Calculus Application
2. A ladder 20 feet long leans a vertical building. If the bottom of the ladder slides away from the building
horizontally at a rate of 2 ft/sec, how fast is the ladder sliding down the building when the top of the
ladder is 12 feet above the ground?
Answers
-8/3 ft/s
Step-by-step explanation:We are given:
distance of the top of the ladder from the ground (h) = 12 ft
height of the ladder = 20 ft
rate of change of the distance of the base of ladder from the wall (dx/dt):
2 ft/s
Finding the distance of the base of the ladder from the wall:
From the Pythagoras's Theorem, we know that:
hypotenuse² = height² + base²
replacing the given values
20² = 12² + x²
400 = 144 + x²
x² = 256 [subtracting 144 from both sides]
x = 16 ft [taking the square root of both sides]
The rate of change of the height of the Ladder from the ground:
We know that:
h = 12 ft
([tex]\frac{dh}{dt}[/tex]) = ?
x = 16 ft
([tex]\frac{dx}{dt}[/tex]) = 2 ft/s
According to the Pythagoras's Theorem:
20² = x² + h²
differentiating both sides with respect to time
[tex]\frac{d(400)}{dt} = \frac{d(x^{2} + h^{2})}{dt}[/tex]
[tex]0 = \frac{d(x^{2})}{dt} + \frac{d(h^{2})}{dt}[/tex]
[tex]0 = \frac{d(x^{2})}{dx}(\frac{dx}{dt}) + \frac{d(h^{2})}{dh}(\frac{dh}{dt})[/tex]
[tex]0 = 2x(\frac{dx}{dt}) + 2h(\frac{dh}{dt})[/tex]
replacing the variables
[tex]0 = 2(16)(2) + 2(12)(\frac{dh}{dt})[/tex]
[tex]0 = 64 + 32(\frac{dh}{dt})[/tex]
[tex]-64 =32(\frac{dh}{dt})[/tex] [subtracting 64 from both sides]
[tex]\frac{-64}{32} =(\frac{dh}{dt})[/tex] [dividing both sides by 32]
[tex]\frac{dh}{dt} = \frac{-8}{3} ft/s[/tex]
Hence, the ladder will slide down at a speed of 8/3 feet per second
Related Questions
Which of the following ordered pairs is not a solution of the inequality y > x2 + 4x +3?
(0,5)
(1,8)
(2,17)
(-3,4)
Answers
Answer:
option :-a (0,5) is right answer
Answer:
(1,8) is not a solution
Step-by-step explanation:
plug in the ordered pairs to the equations to get the answers.
Michael’s class 27 adults and 63 kids on their field trip. Emily’s class had 20 adults and 70 kids on their trip. Both Michael & Emily’s teachers split the class into groups, so that each group has 7 kids. Whose class had more adult chaperones per group?
Answers
Answer:
Michaels class
Step-by-step explanation:
63 kids and 70 kids One group gets 9 groups and the other gets 10. 27/9 is 3, whileas 20/10 is 2 so Michaels class had more. Hope this helps :D
Ethan buys a bag of cookies that contains 6 chocolate chip cookies, 5 peanut butter cookies, 7 sugar cookies and 7 oatmeal cookies.
What is the probability that Ethan reaches in the bag and randomly selects an oatmeal cookie from the bag, eats it, then reaches back in the bag and randomly selects a peanut butter cookie?
Answers
Answer:7/25 × 5/24
Step-by-step explanation:
7 oatmeal 25 all together
Then 5 peanut butter 24 left since he ate one
The probability of randomly selecting an oatmeal cookie first is approximately 7/25, and the probability of selecting a peanut butter cookie second is approximately 5/24.
Use the concept of probability defined as:
Probability is defined as the ratio of the total number of favorable outcomes to the total number of outcomes.
Given that,
Ethan buys a bag of cookies.
The bag contains different types of cookies:
chocolate chip, peanut butter, sugar, and oatmeal.
The quantities of each type of cookie in the bag are:
6 chocolate chip cookies
5 peanut butter cookies
7 sugar cookies
7 oatmeal cookies
To calculate the probability,
To determine the total number of cookies in the bag and the number of oatmeal cookies and peanut butter cookies.
In this case,
Ethan has a total of,
6 + 5 + 7 + 7 = 25
So there is 25 cookies in the bag.
Since there are 7 oatmeal cookies in the bag.
So, the probability of randomly selecting an oatmeal cookie first = 7/25,
After eating the oatmeal cookie,
There are now 24 cookies left in the bag, with 5 peanut butter cookies remaining.
Therefore,
The probability of randomly selecting a peanut butter cookie second is 5/24
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ3
Can someone help me with these math quetions please
Answers
Answer:
x is-4,and ans for y is 1
Step-by-step explanation:
can somebody help me
Answers
Answer:
-2 , 0 , 2
Step-by-step explanation:
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:
the box after 4 is 2, 0, -2
Step-by-step explanation:
-2,0,2,4,6,8
It's counting down by two's
WILL GIVE BRAINLIEST!!! Find the length of DF
Answers
Answer:
190.4
Step-by-step explanation:
Solve the following system:
{2 y - 3 x - 8 = 3 y + 4 x - 1 | (AB=DE)
4 y + 10 x + 3 = -2 y - 17 x + 9 | (BC=EF)
x = -16/5, y = 77/5
DF=AC=-27x+5y+27=190.4
There you go, have a great day
Which of the following equations has a graph with a y-intercept of -8
Answers
can you please help me with this question
Answers
Answer:
$1.22 per pair
The error is the contractor didnt take into account that there are 5 dozen gloves not 5 pairs of gloves. He calculated $73.20/5, which gave him $14.64.
Step-by-step explanation:
1 dozen = 12
5 dozen = 12 * 5 = 60
Therefore, you have 60 pairs of gloves.
He purchased all 60 pairs of gloves for $73.20.
73.20/60 = $1.22
This is how much one pair of gloves cost.
Kevin and Randy Muise have a jar containing 56 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $6.80. How many of each type
of coin do they have?
Answers
Answer:
36 nickels and 20 quarters
Step-by-step explanation:
36x5= 180
25x20=500
500+180=680=6.80
Answer:I won’t give you a full answer but I can explain it.
Step-by-step explanation: Our “goal” is $6.80 we have to figure out how many nickels and quarters are in it. First off, which is bigger? A quarter. Count as far as you can until you can’t go over 6.80. Now add the remaining numbers (the nickels) and you will have your answer. Make sure when your adding to count each quarter and nickel!
In GHJ, GH = 21 inches, HJ = 24 inches, and GJ = 9 inches. Which statement is true? A. G is smallest B. J is smallest C. H is largest D. G is largest
Answers
Answer:
D. G is the largest
Step-by-step explanation:
1. Draw a triangle and label it so it says G, H, and J, on its points.
2. Write 21 between the G and H. Write 24 between the H and J. Write 9 between G and J.
3. Since side HJ is 24 inches, larger than GH and GJ, the angle across from it is also the largest. If you look at your drawn triangle the angle across from side HJ is angle G.
find 20 hours is 30 minutes
Answers
Answer:
24×20×30=14,400 minutes
help !!!! Consider the function below. Explain how you would determine the x and y intercept of the function without using technology? 2x - 9y = 18
Answers
Answer:
To find the x-intercept you have to substitute in o for y and solve for x. To find the y-intercept you can substitute in 0 for x and solve for y.
What is the perimeter of a rectangle whose length is M cm and width is 2 cm
Answers
Answer:
2m plus 4
Step-by-step explanation:
mx2=2m
2x2=4
2m plus 4 = 2m plus 4
My plus button isnt working sorry
Find the missing length of each right triangle
Answers
It could possible be either 21 or 23
Fred, Barney, Wilma and Betty together stacked a total of 50 rocks in the quarry. Fred stacked 0.14 of the rocks, Barney stacked 4 of the 50 rocks, Wilma stacked 24% of the rocks, and Betty stacked the remaining rocks. Who stacked the most rocks? (5 points) a Fred b Barney c Wilma d Betty
Answers
Answer:
the awnser is d
Step-by-step explanation:
what is the sum of ? - (? × ?)= 90
Answers
Answer:
B, because first of all, y = 4x + 6, so you could cross off A. It can't be C either because there are 4x, not 4y. And it can't be D because Y is also 6 more. If it was 6 more, 4x - y would be a negative number since y is more than 4x.
Step-by-step explanation:
What is 13/2 as a percent
Answers
Answer:
650% percent
Step-by-step explanation:
The points N, O, P and Q all lie on the same line segment, in that order, such that the ratio of NO:OP: PQ is equal to 1:5:3. If NQ = 9, find OQ.
Answers
Answer:
8Step-by-step explanation:
If the points N, O, P and Q all lie on the same line segment, in that order, such that the ratio of NO:OP: PQ is equal to 1:5:3, then;
NO + OP + PQ = 1+3+5 = 9
NQ = NO + OP + PQ = 9
Given
NQ = 9
OP + PQ = OQ
According to the ratio;
OP = 5
PQ = 3
Since OP + PQ = OQ
OQ = 5 + 3
OQ = 8
Hence the measure of OQ is 8
60/30 in simplistic form
Need answer quick!!!!!!!!!
Answers
Answer:
2
Step-by-step explanation:
60/30 is 2
HOpe this helps :D
PLz mark brainliest if correct :D
$590 is deposited into a savings account that earns 4.25% simple interest for 3 years. Find the Interest and Account Value. Remember his is money so round your answer to the nearest hundredth.
Interest:
Account total:
Answers
Answer:
Interest:$75.23
Account total: $665.23
Step-by-step explanation:
I=590(0.0425)(3)
Interest=$75.23
75.23+590=665.23
gus is making 48 ounces of spiced cider if he serves an equal amount to 7 people will each person git more than 1 cup of cider or less than 1 cup
Answers
Answer:
Each person will get less than one cup.
Step-by-step explanation:
48 ounces divided by 7 people would allow each person to receive 6.86 ounces. One cup is 8 ounces.
Answer:
i thought cider said spider hahaha
anyways...
Step-by-step explanation
each person gets one cup
Write the explicit formula for the given sequence.
9, 15, 21, 27, ...
I need this done asap
Answers
Answer:
an = 9+ 6(n-1)
or
an = 6n+3
Step-by-step explanation:
9+ what = 15
15-9 = 6
15+6 = 21
21+6 = 27
We are adding 6 each time so the common difference is 6
The explicit formula for an arithmetic sequence is
an = a1+d(n-1) where a1 is the first term and d is the common difference
an = 9+ 6(n-1)
an = 9+6n-6
an = 6n+3
Answer: 3(odd numbers)
Step-by-step explanation:
The following are product of odd numbers that are only multiplied by 3.
answer to 1 and 2 pls!! will mark brainliest if u explain how u got it.
Answers
Answer:
ok so the answer to the first is 23. And how you get that is take 1 +7 and add them next you subtract 30 - 7 and get 23.
Step-by-step explanation:
The answer to 2 is 32. And how you get that is you can split 96 into 3 groops and when you do you will get 32 hope this helps.
-1<9+n<17 how would I solve this compound equality?
Answers
Answer:
n<8
Step-by-step explanation:
subtract 9 from all sides
-10<n<8
add 10
n<8
n divided by 8 is −32. equation first solution second
Answers
Answer:
n/8= -32
-256
Step-by-step explanation:
A system has an MTBF of 2500 h. What is the probability that this system will survive 3000 hours without any failure if the failure is distributed exponentially?
Answers
its 47% kldkfifhnknskdib do sibk jmnbsinslknd
Answers
A college radio station sponsors a contest once a week. One resident from a dormitory calls in and tries to answer ten questions correctly. Each correct answer earns the dorm $50, but each incorrect answer reduces the winnings by $25. Last week’s contestant earned $350. How many answers were correct?
Answers
Answer:
There were 8 correct answers and 2 incorrect answers.
Step-by-step explanation:
The contest consists of paying $50 for each correctly answered question and subtracting $25 for each incorrectly answered question.
Let's call:
x = Number of correct answers
y = Number of incorrect answers
The resident from a dormitory answered 10 questions last week. This leads to the following condition:
[tex]x + y = 10\qquad\qquad [1][/tex]
Since each correct answer adds $50 and each incorrect answer subtracts $25, the weekly balance is
50x - 25y
The contestant earned $350, thus:
50x - 25y = 350
Dividing by 25:
2x - y = 14
Adding this equation with [1]:
x + 2x = 24
Simplifying:
3x = 24
x = 24 / 3
x = 8
From [1]:
y = 10 - x = 10 - 8
y = 2
There were 8 correct answers and 2 incorrect answers.
What is 3,477 ÷ 5 ? Does anybody know? Can anyone help?
Answers
Answer:
695.4
Step-by-step explanation:
Wapi simplified an expression. His work is shown below
7(8.5-1.5)+ 8÷ 2
step 1 7(7) + 8 ÷ 2
step 2 49 + 8 ÷ 2
step 3 57 +2
step 4 28.5
In which step did Wapi make his first mistake?
➪ Step 1
➪ Step 2
➪ Step 3
➪ Step 4
Answers
Answer:
Step 3
explanation:
I got it right on edge, hope it helps :]