Using the new unit you have defined, rewrite the debt for years 1900, 1930, 1960, and 2000.

Elanso [62]

Answer:

1,256 dm^2 and 400π dm^2

Step-by-step explanation:

The circumference is equal to 2pi times the radius. So 40pi=2pi times the radius so the radius is 20. The area of a circle is pi times the radius squared or 400pi and if using 3.14 for pi this would be 1,256 dm^2

6 0

1 year ago

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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

A store sells candles.

maria [59]

Answer:

25%

Step-by-step explanation:

If you start at 45% and it reduces by 20% you are just doing 45-20 which equals 25. (Please let me know if im wrong)

7 0

3 years ago

Your football team gained 4 yards on first down and 2 yards on second down during its last possession. Which number is the addit

Gre4nikov [31]

Your football team gained 4 yards on first down and 2 yards on second down during its last possession. Which number is the additive inverse of the yards gained?

5 0

3 years ago

Read 2 more answers

Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% a

labwork [276]

Answer:

a) P=0.24

b) P=0.31

c) Not independent.

Step-by-step explanation:

Incomplete question.

a) What is the probability that a randomly selected order will be wrapped and sent to another person?

$P(W\&SOP)=P(SOP)*P(W|SOP)=0.30*0.60=0.24$

W: wrapped

SOP: sent to other people

b) What is the probability that a randomly selected order will be gift wrapped?

$P(W)=P(SOP)*P(W|SOP)+P(SR)*P(W|SR)\\\\P(W)=0.3*0.6+0.7*0.1=0.24+0.07=0.31$

SR: sent to the right person

c) Is gift wrapping independent of the destination of the gift? Justify your response statistically.

To prove that they are independent, both of the following conditions must be met:

P(x|y) = P(x), for all values of X and Y.

P(x ∩ y) = P(x) * P(y), for all values of X and Y.

We start for the second condition.

$P(W\cap SR)=0.1\\\\P(W)*P(SR)=0.31*0.7=0.217\\\\\\P(W\cap SR)\neq P(W)*P(SR)$

This condition is not met, so the two variables are not independent.

4 0

3 years ago