A person 6ft tall stands 10ft from point P directly beneath a lantern hanging 30 ft above the ground. The lantern start to fall, thus causing the person shadow to lengthen(L). Given that the lantern falls 16t2 feet in t seconds, how fast will the shadow be lengthening when t=1
Answers
Answer:
[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]
Step-by-step explanation:
In order to solve this it is always a good idea to start by drawing a diagram of the situation (See attached picture).
From the diagram we can see that we are dealing with similar triangles. We can use similar triangles to build an equation that relates the length of the shadow with the height of the lamp, so we get:
[tex]\frac{L}{6}=\frac{10+L}{h}[/tex]
the height of the lamp can be found by subtracting the [tex]16t^{2}[/tex] distance the lamp falls in a given time t from the original 30ft the lamp was located at.
So the equation will now lok like this:
[tex]\frac{L}{6}=\frac{10+L}{30-16t^{2}}[/tex]
So now we can solve the equation for L, we can start by multiplying by the LCD SO WE GET:
[tex]L(30-16t^{2})=6(10+L)[/tex]
next, we can distribute the right side of the equation so we get:
[tex]L(30-16t^{2})=60+6L[/tex]
and subtract 6L from both sides so we get:
[tex]L(30-16t^{2})-6L=60[/tex]
and factor L, so we get:
[tex]L(30-16t^{2}-6)=60[/tex]
and solve for L:
[tex]L=\frac{60}{24-16t^{2}}[/tex]
now, we can differentiate this equation by using the chain rule, so we get:
[tex]dL=-\frac{60}{(24-16t^{2})^{2}}(-32t)dt[/tex]
which can be simplified to:
[tex]\frac{dL}{dt}=\frac{1920t}{(24-16t^{2})^{2}}[/tex]
and now we can substitute t for 1s so we get:
[tex]\frac{dL}{dt}=\frac{1920(1)}{(24-16(1)^{2})^{2}}[/tex]
[tex]\frac{dL}{dt}=30 \frac{ft}{s}[/tex]
Related Questions
The common end point of an angle
Answers
The common endpoint is called the vertex of the angle, and the rays are called the sides of the angle.
hope this helped
given the grph of the function F(x) below, what happens to F(x) when x is a negative number with a large absolute value?
Answers
Answer:
F(x) is a large positive value
Step-by-step explanation:
If it is a negative number with a large absolute value say |-250| it would become positive 250 so f(x) would also be a large positive number
What is the probability of getting a 3 or 7 when drawing a single card from a deck of 52
Answers
Answer:
1/52
Step-by-step explanation:
There are 52 cards you can draw from, 3 is one of them. 7 is another possibility.
Justin needs to make 80 illustrations for an art book. He has made 40% of the illustrations. How many illustrations does he still need to make?
Answers
We can do this by doing 40 divided by 100 which gives us: 0.40
Therefore 40% in decimal form is 0.40.
Next we do 80 x 0.40 which gives us 32, this means Justin has already made 32 illustrations.
Next we do 80 - 32 which gives us 48, this means Justin still has to do 48 illustrations.
I hope this helps!
32 - 80= 48
Answer:48
A student earned a grade of 80% on a math test that had 20 problems. How many problems on this test did the student answer correctly? (round to the nearest whole number)
(Please answer with explination)
Answers
Answer:
Required Answer:-A student earned 80% in a math test which has 20 problems.It means The student answers 80% of 20 problems correctly[tex]\longrightarrow[/tex][tex]\sf 80\%\:of\:20 [/tex]
[tex]\longrightarrow[/tex][tex]\sf {\dfrac{80}{{\cancel{100}}}}\times {\cancel{20}} [/tex]
[tex]\longrightarrow[/tex][tex]\sf {\dfrac {80}{5}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf 16 [/tex]
[tex]\therefore[/tex] The student answered 16 problems correctly
Answer it for Brainliest *URGENT*
Answers
Answer:
Step-by-step explanation:
A = π r²
A = 11²π - 3²π = ( 121 - 9 ) π = 112 π ≈ 112 × [tex]\frac{22}{7}[/tex] = 352 cm²
( 112 × 3.14 = 351.68 cm²)
(-73d4)(4cd3)
answer
Answers
192cd2 is your answer the end 2 should be squared sorry
Answer:
-292d^7c
Step-by-step explanation:
Find the value of 2a2 + 5b2 when a = -6 and b = 2
Answers
Answer:
92
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
2a² + 5b²
a = -6
b = 2
Step 2: Evaluate
Substitute: 2(-6)² + 5(2)²Exponents: 2(36) + 5(4)Multiply: 72 + 20Add: 9275/6 hasta que el residuo sea cero
Answers
75/6 no puede tener un resto de cero ya que 6 solo entra en 7 12 veces con el resto de 3
two students have examined the scatter plot shown in have created in line best fit for the data. student A believes that the line of best fit for the data is y= -2x + 24, while student B believes that the line of best fit for the data is y = 1.5 + 23
*Determine which student created a better line of best fit given the data in the graph.
Answers
Answer:
Step-by-step explanation:
im pretty sure its student a not 100% sure tho
The line of best fit is simply the trending line of a graph
Student A creates a better line of best fit
The linear equations are given as:
[tex]\mathbf{y = -2x + 24}[/tex]
[tex]\mathbf{y =1.5x + 23}[/tex]
The given graph shows a negative linear association.
This is so because, as the x-values increases, the y-values decreases.
This in other words means that:
The slope of the graph is negative
A linear graph is represented as:
[tex]\mathbf{y = mx + c}[/tex]
Where: m represents slope
By comparison
m = -2 and m = 1.5 for the equations of the two students.
Because the slope of the graph is negative, then
m =-2 is correct
Hence, student A creates a better line of best fit
Read more about lines of best fit at:
https://brainly.com/question/14279419
just trying to get this done to get some sleep, thank you!!
Answers
A computer monitor is packaged in a cube-shaped box with an inside edge length of 2.5 feet.What is the volume of the box?
Answers
Answer:
odlxksms
Step-by-step explanation:
skzkxjkdidok
125 centimeters to 87.5 cenitimeters
Answers
Answer:
30
%
d
e
c
r
e
a
s
e
Step-by-step explanation:
Consider that a population of fruit flies grew in a 40-day experiment. Average rate of change: 9 flies/day. Find the average growth rate from day 30 to day05
Answers
Answer: Average Growth Rate is 24.19%
Step-by-step explanation:
Given that;
Average rate of change = 9 flies/day
Average growth rate of change = ?
we can determine the average growth rate of change from the expression;
Average Annual Growth Rate = [((Present Value - Past Value)^1/N) - 1 ] × 100%]
Now our present value; 30th day = 9 × 30 = 270
past value; 05th day = 9 × 05 = 45
the value of N = 30 - 5 = 25
so we substitute
Average Annual Growth Rate = [((270 - 45)^1/25) - 1 ] × 100%]
= ([1.2419 - 1) × 100]
= 24.19%
Therefore Average Growth Rate is 24.19%
Rachel has $1.32 in pennies and nickels. She has twice as many nickels as pennies. How many nickels does she have?
Answers
Answer:
wwwww
ww
Step-by-step explanation:
ww
just occupying space up hear !
and the question is
simplify;
2+3√2!
Answers
Is this relation a function? Justify your answer.
10
9
8
7
6
5
4
.
3
2.
1
1
2
3
4
5
6
7
8
9 10
A. No, because two points with the same y-value have different x-
values.
B. No, because two points with the same x-value have different y-
values.
C. Yes, because every x- and y-value is positive.
D. Yes, because the number of x-values is the same as the number of
y-values
Answers
Answer:
D for every input there is one output
5 3/9 - 2 8/9 simplified
Answers
Answer:
2 4/9
Step-by-step explanation:
Replacing the maximum value of the data set with a smaller number will also affect the mean. A:always B:sometimes C:never
Answers
Answer:
B: sometimes
Step-by-step explanation:
Let's look at two examples.
Example A.
2, 3, 5: mean is 3
Replace 5 with 1. Now you have 1, 2, 3: mean is 2.
In this case, it affected the mean.
Example B.
2, 3, 5: mean is 3
Replace 5 with 4. Now you have 2, 3, 4: mean is 3.
In this case, it did not affect the mean.
As you can see, replacing the maximum value of the data set with a smaller number may or may not change the mean.
Answer: B: sometimes
What is the solution to the system of equations below?
4x - 2y = -4
8x - 4y = 4
Answers
which integer is the smallest?
A: 0
B: 29
C: -30
D: -1
Answers
Answer:
-30
Step-by-step explanation:
0 is greater the -30 and -1 but less then 29
29 is greater then 0, -30, and -1
-1 is less the 0 and 29 but greater then -30
-30 is less then 0, 29, and -1
from greatest to smallest
29, 0, -1, -30
-30 is the smallest integer
PLS HELP MEH!!!
Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today. Write and solve an inequality to solve for the least amount of money she needs to deposit to avoid a fee. (2 points)
A. 524.96 − 32.50 + x ≥ 500; x ≥ $7.54
B. 524.96 − 32.50 + x ≤ 500; x ≤ $7.54
C. 524.96 + 32.50 − x ≥ 500; x ≥ $57.46
D. 524.96 + 32.50 − x ≤ 500; x ≤ $57.46
Answers
Answer:
im sure its B
Step-by-step explanation:
524.96 - 32.5 = 492.46 500 is greater
You sell 200 laptops per month at $499 per laptop. You sell 350 smartphones per month at $399 per phone. Which
generates more sales in dollars for you?
a) Laptops
b) Smartphones
Answers
Answer:
B) Smartphones
Step-by-step explanation:
In order to answer this question we need to find the total revenue for the laptops and smartphones.
Let's start with the laptops.
Given:
200 laptops/month$499 per laptopTo find the total revenue of all these laptops we need to multiply 200 by 499.
[tex](200) *(499) = 99,800[/tex]
Therefore, the total revenue of the laptops alone is $99,800.
Now, let's do the smartphones.
Given:
350 smartphones/month$399 per smartphoneTo find the total revenue of all these smartphones we need to multiply 350 by 399.
[tex](350) * (399) = 139,650[/tex]
Therefore, the total revenue of the smartphones alone is $139,650.
Comparing the two revenues we see that the smartphones generate more sales in dollars.
Hope this helps!
- Kay
What is the range?
5 7 10 7 3 10 9 1 1 6
Answers
Answer:
9
Step-by-step explanation:
10-1=9 thats how you find the range you do the highest number then the lowest number after that you subtract it
You can find range by subtracting the lowest number from the highest number.
10-1=9
Hope this helps ✨❤️
1. Determine the number of combinations of the letters of the word EXAMINATION given that
four letters are taken at a time.
(5marks)
Answers
Answer:
210
Step-by-step explanation:
10 choose 4. 10 letters choose 4. Using the combination formula. C(n,r)
Choose the behaviors that are IF YOU HELP ME IN LESS THATN 2MINS I WILL GIVE YOU BRAINLY MASTER THING!!!exhibited by someone who is using critical thinking.
Questions ideas and beliefs
Assesses information gathered
Gathers relevant information
Tests conclusions against reasonable criteria
Thinks along a narrow track
Jumps to conclusions
Answers
Answer: what do you need
Step-by-step explanation:
How many 2 letter permutations can be made from the word "letter"
Answers
Answer:
Brainliest for Brainliest
Step-by-step explanation:
Mr. Li's bulletin board has area 25 square feet and it is 8 feet long.
What is the width of the bulletin board?
Answers
25 sq feet = 8W
25/8 = width
Width = 3.12 feet
Answer:
3.125
Step-by-step explanation:
Well first you would take 25 and divide it by 8. Once divided you con know what the width is of the bulletin board.
There exists a similarity transformation that maps AABC to AA'B'C'. The measure
of ZAis 68°, and the measure of ZBis 46°. What is the measure of ZC'in
degrees?
Answers
Answer:
∠C' = 66°
Step-by-step explanation:
Because triangles ABC and A'B'C' are similar, their angles are still the same; only their side lengths are different, though still proportionate.
Hence, ∠A = ∠A', ∠B = ∠B', and ∠C = ∠C'.
Here, we're given that ∠A = 68, which means ∠A' = 68; we also know that ∠B = 46, so ∠B' = 46.
We want to find C', so remember that all angles in a triangle sum to 180:
∠A' + ∠B' + ∠C' = 180
68 + 46 + ∠C' = 180
114 + ∠C' = 180
∠C' = 66°
Answer:
∠C' = 66°
Step-by-step explanation:
∠A' + ∠B' + ∠C' = 180
68 + 46 + ∠C' = 180
114 + ∠C' = 180
∠C' = 66°
If 25 is added to 5 times a certain number, the result is 7 times the number minus 35. Find the number.
Answers
Step-by-step explanation:
Required Answer:-Let the certain number =x
According to the question
[tex]{:}\longrightarrow[/tex][tex]\sf 5x+25=7x-35 [/tex]
Simplify[tex]{:}\longrightarrow[/tex][tex]\sf 7x-35=5x+25 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 7x-5x=25+35 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2x=60 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {60}{2}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=30 [/tex]
[tex]\therefore[/tex]The number is 30.