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3 years ago

10

If tomorrow is Wednesday, what day is it today?

2 answers:

wel3 years ago

6 0

Tuesday because the 7 days of the week

max2010maxim [7]3 years ago

4 0

If tomorrow is Wednesday, That means that today is Tuesday

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Find a solution to y'(t) = te^-t satisfying the condition y(1) = 1.

Alex_Xolod [135]

Answer:

$y=-e^{-t}(t+1)+1+\frac{2}{e}$

Step-by-step explanation:

The given differential equation is

$y'(t)=te^{-t}$

It can be written as

$\frac{dy}{dt}=te^{-t}$

$dy=te^{-t}dt$

Integrate both sides.

$\int dy=\int te^{-t}dt$

Apply ILATE rule on right side. Here, t is first function and $e^{-t}$ is the second function.

$y=t\int e^{-t}-\int (\frac{d}{dt}t\int e^{-t})$

$y=-te^{-t}-\int (1\times (-e^{-t}))$ $\int e^{-x}=-e^{-x}+C$

$y=-te^{-t}+\int e^{-t}$

$y=-te^{-t}-e^{-t}+C$ .... (1)

Initial condition is y(1) = 1. It means at t=1 the value of y is 1.

$1=-(1)e^{-t}-e^{-(1)}+C$

$1=-e^{-1}-e^{-1}+C$

$1=-2e^{-1}+C$

$1=-\frac{2}{e}+C$

Add $\frac{2}{e}$ on both sides.

$1+\frac{2}{e}=C$

Substitute the value of C in equation (1).

$y=-te^{-t}-e^{-t}+1+\frac{2}{e}$

$y=-e^{-t}(t+1)+1+\frac{2}{e}$

Therefore, the solution of given initial value problem is $y=-e^{-t}(t+1)+1+\frac{2}{e}$ .

4 0

3 years ago

Simplify the expression. 32 1/5 =

tatuchka [14]

Is it 32 x 1/5?? Then the answer is 6.4

7 0

3 years ago

What is the answer when you simplify?.

soldier1979 [14.2K]

The answer when you simply is B. 4^2

4 0

3 years ago

Read 2 more answers

Determine the holes, vertical asymptotes, and horizontal asymptotes of the rational function y=3x^2+10x-8/x^2+7x+12

kompoz [17]

There would be a hole when x = -4.

If you factor both the top and the bottom, you will see that the factor (x + 4) is in both the numerator and denominator. Therefore, the would be a hole when x = -4 because that would also make the denominator 0.

8 0

3 years ago

It is estimated that there are 10^20 grains of sand on a beach in Florida in April. The beach is heavily eroded by tourists over

lyudmila [28]

$\bf \textit{how much is }\frac{1}{100}\quad of \quad 10^{20}?\implies \stackrel{\textit{one hundredth}}{\cfrac{1}{100}}\cdot 10^{20}\implies \cfrac{1}{10^2}\cdot 10^{20}
\\\\\\
10^{-2}\cdot 10^{20}\implies 10^{-2+20}\implies 10^{18}
\\\\\\
1,000,000,000,000,000,000~grains$

5 0

3 years ago