Answer:
(
,
) = (30, 16)
Step-by-step explanation:
First find the similarity
Since you know the legnth of the hypotenuse (the longest one) for both traingles, you can find the similarity by dividing the longer by the shorter:
50 ÷ 20 = 2.5
The similarity between the 2 triangles is 2.5.
Now find the length of
on the longer one, use the shorter one's length and the similarity:
12 × 2.5 = 30
So the length of
is equal to 30
Now lets find
, lets use the length of the larger triangle this time and divide the length of the longer leg (there are 2 legs in every triangle, if you don't know the hypotenus's length, use the pythagorean theorem) and divide it by the similarity:
40 ÷ 2.5 = 16
= 16
WooHoo! (
,
) = (30, 16)
25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.
<h3>How fast is the tip of his shadow moving?</h3>
Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.
Then y - x will be the length between the man and the tip of the shadow.
Since two triangles are similar, we can write
![\frac{y-x}{y} =\frac{6}{15}](https://tex.z-dn.net/?f=%5Cfrac%7By-x%7D%7By%7D%20%3D%5Cfrac%7B6%7D%7B15%7D)
⇒15(y-x) = 6y
15 y - 15 x = 6y
9y = 15x
y = 15/9 x
y = 5/3 x
Differentiate both sides
dy/dt = 5/3 dx/dt
dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.
Given that dx/dt = 5 ft/s
Thus dy/dt = (5/3)×5 ft/s
dy/dt = 25/3 ft/s
Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.
Learn more about similar triangles here:
brainly.com/question/8691470
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Answer:
donor task is a tax on a donation or gift
Step-by-step explanation:
Like giving something to someone
Answer:
$14.12 (after 3 years) and $24.62 (after 5 years)
Step-by-step explanation:
Use the compound amount formula (assuming annual compounding):
A = P(1 + r)^t
Here A = $100(1 + 0.045)^3 (after 3 years)
= $100(1.045)^3 = $114.12.
The interest earned (alone) would be $14.12.
After 5 years:
Here A = $100(1 + 0.045)^5 (after 5 years)
= $100(1.045)^5 = $124.62
The interest earned (alone) would be $24.62.
The bottom layer of a decision tree provides information on: D. How all the connected factors lead to a final decision or outcome.
<h3>What is a decision tree?</h3>
A decision tree can be defined as a tree-like model that is used by mathematicians (statisticians) or researchers as a decision support tool, so as to graphically display decisions with respect to their potential outcomes, consequences, utility and resource costs.
This ultimately implies that, it is used for making decisions in business management or computer programming by graphically displaying all the possible (expected) outcome of a decision in layers.
In conclusion, the bottom layer of a decision tree provides information on how all the connected factors lead to a final decision or expected outcome.
Read more on decision tree here: brainly.com/question/26675617