Answers
Refer to the diagram below. We have the following points
A = base of the streetlampB = base of the personC = tip of the person's shadowD = top of the streetlampE = head of the personThe shadow extends from point B to point C. If we let x be the the horizontal distance from the lamp to the person, then dx/dt represents the speed at which the person is walking away from the lamp. In this case, dx/dt = 4 feet per second.
Let y be the length of the shadow. We can use similar triangles and proportions to help find what y is equal to in terms of x
AD/BE = AC/BC
15/6 = (x+y)/y
15y = 6(x+y)
15y = 6x+6y
15y-6y = 6x
9y = 6x
y = 6x/9
y = 2x/3
y = (2/3)*x
The length of the shadow is 2/3 that of the distance from the person to the lamp.
Now apply the derivative to both sides to compute dy/dt, which represents how fast the shadow is changing.
y = (2/3)x
dy/dt = d/dt[ (2/3)x ]
dy/dt = (2/3)*d/dt[ x ]
dy/dt = (2/3)*dx/dt
dy/dt = (2/3)*4
dy/dt = 2.667
The rate in which the shadow is lengthening is approximately 2.667 ft per second.
Related Questions
The Brazos River is the longest river in Texas with a length of 1, 352 km. The elevation of the source is 453 m above sea level, and the mouth is the Gulf of Mexico, with an elevation of m above sea levelAt what angle does the Brazos River flow, on average , in degrees ? (Round to the nearest hundredth .)
Answers
Answer:
0.02degrees
Step-by-step explanation:
Given the following
Length of the river (adjacent) = 1352km = 1352000m
Height of the source (opposite) = 453m
Required
angle of elevation theta
Using the SOH CAH TOA identity
tan theta = opposite/adjacent
tan theta = 453/1352000
tan theta = 0.0003351
theta = arctan(0.0003351)
theta = 0.02 degrees
Hence the Brazos river flows at an angle of 0.02degrees to the nearest hundredth
Lily makes regular deposits to a savings account to save
money for retirement. She deposits $1000 to the account
and didn't add any additional money. The account offers
compound interest annually at a rate of 4%. How much
money does Lily have in her account in 2 years?
Step 1:
What is the Pr?
Pis ris
A=P(1+
tis
Step 2
Totalmolol is
(final answer)
1% 1+100
1/100
4% 4 +100 4100
92 9 +1000/100
1102.4
1081.6
O 1020.8
O 1108.6
Answers
Answer:
Step-by-step explanation:
jus needed the points lolz
The prism below is packed with no gaps between the cube that measure 1/4 ft. What is the volume, in cubic feet of the right rectangular prism?
Answers
Answer: 1/2
First you do 4/4 times 4/4. Which is equal to 1. Then, you multiply by 2/4 to get 1/2.
Which of the statements below are true? Select all that apply. A) The table shows a proportional relationship B) The table does not show a proportional relationship C) With $3.00, you could buy 10 bananas D) Each banana costs $0.30
Answers
Answer:
go to school, do your work, you are only cheating yourself, not the school, or end up homeless
Step-by-step explanation:
I would appreciate it if someone could help answer this problem:)
Answers
Answer:
[tex]x=85^{\circ}[/tex]
Step-by-step explanation:
The sum of the interior angles of any polygon with five sides is equal to [tex](5-2)\cdot 180=3\cdot 180=540^{\circ}[/tex]. Therefore, we can set up the following equation and solve for [tex]x[/tex]:
[tex]115+95+115+130+x=540,\\455+x=540,\\x=\boxed{85^{\circ}}[/tex]
If a conversion rate of 8 dollars is worth 13 euros, how many euros do you get
when you convert 500 dollars?
Answers
8/13 =500/x
(Cross multiply)
8x= 6,500
(Divide by 8 to isolate the variable)
x= 812.5
(Euros are paper money, not a coin system and they won’t give you more money than what you gave them so you must round down to the nearest whole number which is 812 Euros)
ANSWER:
812 Euros
look at pic will mark brainilest
Answers
Answer:The first one 18in.2
Step-by-step explanation:
A rectangular tank measuring 35 cm by 28 cm by 16 cm is 2/5 filled with
water. The water is poured into an empty cubical tank of edge 18 cm until
it is full. How much water is left in the rectangular tank? Give your answer
in millilitres.
Answers
Answer:
Amount of water left in tank = 440 cm³
Step-by-step explanation:
Given:
Sides of tank respectively = 35 cm , 28 cm , 16 cm
Water level in tank = 2/5
Side of a cubic tank = 18 cm
Find:
Amount of water left in tank
Computation:
Volume level in rectangular tank = [2/5][35 x 28 x 16]
Volume level in rectangular tank = [2/5][15,680]
Volume level in rectangular tank = [31,360/5]
Volume level in rectangular tank = 6,272 cm³
Volume of cube = side³
Volume of cube = 18³
Volume of cube = 5,832 cm³
Amount of water left in tank = Volume level in rectangular tank - Volume of cube
Amount of water left in tank = 6,272 - 5,832
Amount of water left in tank = 440 cm³
you're having a bbq this weekend, and you're in charge of hamburger meat. right now there is a sale where you can buy 5 pounds of meat for $10. At this rate how much meat could you buy for $30
Answers
Answer:
15 pounds
Step-by-step explanation:
we can set up a proportion:
5/10=x/30
solve for x:
5/10=x/30
10x=150
x=15
(or you could've done 5*3=15 since $30/$10=3)
Which type of graph would be best for showing the average yearly bonus amounts for employees in different departments of an IT company?
A. a bar graph
B. a circle graph
C. a histogram
D. a line graph
Answers
(if it’s not then sorry)
Answer:
A
Step-by-step explanation:
It was the correct answer when I submitted my assignment. A histogram is best for continuous data thats why a bar graph is best.
Here is my question it is worth 15 points!
Answers
Answer:
What is your question????
Answer:
you don't have a question here tho
Step-by-step explanation:
Dr. Gavin is conducting a 2 x 4 independent-groups factorial design. Assuming he wants 25 people in each cell, how many participants does Dr. Gavin need to recruit
Answers
Answer:
Dr. Gavin needs to recruit 200 participants.
Step-by-step explanation:
Dr. Gavin is conducting a 2 x 4 independent-groups factorial design.
This means that there will be 2*4 = 8 cells.
Assuming he wants 25 people in each cell, how many participants does Dr. Gavin need to recruit?
25 people in each cell, 8 cells. So
25*8 = 200
Dr. Gavin needs to recruit 200 participants.
Question 8
8. Ray is making face masks and needs to
purchase elastic cord. He needs 10.25 cm
elastic cord for each face mask. He orders 20
m of elastic cord. If he doesn't want any of
the cord to be wasted, what is the least
amount of extra cord that he would need to
add to his order of 20 m?
A.
B.
9 cm
10.25 cm
C.
D.
20.09 m
20.9 m
Answers
9514 1404 393
Answer:
B. 9 cm
Step-by-step explanation:
The number of face masks Ray can make with 20 m of cord is ...
(20 m)(100 cm/m)/(10.25 cm/mask) = 195.12195 masks
To make one more mask, he will need to buy an additional amount of ...
(196 -195.12195)×(10.25 cm) ≈ 9.00 cm
Ray would need to add 9 cm of cord to his order.
Make r the subject of x= e + r/d
Answers
Step-by-step explanation:
X=e+r/d
swap both sides
e+r/d=x
subtract e from both sides
e-e+r/d=x-e
r/d=x-e
multiply d to both sides
d×r/d=x-e×d
r=x-e×d
For each of the following variables, identify the type of variable (categorical vs. numerical).
(I) Fuel economy (miles per gallon) of used car
(II) Number of auto insurance claims in a month
1) (I) Categorical , and (II) Categorical
2) (I) Categorical , and (II) Numeric
3) (I) Numeric , and (II) Numeric
4) There is no correct match.
5) (I) Numeric , and (II) Categorical
Answers
Answer:
3) (I) Numeric , and (II) Numeric
Step-by-step explanation:
Numeric variable:
The variable assume number values.
Categorical values:
The variable assumes labels. Examples are yes/no, good/bad.
(I) Fuel economy (miles per gallon) of used car
(II) Number of auto insurance claims in a month
Both of these variables are numbers, none have labels, so they are both numeric. The correct answer is given by option 3).
Solve for
X/11=10/12
Give your answer as an improper
fraction in its simplest form.
Answers
12x = (10)(11)
12x=110
x=110÷12
x=55/6
Hey May I Ask Whats The Rule Of This Number
Answers
Answer:
add 4x1, then 4x2, then 4x4, then 4x8, etc
Step-by-step explanation:
4 + (m -n )^4 when m =7 and n = 5 whats the value ?
Answers
Answer:
20
Step-by-step explanation:
We plug m and n into the expression because we know that it is. Therefore, the expression is 4+ (7-5)^4. Simplify this to get 4+(2)^4. 2^4 is equal to 2x2x2x2 which is equal to 4x4 which is equal to 16. Therefore, 2^4 is 16. 4+16 is equal to 20. Therefore, the answer is 20.
If this has helped please mark as brainliest
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{Equation:}[/tex]
[tex]\mathsf{4 + (m - n )^4}[/tex]
[tex]\large\textsf{Solving:}[/tex]
[tex]\mathsf{4 + (m - n )^4}[/tex]
[tex]\mathsf{\mathsf{= 4 + (7 - 5)^4}}[/tex]
[tex]\mathsf{= 4 + (2)^4}[/tex]
[tex]\mathsf{= 4 + (2\times2\times2\times2)}[/tex]
[tex]\mathsf{= 4 + 2\times2\times2\times2}[/tex]
[tex]\mathsf{= 4 + 4\times 4}[/tex]
[tex]\mathsf{= 4 + 16}[/tex]
[tex]\mathsf{= 20}[/tex]
[tex]\large\textsf{Therefore, your answer should be:}[/tex]
[tex]\large\boxed{\frak{20}}\large\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
If somebody keeps on trying to take something from you and u tell them to quit or youll punch them should u actually do it? first gets brainliest
Answers
Answer:
yes
Step-by-step explanation:
Oak Street and Elm Street run parallel to each other. When Main Street
intersects them, it forms exterior 28, measuring 60°. What is the-
measure of
22?
Answers
Answer:
100degrees
Step-by-step explanation:
From the given diagram;
<2 = <6 (corresponding angle)
Since <6 + 80 = 180
<6 = 180 - 80
<6 = 100 degrees
Since <2 = <6, hence <2 = 100degrees
Find the measure of angle A
Pls help
Answers
Step-by-step explanation:
x+85+x+44+63=180(sum of angles of a triangle)
or,2x+192=180
or,2x=180-192
or,x=-12
Angle A=x+44
=-12+44
=32°
Give brainliest plse .
A piece of aluminum that is 20 cm³ has a mass of 54 g.
a. What is the density of the aluminum?
Answers
Help plzzzzz fast and no links
Answers
Answer:
x=60
Step-by-step explanation:
I am going to try to explain this to the best of my abilities, but if you dont understand please let me know and I'll clarify. There is a straight ine tha that equals 180, so you do 180-120=60
What is the distances between (3, 10) and (3, -8)
Answers
Answer:
(0,-12)
Step-by-step explanation:
is this what your looking for? what form would you like me to answer this in?
Evaluate 4 ÷ 3/5 Give your answer as a mixed number in its simplest form.
Answers
9514 1404 393
Answer:
6 2/3
Step-by-step explanation:
4/(3/5) = (4/1)×(5/3) = 20/3 = 6 2/3
what 8 × 3 to the 14th power multiplied by 136???
[tex]23x {5521}^{?} [/tex]
Answers
om de har har mahadev har har mahadev har har mahadev mahadev har har mahadev
5,203,870,272
Step-by-step explanation:
8×3^14×136
=(8)(4782969)(136)
=(38263752)(136)
=5,203,870,272
i think this is the answer
Find the length of side x in simplest radical form with a rational denominator
60°
3
30
X
Answers
Answer: 5/2
Explanation:
According to 30-60-90 triangle rule:
The side opposite of 30 degree is equal to half of the hypotenuse and the hypotenuse here is 5 so therefore x = 5/2
A turtle can walk 2/24 of a kilometer in an hour. The turtie is 2/10 of a kilometer away
from a pond. At this speed, how long will it take the turtle to reach the pond?
2 2/5hours
1 3/5hours
2 hours
3 1/5hours
Answers
what is the absolute value of the complex number −4−i 2√?
Answers
Answer:
-4-i2
The absolute value is the Square root of the real and Imaginary Parts of the Complex No
= √(-4)²+(-2)²
=√16+4
=√20
=2√5
Find cotθ if θ terminates in Quadrant III and secθ = 2
a. - (sqrt 3)/3
b. (sqrt 3)/3
c. - sqrt 3
d. sqrt 3
Answers
Answer:
we have
secθ = 2
[tex] \frac{1}{cos θ} [/tex]=2
Cosθ =[tex] \frac{1}{2 }[/tex]
[tex] \frac{b}{h }=\frac{1}{2 }[/tex]
b=1
h=2
p=[tex] \sqrt{2²-1} = \sqrt{3} [/tex]
again
Cot θ=[tex] \frac{b}{p }[/tex]
Cot θ=[tex] \frac{1}{ \sqrt{3}} [/tex]
Cot θ=[tex] \frac{\sqrt{3}}{3} [/tex]
It lies in Quadrant III cot is positive
Cot θ=[tex] \frac{\sqrt{3}}{3} [/tex]
b. (sqrt 3)/3