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3 years ago

15

The graph of y = e−x + 3 is shown. What are the y-intercept and the horizontal asymptote, and do they represent exponential grow

th or decay?
The y-intercept is (0, 3), the horizontal asymptote is y = 4, and the graph represents exponential growth.
The y-intercept is (0, 4), the horizontal asymptote is y = 3, and the graph represents exponential decay.
The y-intercept is (0, 4), the horizontal asymptote is y = 3, and the graph represents exponential growth.
The y-intercept is (4, 0), the horizontal asymptote is x = −3, and the graph represents exponential decay.

1 answer:

JulsSmile [24]3 years ago

7 0

The y-intercept is (0; 4).

The horizontal asymptote is y = 3.

The graph represents exponential decay.

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The path from the whales to the sharks is parallel to the path from the penguins to the stingrays. What is the distance between

gulaghasi [49]

The distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.

<h3>What is proportional segment between parallel lines?</h3>

In two triangle in which the one side of the first triangle is parallel to the one side of the other triangle, two similar triangle formed.

Due to this similar triangle the segment formed by the parallel line are proportional segment.

The path from the whales to the sharks is parallel to the path from the penguins to the stingrays.

The map of the zoo is attached below.

The distance from whale to shark is 18 ft, and this side is parallel to the path from the penguins to the stingrays. Suppose the distance between the penguins and the stingrays is x meters.

Thus, in the given triangle, the ratio of these two sides will be equal to the ratio of their corresponding sides. Hence,

$\dfrac{x}{18}=\dfrac{42}{27}\\x=\dfrac{42}{27}\times18\\x=28\rm\; ft$

Thus, the distance between the penguins and the stingrays which is parallel to the path from the whales to the sharks is 28 ft.

Learn more about the similar triangle here;

brainly.com/question/14285697

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2 years ago

Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

If the m angle 2 = 113 what is the angle 6

amid [387]

im pretty sure that the both of the angles added have to make a total of 180 degrees so, 180-113=67

7 0

3 years ago

Read 2 more answers

Answers plzzzzz I need then now

Misha Larkins [42]

3.99/0.019=210
0.05/0.07=0.7
14.13/0.341=41.44
0.9/0.84=1.07
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answer: His bark was worse than his bite.

4 0

4 years ago

A group consisting of 10 children an adult went to a movie theater children tickets cost 5 each and adults tickets cost 8 each a

wlad13 [49]

9514 1404 393

Answer:

6 children

Step-by-step explanation:

If all of the group were adults, the total cost of tickets would be 8×$10 = $80. The actual cost was $80 -62 = $18 less than that. Since each children's ticket saves $3 off the cost of an adult ticket, there were $18/$3 = 6 children's tickets.

There were 6 children in the group.

_____

If you want an equation, you can let c represent the number of children. Then the cost of tickets is ...

8(10 -c) +5c = 62 . . . . 10-c is the number of adults

-3c = -18 . . . . . . . subtract 80

c = -18/-3 = 6 . . . divide by 3

3 0

3 years ago