g A person who is 6 feet tall is walking away from a lamp post at the rate of 40 feet per minute. When the person is 10 feet from the lamp post, his shadow is 20 feet long. Find the rate at which the length of the shadow is increasing when he is 30 feet from the lamp post.
Answers
Answer:
80 ft/min
Step-by-step explanation:
Let h represent the height of the person shadow, x represent the distance between the person and the lamppost, y represent the length of the man shadow.
Therefore:
[tex]\frac{h}{x+y} =\frac{6}{y} \\\\substituting\ x=10,y=20:\\\\\frac{h}{10+20} =\frac{6}{20}\\\\\frac{h}{30} =\frac{6}{20}\\\\h=30*6/20\\\\h=9\ feet\\\\Therefore:\\\frac{h}{x+y} =\frac{6}{y}\\\\\frac{9}{x+y} =\frac{6}{y}\\\\9y=6x+6y\\\\9y-6y=6x\\\\3y=6x\\\\y=2x\\\\The\ person\ is\ walking\ from\ the\ lamppost\ at\ 40ft/min(\frac{dx}{dt}=40\ ft/min) \\\\y=2x\\\\Differentiating\ with\ respect\ to\ t:\\\\\frac{dy}{dt} =\frac{d}{dt}(2x)\\\\\frac{dy}{dt} =2\frac{dx}{dt}\\\\[/tex]
[tex]\frac{dy}{dt} =2(40\ ft/min)\\\\\frac{dy}{dt}=80\ ft/min[/tex]
The rate at which the length of the shadow is increasing when he is 30 feet away from the lamp post is 80 [tex]\frac{ft}{min}[/tex].
The height of the person shadow is to be = h
Given ,
The distance between the person and the man = x = 10
The length of the man shadow is = y = 20
By the similar triangle property corresponding sides of similar triangles are in the same ratio.
[tex]\frac{h}{x+y} = \frac{6}{y}[/tex]
[tex]\frac{h}{10+20} = \frac{6}{20}[/tex]
20h = 60 + 120
20h = 180
h = [tex]\frac{180}{20}[/tex]
h = 9feet
Therefore,
[tex]\frac{h}{x+y} = \frac{6}{y} \\\frac{9}{x+y} = \frac{6}{y} \\[/tex]
9y= 6x + 6y
9y-6y = 6x
6x = 3y
y = [tex]\frac{6}{3}x[/tex]
y = 2x
Differentiating both the sides with respect t,
[tex]\frac{dy}{dt} = 2\frac{dx}{dt}[/tex]
we know that ;
[tex]\frac{dx}{dt} = 40 \frac{ft}{sec}[/tex]
Therefore, by substitute the value
[tex]\frac{dy}{dt} = 2 . 40\frac{ft}{min}[/tex]
[tex]\frac{dy}{dt}[/tex] = 80[tex]\frac{ft}{min}[/tex].
The rate at which the length of the shadow is increasing is 80[tex]\frac{ft}{min}[/tex] .
For more details about the Rate change problem click the link given below.
https://brainly.com/question/20414862
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Step-by-step explanation:
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A major airline knows that about 2 percent of passengers do not manage to show up for their flight. Consider a small aircraft having 50 seats, and suppose that an airline sells precisely 50 tickets for a specific flight. Assuming that all passsengers are independent and have the same probability of not showing up, compute the probability that
Answers
Answer:
a. The probability that the aircraft is fully occupied = 0.3642
b. The probability that between 1 and 5 (including 1 and 5) passengers do not show up is = 0.6354
Step-by-step explanation:
From the given information:
We are to compute the probability that:
a. The aircraft is fully occupied( i.e. all the passengers show up)
b. Between 1 and 5 (including 1 and 5) passengers do not show up
Given that:
Percentage of passengers that do not show up = 2% = 0.02
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= 0.3642
Hence, The probability that the aircraft is fully occupied = 0.3642
b. The probability that between 1 and 5 (including 1 and 5) passengers do not show up is:
= P(X = 1) + P(X =2) + P(X = 3) + P(X = 4) + P(X = 5)
= [tex]=(^{50}_1) 0.02(1-0.02)^{50-1} +(^{50}_2) 0.02(1-0.02)^{50-2} + (^{50}_3) 0.02(1-0.02)^{50-3} + ... + (^{50}_5) 0.02(1-0.02)^{50-5}[/tex]
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
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Answers
Answer: 2/4
Step-by-step explanation:
Rise=2
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Rise/Run(2/4)
Answer:
slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
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m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]
Find the surface area and volume. show your work.
Answers
9514 1404 393
Answer:
area = 211 +7√205 ≈ 311.22 square unitsvolume = 273 cubic unitsStep-by-step explanation:
Surface area
The length of the hypotenuse of the front facing triangle is given by the Pythagorean theorem:
d^2 = 13^2 +6^2 = 169 +36 = 205
d = √205
So, the perimeter of that triangle is ...
P = 13 +6 +√205 = 19 +√205
The total area of the rectangular faces of this triangular prism is then ...
rectangular face area = (base perimeter)·(prism height)
= (19 +√205)(7) = 133 +7√205
The area of the two triangular faces will be ...
triangular face total area = 2·(triangle area) = 2(1/2)(6)(13) = 78
Then the total surface area is ...
total surface area = rectangular face area + triangular face total area
total surface area = (133 +7√205) +78
surface area = 211 +7√205 ≈ 311.22 . . . . square units
__
Volume
The volume is the product of the area of the triangular base and the height of the prism.
V = Bh
V = (39)(7)
volume = 273 . . . . cubic units
Decide whether a line with the given slope m=7/6 slants upward or downward from left to right, or whether its horizontal or vertical
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Answers
Answer:
60
Step-by-step explanation:
4*15=60=12*5
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Answers
Answer:
1st box: -1/2
2nd box: 2/1 or just 2
Step-by-step explanation:
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2nd box: perpendicular slopes are the negative reciprocal of the original
