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3 years ago

Estimate the value of 102.3 divided 4.7

Mathematics

2 answers:

tester [92]3 years ago

7 0

Answer: 21

Step-by-step explanation: 21.7659574 would be the exact awnser but to estimate you can just say 21

Lena [83]3 years ago

4 0

Answer:

It is actually 20.

Step-by-step explanation:

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Find the solution of the given initial value problem: 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

What is the value of 20 ÷ (-4)?

DerKrebs [107]

Answer:

-5

Step-by-step explanation:

20 ÷ (-4)=-5

8 0

4 years ago

Someone please help!

Sloan [31]

Answer:

plot the points & find where they insect then calculate the mid-point

4 0

3 years ago

Read 2 more answers

G(a) = 2a - 4 h(a) = 3a- 3 Find (g o h)(10) A) 50 B) 44 C) -75 D) 45

Alexeev081 [22]

Answer: i think its D

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

(x+14)-(8-2x) equivalent to

kipiarov [429]

We are given the expression (x + 14) - (8 - 2x). The question is asking us to simplify this expression, and we can do that by first using the distributive property. This gives us x + 14 - 8 + 2x. Now, just combine like terms, which gives us 3x + 6. Therefore, the answer to your query is 3x + 6. Hope this helped and have a phenomenal day!

7 0

3 years ago