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dangina [55]
3 years ago
11

Ilya builds a slide that is 2.9 meters long. It is 1.5 meters above the ground. He wants to determine the distance from the bott

om of the slide to the base of the ladder leading up to the slide. Which diagram represents this situation?
WHICH TRIANGLE A,C, OR D
Mathematics
2 answers:
aalyn [17]3 years ago
6 0
The answer is the first diagram (light blue color in the choices) where 2.9m is the hypotenuse or the longest length. The height of the altitude is 1.5 meter and it is perpendicular from the ground level. The angle opposite to 2.9m is 90°.
masha68 [24]3 years ago
4 0

Answer:

Option A is correct.

triangle with light blue color

Step-by-step explanation:

As per the statement:

Ilya builds a slide that is 2.9 meters long.

⇒\text{Length of ladder} = 2.9 m

It is also given that 1.5 meters above the ground.

Since, this height is perpendicular from the ground level.

⇒\text{Vertical height from the ground level} = 1.5 m

As, he wants to determine the distance from the bottom of the slide to the base of the ladder leading up to the slide.

Therefore, the diagram in option A (with light blue color) represents the given situation as shown below in the attachment.

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Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and
zloy xaker [14]

Answer:

(0,0)   (4000,0) and (500,79)

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW

\frac{dW}{dt} = -0.02W + 0.00004RW

To solve this, we first equate \frac{dR}{dt} and \frac{dW}{dt} to 0.

So, we have:

0.09R(1 - 0.00025R) - 0.001RW = 0

-0.02W + 0.00004RW = 0

Factor out R in 0.09R(1 - 0.00025R) - 0.001RW = 0

R(0.09(1 - 0.00025R) - 0.001W) = 0

Split

R = 0   or 0.09(1 - 0.00025R) - 0.001W = 0

R = 0   or  0.09 - 2.25 * 10^{-5}R - 0.001W = 0

Factor out W in -0.02W + 0.00004RW = 0

W(-0.02 + 0.00004R) = 0

Split

W = 0 or -0.02 + 0.00004R = 0

Solve for R

-0.02 + 0.00004R = 0

0.00004R = 0.02

Make R the subject

R = \frac{0.02}{0.00004}

R = 500

When R = 500, we have:

0.09 - 2.25 * 10^{-5}R - 0.001W = 0

0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0

0.09 -0.01125 - 0.001W = 0

0.07875 - 0.001W = 0

Collect like terms

- 0.001W = -0.07875

Solve for W

W = \frac{-0.07875}{ - 0.001}

W = 78.75

W \approx 79

(R,W) \to (500,79)

When W = 0, we have:

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0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0

0.09 - 2.25 * 10^{-5}R = 0

Collect like terms

- 2.25 * 10^{-5}R = -0.09

Solve for R

R = \frac{-0.09}{- 2.25 * 10^{-5}}

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(R,W) \to (4000,0)

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(R,W) \to (0,0)

Hence, the points of equilibrium are:

(0,0)   (4000,0) and (500,79)

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