion always have a denominator of 100 because 100 % is the whole

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers