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3 years ago

GIVING BRAILEST Describe a situation that the equation could represent g+3 _____ =15 6

Mathematics

1 answer:

krek1111 [17]3 years ago

6 0

Answer:

g=153

Step-by-step explanation:

i hope this helped...

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Find the solution of the given initial value problem:<br><br> y''- y = 0, y(0) = 2, y'(0) = -1/2

igor_vitrenko [27]

Answer: The required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Step-by-step explanation: We are given to find the solution of the following initial value problem :

$y^{\prime\prime}-y=0,~~~y(0)=2,~~y^\prime(0)=-\dfrac{1}{2}.$

Let $y=e^{mx}$ be an auxiliary solution of the given differential equation.

Then, we have

$y^\prime=me^{mx},~~~~~y^{\prime\prime}=m^2e^{mx}.$

Substituting these values in the given differential equation, we have

$m^2e^{mx}-e^{mx}=0\\\\\Rightarrow (m^2-1)e^{mx}=0\\\\\Rightarrow m^2-1=0~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mx}\neq0]\\\\\Rightarrow m^2=1\\\\\Rightarrow m=\pm1.$

So, the general solution of the given equation is

$y(x)=Ae^x+Be^{-x},$ where A and B are constants.

This gives, after differentiating with respect to x that

$y^\prime(x)=Ae^x-Be^{-x}.$

The given conditions implies that

$y(0)=2\\\\\Rightarrow A+B=2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$y^\prime(0)=-\dfrac{1}{2}\\\\\\\Rightarrow A-B=-\dfrac{1}{2}~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Adding equations (i) and (ii), we get

$2A=2-\dfrac{1}{2}\\\\\\\Rightarrow 2A=\dfrac{3}{2}\\\\\\\Rightarrow A=\dfrac{3}{4}.$

From equation (i), we get

$\dfrac{3}{4}+B=2\\\\\\\Rightarrow B=2-\dfrac{3}{4}\\\\\\\Rightarrow B=\dfrac{5}{4}.$

Substituting the values of A and B in the general solution, we get

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

Thus, the required solution of the given IVP is

$y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.$

4 0

3 years ago

I need help with this question! Will mark brainliest :)

frez [133]

Answer:

A. -1/5

B. 8 gallons

C. 75 miles driven

Step-by-step explanation:

Part A is essentially just asking for the slope, which is written as a fraction with the numerator being the number of units the line goes up/down and the denominator being the number of units the line goes left/right. Because the line is going down from left to right, the slope is negative. The slope is -1/5.

Part B can be answered by simply looking at the graph and seeing where the line is at above 175 miles, which is 8 gallons.

Part C can be answered in the same way as Part B, by looking at where the line is at when level with 12 gallons, which is 75 miles driven.

8 0

3 years ago

Reggie read a 400- page book in 5 days. On the first day, he read 120 pages .each day after that , he read the same number of pa

iris [78.8K]

400 pages in 5 days
but 120 on the first day
so 400-120=280
280 is what he read in the 4 days following
so divide 280 equally among the 4 days
You get 70 per day after the first

7 0

3 years ago

Read 2 more answers

What is the equivalent ratio to 12:20

vfiekz [6]

Divide both sides by 4:
3:5

7 0

3 years ago

PLEASE HELP ME!! I WILL GIVE YOU BRAINLIEST

jekas [21]

Answer:

Use $a^{2} +b^{2} = c^{2}$