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3 years ago

Which function will have the largest output value when x=100

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

7 0

= 100 I think I'm not for sure

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family of solutions of the second-order DE y y 0. Find a solution of the second-order IVP consisting of this differential equati

Anna35 [415]

Answer:

$y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}$

Step-by-step explanation:

Given

$y=c_1e^x +c_2e^{-x$

$y(1) = 0$

$y'(1) =e$

Required

The solution

Differentiate $y=c_1e^x +c_2e^{-x$

$y' = c_1e^x - c_2e^{-x}$

Next, we solve for c1 and c2

$y(1) = 0$ implies that; x = 1 and y = 0

So, we have:

$y=c_1e^x +c_2e^{-x$

$0 = c_1 * e^1 + c_2 * e^{-1}$

$0 = c_1 e + \frac{1}{e}c_2$ --- (1)

$y'(1) =e$ implies that: x = 1 and y' = e

So, we have:

$y' = c_1e^x - c_2e^{-x}$

$e = c_1 * e^1 - c_2 * e^{-1}$

$e = c_1 e - \frac{1}{e}c_2$ --- (2)

Add (1) and (2)

$0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2$

$e = 2c_1e$

Divide both sided by e

$1 = 2c_1$

Divide both sides by 2

$c_1 = \frac{1}{2}$

Substitute $c_1 = \frac{1}{2}$ in $0 = c_1 e + \frac{1}{e}c_2$

$0 = \frac{1}{2} e+ \frac{1}{e}c_2$

Rewrite as:

$\frac{1}{e}c_2 = -\frac{1}{2} e$

Multiply both sides by e

$c_2 = -\frac{1}{2} e^2$

So, we have:

$y=c_1e^x +c_2e^{-x$

$y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}$

$y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}$

6 0

3 years ago

Evaluate 7m+ 3mn when m=8 and n=14?Answers:aA:84,B:196,C:392,D=168

Aleksandr-060686 [28]

Answer:

c) 392

Step-by-step explanation:

4 0

4 years ago

Wiat number should be added to both sides of the equation to complete the square? X^2+x=11

Ivahew [28]

Answer:

add 1/4 to each side

Step-by-step explanation:

x^2+x=11

We take the coefficient of the x term

Then divide it by 2

1/2

Then square it

(1/2) ^2 = 1/4

Add this to both sides of the equation

x^2 + x + 1/4 = 11+1/4

(x+1/2)^2 = 11 1/4

7 0

4 years ago

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Which expression represents the sum of ( 2x-5y) and (x+y)?

nekit [7.7K]

Sum of ( 2x-5y) and (x+y)?
=2x-5y+x+y
=3x-4y

6 0

4 years ago

From the given angle measurements, you can’t directly find the measure of angle L. However, you can find the measurement of angl

DaniilM [7]

The measurement of angle L = 50°.

Solution:

The given image is a rectangle.

The measurement of ∠A = 25°

The measurement of ∠B = 25°

ABC is a triangle.

Sum of the interior angles of the triangle = 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 25° + 25° + m∠C = 180°

⇒ 50° + m∠C = 180°

⇒ m∠C = 180° – 50°

⇒ m∠C = 130°

Sum of the adjacent angles in a straight line = 180°

⇒ m∠C + m∠L = 180°

⇒ 130° + m∠L = 180°

⇒ m∠L = 180° – 130°

⇒ m∠L = 50°

Hence the measurement of angle L = 50°.

8 0

3 years ago

Read 2 more answers