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2 years ago

What is the midpoint between points A and B? A. 1.75 B. 1.75 C. 0.875 D. 3.375

Mathematics

1 answer:

Alexeev081 [22]2 years ago

3 0

(-4.25 + 2.5)/2 = -1.75/2 = -0.875
C is correct

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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

_____% of 145 = 75 48.3% 193.3% 76.5% 51.7%

Pavlova-9 [17]

48.3 i’m pretty sure! your welcome:)

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2 years ago

Solve each equation. Show your work, or explain your reasoning. -3x + 5 = 16

Vesna [10]

-3x + 5 = 16

First, subtract 5 from both sides.

-3x = 11

Then, divide -3 by both sides.

x = -11/3 or -3.66....

8 0

3 years ago

PLEASE HELP WILL MARK YOU AS BRAINLIEST

Alenkasestr [34]

I want to help, but I’m not seeing a question though.

4 0

3 years ago

If you wish to calculate the interest on an investment with a rate of 3.58%, what number will you plug into your equation?

irina [24]

To get a certain percentage as a decimal, all you have to do is divide this percentage by 100.

Applying this on the given question, we will find that:
3.58% = (3.58) / (100) = 0.0358

Comparing the calculated value to the given choices, we will find that the correct choice is:
c) 0.0358

6 0

3 years ago

Read 2 more answers