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4 years ago

I need help on both of these questions 5/12 + 3/5 and 7/9 - 1/2 please

Mathematics

1 answer:

SSSSS [86.1K]4 years ago

3 0

1) u would have to find the lcd of both. And that is 60 so it would be 25/60 +36/60 = 61/60 = 1 1/60

2) do the same thing as in number 1. Find the LCD it is 18. So 14/18 - 9/18 = 5/18

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Write the equation of each line in slope-intercept form and identify the slope. 4x=2+y

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Answer:

y = 4x - 2

Step-by-step explanation:

Given: 4x=2+y

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Once subtracted, you get: 4x-2=y

Rearrange it, and you get: y=4x-2

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3 years ago

Find the approximate difference in the area of the two circles shown below. Use 3.14 for pi.

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3 years ago

What is the answer to:<br> 18 - 5z + 6z > 3 + 6

miv72 [106K]

18 - 5z + 6z > 3 + 6
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3 years ago

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

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

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3 years ago

Explain how to translate the phrase into an algebraic expression.

ASHA 777 [7]

Hey there.. I will be more than happy to help you today.. :)

A Number squared decreased by ten

We will do this with steps:-

Step 1 - "A number ". So, Let's say any number be x

Step 2 - "A number squared". Our number x is squared i.e. x²

Step 3 - "A number squared" ( i.e. x² ) is decreased by ten
x² - 10

This is your answer.
Hope this helps you :)

4 0

3 years ago

Read 2 more answers