g A spotlight on the ground is shining on a wall 20m away. If a woman 2m tall walks from the spotlight toward the building at a speed of 0.8m/s, how fast is the length of her shadow on the building decreasing when she is 4m from the building
Answers
Answer:
0.3 m/s
Step-by-step explanation:
[tex]\dfrac{dx}{dt}=\text{Speed of person}=0.8\ \text{m/s}[/tex]
As the two triangles in the diagram are similar to each other we have
[tex]\dfrac{y}{12}=\dfrac{2}{8}\\\Rightarrow y=12\times \dfrac{2}{8}\\\Rightarrow y=3\ \text{m}[/tex]
Again as the triangles are similar we have
[tex]\dfrac{y}{2}=\dfrac{12}{12-x}\\\Rightarrow x=12-\dfrac{24}{y}[/tex]
Differentiating the above equation with respect to time we get
[tex]\dfrac{dx}{dt}=\dfrac{-24\times-1}{y^2}\dfrac{dy}{dt}\\\Rightarrow \dfrac{dy}{dt}=\dfrac{dx}{dt}\times\dfrac{y^2}{24}\\\Rightarrow \dfrac{dy}{dt}=0.8\times \dfrac{3^2}{24}\\\Rightarrow \dfrac{dy}{dt}=0.3\ \text{m/s}[/tex]
The speed at which the shadow is changing is 0.3 m/s.
Related Questions
Find the missing term 24:96=5:?
Answers
Answer:
24:96=5:x
Step-by-step explanation:
x=(96*5)/24=20
make it braintliest please
1. What percent of 60 is 15?
Answers
Answer:
25%
Step-by-step explanation:
Mental math approach: 15 is 1/4 of 60, and 1/4 is 25%. So, 15 is 25% of 60.
Answer:
25% or 1/4
Step-by-step explanation:
What is the domain of the function
f(x) = √ 1/3x + 2?
100 points to correct answer
Answers
hope this helps
also the underscore is supposed to go under the symbol
4. 44 + s + 65 = 180
Answers
Answer:s=71
Step-by-step explanation:44+65=109 109-180=71
The polynomial x2 + 3x – 1
is a factor of x2 + 2x2 – 5x - 6.
Please select the best answer from the choices provided
т
F
Answers
Answer:T
Step-by-step explanation:
College students are a major target for advertisements for credit cards. At a university, 65% of students surveyed said they had opened a new credit card account within the past year. If that percentage is accurate and you survey 100,000 college students in California, how many students would you expect to not have opened a new credit card account
Answers
Answer:
35,000 students did not open a new credit card account
Step-by-step explanation:
If 65% of students surveyed said they opened a new credit card account, the percentage of students that did not open a new credit card account is calculated as follows:
Total percentage = 100%
100% = 65% + (% of students that did not open a new account)
100 - 65 = % of students that did not open a new account
∴ % of students that did not open a new account = 100 - 65 = 35%
Next, let us convert this percentage to actual number
Total number of Students surveyed = 100,000
% of students that did not open a new account = 35%
35% of 100,000
= 35/100 × 100,000
= 0.35 × 100,000 = 35,000
what is 19% of 103?
Answers
Answer:
19.57Step-by-step explanation:
When you do 19% of 103
you get 19.57
Hope this helps! <3
Answer: 19% of 103 is 19.57
solve for n: 2m+7n=10
(also explain how you did it so i can follow the same steps for the rest of the questions)
Answers
Answer:
n=(10-2m)/7
Step-by-step explanation:
2m+7n=10
subtract 2m from both sides
7n= 10-2m
divide by 7 on both sides
n=(10-2m)/7
Which expression has a value that is greater than 43.537
Answers
Answer:
I need to c the expressions to answer
A color printer prints 19 pages in 10 minutes . how many pages does it print per minute
Answers
Answer:
Step-by-step explanation:
600
Answer:
1,9 per minute
Step-by-step explanation:
19 divided by 10
Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the height increases at a constant rate of 5 feet per minute, at what rate is the sand pouring from the chute when the pile is 10 feet high
Answers
Answer:
125π ft³/min
Step-by-step explanation:
Volume of a cone = 1/3πr²h
r is the radius
h is the height.
r = d/2
Volume = 1/3π(d/2)²h
Volume = 1/3π(d²/4)h
Volume = 1/3πd²h/4
Since the diameter is equal to height, hence d = h
V = 1/3πh³/4
V = 1/12πh³
dV/dt = dV/dh × dh/dt
Given
dh/dt = 5ft/min
dV/dh = 3/12πh²
dV/dh = πh²/4
Given h = 10ft
dV/dh = π(10)²/4
dV/dh = 25πft²
Next is to get dV/dt
dV/dt = 25π × 5
dV/dt = 125π ft³/min
Hence the rate at which the sand is pouring from the chute when the pile is 10 feet high is 125π ft³/min
What is the Equivalent expression in standard form: 3x + (2 - 4x)
Answers
It would become 3x+2-4x
Combine like terms 3x-4x=-x
The answer is -x+2
In a building construction project, the on-time completion of the building requires the successive completion of a series of activities. Define E = excavation completed on time; and P[E] = 0.8 F = foundation completed on time; and P[F] = 0.7 S = superstructure completed on time; and P[S] = 0.9 Assume statistical independence among these events.
Answers
Answer:
The probability of the completion of the project on time is 0.504.
Step-by-step explanation:
The question is:
Define the event C : (project completed on time) in terms of E, F and S. Compute the probability P(C) operations will not be on time in terms of E, F and S.
Solution:
The events are:
E = excavation completed on time; P [E] = 0.8
F = foundation completed on time; P [F] = 0.7
S = superstructure completed on time; P [S] = 0.9
The event C denotes the completion of the project on time.
Compute the probability of event C as follows:
P (C) = P (E ∩ F ∩ S)
= P (E) × P (F) × P (S)
= 0.8 × 0.7 × 0.9
= 0.504
Thus, the probability of the completion of the project on time is 0.504.
The telephone company offers two billing plans for local calls. Plan one charges $28 per month for unlimited calls and plan to charges $14 per month $0.04 per call.
Answers
Answer:
So I believe we're looking for the best long term plan
the first plan is staight forward so lets look at the secod one
14 + .04 times X
so if you make more than 350 calls (or more than 35o mins worth of calling time) you'll be charged more than the first plan due to 350 calls will equal 14 dollars with makes the bill 28 dollars which equals out the second and first plan
Spooky Story with figurative language, it needs to have what figurative language you used and the words, and the pov and the end
Answers
Answer:
THIS IS NOT MATHEMATICS!!!!!
Step-by-step explanation:
Please help me I need help
Answers
Answer:
what do you need help on???
Step-by-step explanation:
do you wanna know the alphabet ?
ABCDEFGHIJKLMNOPQRSTUVWXYZ
do u wanna know how to count to ten?
one , two ,three ,four ,five ,six ,seven ,eight ,nine,ten
Do u wanna know how to say hi in spanish?
Hola
Do u wanna know how old Beyonce is?
39
: If (26)x = 1, what is the value of x? Explain your answer.
Answers
Answer:
All you have to do is divide 1 by 26 and that should be the value of x.
Step-by-step explanation:
Can I just say that is a very strange math equation XD
The width of a rectangle is 15 inches less than three times it’s length. If the perimeter is 26 inches , what is the area of the rectangle
Answers
Length can be expressed as 2L + 2w = 26 since we know the total perimeter is 26 inches. Width can expressed as w = 3L - 15, since we know that it is 15 inches less than 3x the length. Then substitute the width into the length formula.
2L + 2w = 26
2L + 2(3L - 15) = 26
2L + 6L - 30 = 26
8L = 56
L = 56/8
L = 7 inches
Substitute 7 into the width formula to find width:
w = 3L - 15
w = 3 x 7 - 15
w = 6 inches
Finally use the area formula:
A = L x W
A = 7 x 6
A = 42 [tex]inches^{2}[/tex]
A triangle has side lengths of 2x, 4x, and 5x inches. If the perimeter of this triangle is 44 inches, what is the value of x?
Answers
Answer:
4
Step-by-step explanation:
2x+4x+5x=44
11x=44
x=11
Value of the given x is 4 units
Given that;
Sides of perimeter = 2x, 4x, 5x
Perimeter of triangle = 44 inches
Find:
Value of x
Computation:
Perimeter of triangle = Sum of all sides
44 = 2x + 4x + 5x
11x = 44
x = 4
Value of x = 4
Learn more:
https://brainly.com/question/9916945?referrer=searchResults
WILL GIVE 30 PIONTS AND A BRAINLY PLZ I NEED HELP
Answers
Answer:
1. 16 2. 8
Step-by-step explanation:
Answer:
The first one is 16 the other one is 8
Step-by-step explanation:
In partictual, you will never arrive at the truth.
what statement about the angles in this diagram is false
Answers
Answer:
i cannot see the statments
Step-by-step explanation:
Answer:
the statements aren't showing
Step-by-step explanation:
Write an equation in slope-intercept form for the line described.
Slope 4, y-intercept (0,-7)
Answers
Answer:
y=4x-7
Step-by-step explanation:
The y intercept is -7, the slope is 4
y=mx+b
m=slope b=y intercept
Answer:
y = 4x - 7
Step-by-step explanation:
y = mx + b
m is slope, which is 4
b is y-intercept, which is -7
can i get brainliest please?
Solve the equation.
(1/6)^x = 216
O (3)
O {-3)
O 1/3
O {-1/3)
Answers
The answer is the second choice
Jose bought 12 pounds of rice for $5. How many dollars did he pay per pound of rice.
Answers
Answer: $2 4cents
Step-by-step explanation: You divide 12 by 5 and that gives you 2.4. In money that 2 dollars and 4 cents
What is the reciprocal of 4 1/6
Answers
Answer:
0.24
Step-by-step explanation:
To find the reciprocal of a fraction, switch the numerator and the denominator the top and bottom of the fraction, respectively. So, simply speaking, the reciprocal of a/b is b/a. To find the reciprocal of a number, divide 1 by the number.
Please
Jacoby writes 1/12 page in 1/3 of a minute. How much time will it take Jacoby to write a full page?
Answers
Answer:
4 Minutes
Step-by-step explanation:
If 1/12th of a page is 1/3 of a minute, you have to ask what number do you multiply 1/12th by to equal 1?
12.
So then multiply both 1/12th and 1/3rd by 12. You get 12/12 and 12/3
12/12=1 page
12/3=4 minutes
So every 4 minutes he writes one page.
How many degrees is 15/16pi radians?
Answers
Answer:
192 °
Step-by-step explanation:
Hope this helped! <3
Answer:
168.75°
Step-by-step explanation:
I think
A fair coin is tossed three times. Let X be the number of heads in thetosses minus the number of tails. Find the probability distribution of X.
Answers
Answer:
P(3) = 1/8
P(1) = 3/8
P(-1) = 3/8
P(-3) = 1/8
Step-by-step explanation:
Given that :
Coin is tossed 3 times :
Kindly check attached picture for detailed explanation
x - 2y = -2
3х -6y = 30
Answers
Answer:
EEEEEEEEEEEEEEE
(ノಠ益ಠ)ノ彡┻━┻
An automobile manufacturer has four different subcompact cars on the line. Customers selecting one of these cars have a choice of three engine sizes, three body styles, and seven color schemes. How many different selections can a customer make
Answers
Answer:
The customer can make 42 different selections
Step-by-step explanation:
Here, we want to know the different selections a customer can make
A customer can request 1 engine size, 1 body style and 1 colour scheme from the available set for his car
Out of 3 engine sizes , he will select 1; that will be 3 C 1
Out of 3 body styles, he will select 1, that will be 3 C 1
Out of 7 color schemes, he will select one and that is 7 C 1
So the number of different selections will be;
3 C 1 * 3 C 1 * 7 C 1
= 3 * 3 * 7 = 42 different selections
