The triangles are similar. Write a similarity statement for the triangles.

Consider the differential equation y'' − y' − 30y = 0. Verify that the functions e−5x and e6x form a fundamental set of solution

Alex Ar [27]

Answer:

Step-by-step explanation:

We have to take the derivatives for both functions and replace in the differential equation. Hence

for y=e^{-5x}:

$y(x)=e^{-5x}\\y'(x)=-5e^{-5x}\\y''(x)=25e^{-5x}\\$

for y=e^{6x}:

$y(x)=e^{6x}\\y'(x)=6e^{6x}\\y''(x)=36e^{6x}\\$

Now we replace in the differential equation y'' − y' − 30y = 0

for y=e^{-5x}:

$25e^{-5x}+5e^{-5x}-30e^{-5x}=0\\25+5-30=0$

for y=e^{6x}:

$36e^{6x}-6e^{6x}-30=0\\36-6+30=0$

Now, to know if both function are linearly independent we calculate the Wronskian

$W(f,g)=fg'-f'g$

$W(e^{-5x},e^{6x})=(e^{-5x})(6e^{6x})-(-5e^{-5x})(e^{6x})\neq 0$

I hope this is useful for you

Best regard

7 0

4 years ago

8% of what is 2.8??

Ilia_Sergeevich [38]

Write that as an equation and solve. (In math, "of" often means "times".)
8% × what = 2.8
0.08 × what = 2.8
what = 2.8/0.08
what = 35

8% of 35 is 2.8.

6 0

3 years ago

Determine the value of g(4), g(3 / 2), g (2c) and g(c+3) then simplify as much as possible.

jeka94

Answer:

$g(4) = 8 \pi h\\\\g(\frac{3}{2}) = 3 \pi h\\\\ g(2c) = 4 \pi ch\\\\g(c+3) = 2 \pi hc+6\pi h$

Step-by-step explanation:

You need to substitute $r=4$ into $g(r) = 2 \pi r h$ . Then:

$g(4) = 2 \pi(4)h\\\\g(4) = 8 \pi h$

Substitute $r=\frac{3}{2}$ into $g(r) = 2 \pi r h$ . Then:

$g(\frac{3}{2}) = 2 \pi(\frac{3}{2})h\\\\g(\frac{3}{2}) = 3 \pi h$

Substitute $r=2c$ into $g(r) = 2 \pi r h$ . Then:

$g(2c) = 2 \pi(2c))h\\\\g(2c) = 4 \pi ch$

Substitute $r=c+3$ into $g(r) = 2 \pi r h$ . Then:

$g(c+3) = 2 \pi (c+3)h\\\\g(c+3) = 2 \pi hc+6\pi h$

8 0

4 years ago

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A bird (B) is spotted flying 6,000 feet from a tower (). An observer (0) spots the top of tower (T) at a distance of 9,000 feet.

Kobotan [32]

Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.

<h3>What are the relations in a right triangle?</h3>

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

For this problem, we have that:

The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.

The adjacent side to the angle is the distance to the bird, of 6000 feet.

Hence, considering θ as the depression angle, we have that:

tan(θ) = 9000/6000

tan(θ) = 1.5

θ = arctan(1.5)

θ = 56.31º.

More can be learned about relations in a right triangle at brainly.com/question/26396675

#SPJ1

8 0

2 years ago

The expression 1.5t + 20 predicts the height in centimeters of a plant tt days from today. What is the predicted height of the p

Leokris [45]

Hi there! :)

Answer:

The predicted height of the plant is 102.5

Step-by-step explanation:

The variable "t" in your expression is the number of days from today, and that the whole expression is equal to the predicted height of the plant :

"t" = number of days from today

1.5t + 20 = predicted height of the plant

You want to know the predicted height of the plant 55 days from today.

SO, in other words, you want to know what the expression is equal to when "t" is equal to 55.

In order to answer your question, you'll have to replace the "t" in the expression by its value, which is 55, and solve the expression to find what it equals to:

1.5t + 20 = X

1.5(55) + 20 = X

Multiply 1.5 by 55 → 1.5 × 55 = 82.5

82.5 + 20 = X

Add 20 to 82.5 → 82.5 + 20 = 102.5

102.5 = X

There you go! I really hope this helped, if there's anything just let me know! :)

6 0

3 years ago

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