The variable a is the length of the ladder. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. Suppose that the length of the ladder is 5.0 meters and the top is sliding down the wall at a rate of 0.4 m/s. Calculate dx dt when h = 3.1.
Answers
Answer:
dx/dt= 0.2608 at h= 3.1 m
Step-by-step explanation:
a is the length of the ladder. a=5
by pythagorus theorem
differentiating with respect to t we get
......1
The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom
At h= 3.1
x^2= 6^2-3.1^2 = 9.1×2.9
x= 5.1371 m
given
putting values in 1 to get dx/dt
.
dx/dt= 0.2608 at h= 3.1 m
Answer:
= 0.3
Step-by-step explanation:
The given situation forms a right triangle. We have to use the Pythagorean theorem's statement to solve this problem.
The theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse.
Here Hypotenuse = length of the ladder (a)
Legs are h and x.
So, using the Pythagorean theorem, we get
-------------(1)
We are given a = 5 meters, = 0.4
Now plug in a = 5 in the above equation, we get
25 = -----(2)
To find the . Differentiate the above equation with respective to the time t, we get
-------(3)
We know that h = 3.1 and = 0.4.
We can find x, by plug in h = 3.1 from the equation (2)
25 =
x = 3.9
Now plug h = 3.1, x = 3.9 and = -0.4 in the derivative (3) and find dx/dt
Here we represents = -0.4 because it is sliding down
2(3.1)(-0.4) + 2(3.9) = 0
-2.48 + 7.8 = 0
7.8 = -2.48
= -2.48 ÷ -7.8
= 0.3179
When we rounding off to the nearest tenths place, we get
= 0.3
Related Questions
Which is f(5) for the function –2x2 + 2x – 3? –107 –63 –43 –37
PLEASE HELP.!! ILL GIVE BRAINLIEST *EXTRA POINTS* DONT SKIP.!! :((
Calculate the area of a parallelogram with a 4 inch side, a 10 inch side, and 3 inches tall
Joshua does not want to spend more than $22 on a long-sleeve shirt. Which description of shirt prices would keep joshua within his spending limit, not including tax? Select all that apply a- 15% off %25 b- 30% off 32% c-19.65 plus 2.35 shipping fee d- 20.45 plus a $1.60 shipping fee
Answers
time = distance / speed
Given that the entire journey takes four hours, add up the time it takes David to row upstream with that of him travelling downstream. This is mathematically represented as,
total time = time upstream + time downstream
4 = 3/(x - 1) + 3/(x +1)
Solving for x in the equation gives 2. Thus, David's speed in still water is 2 miles per hour.
Answers
Answer:
- E(X) = 60*1/6 = 10
- sd(X) = √8.666 = 2.886
- E(Y) = 600*1/6 = 100
- sd(Y) = √86.666 = 9.1287
Step-by-step explanation:
Lets call X the amount of aces obtained in 60 rolls, and Y the amount of aces obtained in 600 rolls.
Note that both X and Y are obtained from counting the amount of successful tries from repetitions of independent experiments that have 1/6 of probability of success. Thus, both X and Y are random variables with binomial distribution, with n = 60 and 600 respectively and probability 1/6.
Remember that if Z is a random variable, Z ≈ Bi(n,p), then
- E(Z) = np, where E(Z) denotes the expected value of Z
- V(Z) = np(1-p), where V(Z) denotes the variance of Z. Hence, the standard deviation is the square root of V(Z), √(np(1-p)).
As a result
- E(X) = 60*1/6 = 10
- V(X) = 10*(1-1/6) = 50/6 ≅ 8.666
- sd(X) = √8.666 = 2.886
- E(Y) = 600*1/6 = 100
- V(Y) = 100*(1-1/6) = 500/6 ≅ 86.666
- sd(Y) = √86.666 = 9.1287
The observed amount of aces is more likely to be closer from the expected value with 60 rolls because, since we have less rolls, it is more difficult to obtain spread results.
You can also notice that X and Y can be obtained by summing independent variables with distribution BI(1,p) (also called Bernoulli(p) ). When you sum independent variables with the same distribution you have this property:
- E(r1+r2+...+rn) = n*E(r1)
- V(r1+r2+...+rn) = n*V(r1)
- sd(r1+r2+...+rn) = √n*sd(r1)
X can be obtained by summing 60 independent variables r1, ...., r60 with mean 1/6 and variance 1/6*(5/6) = 5/36. So we obtain that V(X) = 60*5/36, and sd(X) = √60 * √(5/36). While for the same argument sd(Y) = √600*√(5/36). The higher the number of rolls, the more spread the results are.
I hope this helped you!
The expected number of aces from 60 rolls of a fair die is 10 with a standard deviation of approximately 3.72. For 600 rolls, the expected number is 100 with a standard deviation of about 11.79. The observed count of aces is more likely to be closer to the expected value with fewer rolls due to the smaller standard deviation relative to the number of trials.
The expected value for the number of aces in a fair die roll is computed by multiplying the probability of rolling an ace by the number of rolls. For 60 rolls, the expected number is
. For 600 rolls, the expected number is
The standard deviation for the number of aces is calculated using the formula for the standard deviation of a binomial distribution, , where n is the number of trials, p the probability of success (
for an ace). For 60 rolls, it is
. For 600 rolls, it's
.
When you roll the die 60 times, the chances of the observed count of aces being within 2 from the expected value (10) is higher because the standard deviation is smaller relative to the number of trials than when you roll the die 600 times.
As the number of trials increases, the expected standard deviation grows larger, and the observed count is more likely to be within a wider range from the expected value (100).
Learn more about standard deviation here:
#SPJ3
What is the interquartile range of the data set below? Growth in feet of oak trees: 68,80,73,90,120,94,76,112,101,94,72 (1) 22 (2) 28 (3) 52 (4) 73
Answers
68, 72, 73, 76, 80, 90, 94, 94, 101, 112, 120
Median = 90
Lower Median = 73
Upper Median = 101
IQR = 101 - 73
IQR = 28
A) X = 1/3
B) X = 17/5x
C) X = 1/5
D) X = 1/6
Answers
B) Endpoint at both ends.
C) No endpoint or arrow on the ends.
D) Endpoint at one end and an arrow at the other end.
Answers
Answer:
D: an endpoint at one end and an arrow on the other or answer hope this helped,
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
A line segment has an endpoint at both ends. A has arrows at both ends.A ray has a endpoint at one end and an arrow at the other.
Answers
Answer: It is an isometry.
The transformation is done over a line of reflection.
Step-by-step explanation:
A reflection is a transformation that flips a figure on the coordinate plane across a given line without changing the shape or size of the figure.
From the definition of reflection, the figure and its image are congruent ,thus it is an isometry.
It does not slides a plane or flips a plane and does not changes the size of the figure.
It is an isometry and the transformation is done over a line of reflection. Option (a) and option (c) is correct.
Further explanation:
Given:
The statements about reflection are as follows,
(a). It is an isometry.
(b). It slides a plane.
(c). The transformation is done over a line of reflection.
(d). It flips a plane about a fixed line.
(e). It changes the size of the figure being reflected.
Explanation:
Isometryis a mapping of space to another space so that the length between the points is same as the length in the original space. Translation and the rotation are the isometries of plane.
Reflection is a transformation. The preimage is just flipped along a line of reflection to get a new image.
It is an isometry and the transformation is done over a line of reflection.
Option (a) is correct.
Option (b) is not correct.
Option (c) is correct.
Option (d) is not correct.
Option (e) is not correct.
Learn more:
- Learn more about inverse of the function brainly.com/question/1632445.
- Learn more about equation of circle brainly.com/question/1506955.
- Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Number System
Keywords: statements, true, reflection, isometry, slides, plane, transformation, done, over, line of reflection, flips, plane, fixed line, changes, the size, reflected, translation.