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3 years ago

Solve: 92x + 1 = 93x – 2

Mathematics

2 answers:

vichka [17]3 years ago

6 0

Answer:

x equals 3 :) if i helped, please give brainliest!

Step-by-step explanation:

Scrat [10]3 years ago

5 0

Answer:

x=3

The follow up is C.

Good luck!!

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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

A construction worker is filling a container in the shape of a right circular cylinder with cement. the container has a base dia

kirza4 [7]

The volume of this container is 5990 feet³.

<h3>How to calculate the volume?</h3>

Volume of a cylinder = πr²h

π = 3.14

r = radius = 17.5/2 = 8.75

h = 24.5

The volume will be:

= πr²h

= 3.14 × 8.75² × 24.5

= 5990 ft³

Therefore, the volume of this container is 5990 feet³.

Learn more about volume on:

brainly.com/question/463363

#SPJ1

3 0

2 years ago

Number 3 and 4 please ASAP

Tpy6a [65]

Step-by-step explanation:

Question 3) there's 60 minutes in a hour

3 times 60 = 180 books in 1 hour

3 times 180 = 540 books in 3 hours

540 + 180 + 180 = 900 books in 5 hours

The difference between those numbers : 900-540= 360 and 540-180= 360 so every 2 hours 360 books is done each time so just add 360 books each time for every 2 hours added

3 0

3 years ago

Help pls and thank you!!!

max2010maxim [7]

Answer:

Consistent and independent

Step-by-step explanation:

The only touch at one point and they are not the same line and are not parallel

5 0

3 years ago

Does anyone know this answer?

vladimir1956 [14]

It is leaner because the progress of the tree growth is constant. Every year it increases 2 feet staring at 20 feet

3 0

3 years ago

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