find the exact length of the curve. x = 8 6t2, y = 5 4t3, 0 ≤ t ≤ 5
Answers
The exact length of the curve is 549.15 units, for parameters x = 8 6t2, y = 5 4t3, 0 ≤ t ≤ 5 using derivative & integration.
The curve has the parametric equations
x = 8 6t² and
y = 5 4t³,
where 0 ≤ t ≤ 5.
Step 1: Find the derivative of x with respect to t
dx/dt = 96t
Step 2: Find the derivative of y with respect to t
dy/dt = 60t²
Step 3: Calculate the integrand
\(\sqrt{[(dx/dt)² + (dy/dt)²]}\)
Substitute the expressions for dx/dt and dy/dt and
=`\(\sqrt{[(96t)² + (60t²)²] }\)
= \(\sqrt{[9216t² + 3600t^4]}\)
`Step 4: Integrate with respect to t, from `0` to `5`:
\(\int_0^5\ \sqrt(9216t^2+3600t^4)dt\\\\225/4\int_0^5\sqrt36t^2+25t^4]dt\)
Use the substitution `u = t²` and `du/dt = 2t`.
The limits of integration change to `u = 0` when `t = 0` and `u = 25` when `t = 5`.
Then, the integral becomes:
=225/4 int_0⁵ \(\sqrt{[36t^2 + 25t^4]} dt\)
= 225/4 int_0²⁵ \(\sqrt{[36u + 25u²]) } /2\sqrt{u} du\)
=225/4 int_0^25 (3\(\sqrt{[u + 4u²/9]}\))/(2\(\sqrt{[u]}\)) du
= 75/2 int_0^25 (\(\sqrt{[9u² + 4u³] }\)\(u^{-\frac{1}{2} }\)) du`
Use the substitution `v = 9u² + 4u³`, `dv/du = 18u + 12u²`.
When `u = 0`, `v = 0`, and when `u = 25`, `v = 24375`.
Thus, the integral becomes:
=`75/2 int_0^24375 \(v^{-\frac{1}{2} }\) (18u + 12u²) du
=`75/2 int_0^24375 (18/2 \(v^{-\frac{1}{2} }\) + 12/2 \(v^{-\frac{1}{2} }\) u) du
= 675/2 int_0^24375 \(v^{-\frac{1}{2} }\) + 450/2 \(v^{-\frac{1}{2} }\)]_0^24375
=675/2 int_0^24375 \(v^{-\frac{1}{2} }\) + 450/2\(v^{-\frac{1}{2} }\)]_0^24375
= 675/2 [\(2(24375)^{-\frac{1}{2} }\) + \(3(24375)^{-\frac{1}{2} }\) - \(2(0)^{-\frac{1}{2} }\) - \(3(0)^{-\frac{1}{2} }\)]
= 549.15`
Therefore, the exact length of the curve is `549.15` units.
To know more about derivative, visit:
https://brainly.com/question/29144258
#SPJ11
Related Questions
What is the square root 25
Answers
Answer:
5
Step-by-step explanation:
you could use a calculator, but it works like this too i guess. :P also you could just try and guess, "what squared (multiplied by itself) is 25" good luck
Answer:
5 should be the answer for the square root
can i get some help ?::
Answers
Answer:
7+3^2-2*5/4-1*2=
7+9-10/-2=
6/-2 or -3
3/4+1/8=
7/8 divided by 1/8=
7-2^2
3
-3<3
the second one is larger
Hope This Helps!!!
Find the velocity of the car at the end of a drag race. Round to the nearest whole number.
Answers
Answer:
183 miles per hour.
Explanation:
The estimated velocity(v) at the end of a drag race is modeled using the formula below:
\(v=234\sqrt[3]{\frac{p}{w}}\)Given:
• The horsepower, p = 1311
,• The weight (in pounds), w = 2744 pounds.
Substitute into the formula above:
\(\begin{gathered} v=234\sqrt[3]{\frac{1311}{2744}}=182.9 \\ v\approx183\text{ miles per hour} \end{gathered}\)The velocity is approximately 183 miles per hour.
Suri decided to get braces to straighten her teeth. The cost of the treatment plan was $5,000 which Suri was able to pay off over time. Each month Suri paid $125 until her account balance was $0 Which of the
following equations represents the account balance B (m) after m months?
A: B(m) 5000m- 40
B: B(m)-4Om + 5000
C: B(m) = 5000m- 125
D: B(m) =-125m + 5000
Answers
Answer:
d
Step-by-step explanation:
you have to divide 125 from 5000 so i believe i am right but if im not then im sorry
How do you find the slope if a line of two points are given?
Answers
If it is the two ordered pairs that are given then use the following slope formula.
\(m = \frac{y_2-y_1}{x_2-x_1}\)
also known as m = rise / run
Step-by-step explanation:
Fonts for Android and iPhone - www.fontskeyboard.com
C) if two individuals are chosen at random from the population, what is the probability that at least one will have some college or a college degree of some sort?
Answers
The probability that neither of the two individuals has some college or a college degree is (1 - P(college))^2.
To calculate the probability that at least one of the two individuals chosen at random from the population will have some college or a college degree, we need to consider the complement of the event, which is the probability that none of the individuals have a college degree.
Let's assume that the population size is N, and the number of individuals with a college degree is C. The probability that an individual does not have a college degree is (N - C) / N.
When choosing the first individual, the probability that they do not have a college degree is (N - C) / N.
When choosing the second individual, the probability that they do not have a college degree is also (N - C) / N.
Since these events are independent, we can multiply the probabilities together:
P(no college degree for either individual) = (N - C) / N * (N - C) / N = (N - C)² / N².
Now, to find the probability that at least one of the individuals has a college degree, we subtract the probability of none of them having a college degree from 1:
P(at least one with a college degree) = 1 - P(no college degree for either individual) = 1 - (N - C)² / N².
For more such question on probability. visit :
https://brainly.com/question/251701
#SPJ8
please help asap, show your work then choose an answer
Answers
Note that where the figure below contains two semi-circles that are tangent to each Other at point B and ray DE is tangent to both semicircles at points E and F, it is correct to state that ED = 6√2 (Option A).
What is a Semi Circle?A semicircle is a one-dimensional point collection that forms half of a circle in mathematics. It is a circular arc with a circumference of 180°. It just has one symmetry line.
Solving the ED, we have:
ΔDEM ~ ΔDFP
This means that MD/PD = EM/FP
MD/(MD + 9) = 3/6
6MD = 3MD + 27 (Collect like terms over the equation)
3MD = 27
MD = 9 (If both sides are divided by 9)
Note that
ED = √[MD²-EM²]
ED = √9²-3²]
ED = 6√2
Thus, it is correct to state that ED = 6√2
Learn more about Tangents:
https://brainly.com/question/10053881
#SPJ1
4.5a - 2.6a =
helpp me
Answers
Answer:
1.9a
Step-by-step explanation:
Find the equation of this line.
Answers
using the two dots Rise/run =-4/10 simplifies tp -2/5 y-intercept is 1
help please!!!!!!!!!!
Answers
Answer:
3125
Step-by-step explanation:
cubed root of 125 = 5
5^5 = 3125
Hope this helps!!
La ultima alternativa es la correcta: 3 125
Please Help if you can'
Answers
A.) n = 68
B.) n = 21/2
C.) n = 77/5
ANSWER ASAP. ALGEBRA WILL GIVE BRAINLIEST AND 70 POINTS
Write an equation in point-slope form of the line that passes through the point (0, 2) and has a slope of m=4
Answers
Answer:
y - 2 = 4 (x - 0)
Step-by-step explanation:
Answer:
y = 4x - 8
Hope this helps
Solve for x
A 130
B 120
C 23
D 70
Answers
Answer:
B)120º
Step-by-step explanation:
70+50=x
120=x
Sum of two interior angles=exterior angle
\(\\ \sf\longmapsto 50+70=x\)
\(\\ \sf\longmapsto x=120\)
Option B
60 PTS [see image] "Identify the parent function that can be used to graph the function"
![60 PTS [see image] "Identify the parent function that can be used to graph the function"](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/WI9CgWlZ6g1w29k0ih4eLp3FEhic4KAx.png)
Answers
Answer:
The parent is x^2
Step-by-step explanation:
We are shifting the function and stretching the function
The parent function is x^2
f(x) = x^2
Then shift
f(x) = (x-9)^2
Then stretch
3 (x-9)^2
Answer:
f(x)=x^2
Step-by-step explanation:
The x is the parent function and is surround by parenthesis with a ^2 so u have to included this with the function.
Hope this helps :3
(feedback is always helpful) <3
Write a system of linear inequalities so the points,(1,2) and (4,-3) are solutions of the system, but the point (-2,8) is not a solution of the system.
Answers
Answer:
The sample system is:
y < 5y > x - 8see the attached
The points (1, 2) and (4, -3) are in the intersected region but the point (-2, 8) is outside
information for questions 13-18: an insurance company determines that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station. a sample of 20 recent fires in a large suburb of a major city was selected. for each fire, the following variables were recorded: x
Answers
We can make predictions about the cost of fire damage based on the distance from the house to the nearest fire station. This information can be useful to insurance companies, fire departments, and homeowners in determining the risk of fire damage and the appropriate level of insurance coverage needed.
In this particular study, the insurance company has determined that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station. The cost of fire damage is the dependent variable, while the distance from the house to the nearest fire station is the independent variable.
For this study, a sample of 20 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded:
- the cost of fire damage in thousands of dollars (the dependent variable)
- the distance from the house to the nearest fire station in miles (the independent variable)
It is expected that the cost of fire damage increases as the distance from the house to the nearest fire station increases. This is because, as the distance from the fire station increases, the response time also increases, which can result in more damage being done to the property.
To analyze this data, a linear regression model can be used. The model will help to determine the nature and strength of the relationship between the two variables. The model will generate an equation in the form of y = mx + b, where y is the cost of fire damage, x is the distance from the house to the nearest fire station, m is the slope of the line, and b is the y-intercept.
For more such questions on distance
https://brainly.com/question/30395212
#SPJ8
A scale model of a bicycle
has a scale of 1:30. The
reau bicyde has a length
of 1.5m. What is the length
of the model in cm.
Answers
Answer:
5cm
Step-by-step explanation:
Convert 1.5m into cm to make it easier to solve.
1.5m --> 150cm (*100)
The real bike length is 30 times larger than the scale. So to undo this we need to divide by 30.
150cm / 30 = 5cm
g a process is normally distributed with a mean of 10.6 hits per minute and a standard deviation of 0.49 hits. if a randomly selected minute has 11.8 hits, would the process be considered in control or out of control? use a control chart to answer the question.
Answers
Based on a control chart analysis, the process with 11.8 hits per minute would be considered out of control.
In order to determine whether the process is in control or out of control, we can use a control chart.
A control chart is a graphical representation of process data that shows the behavior of the process over time and allows us to determine whether the process is in control or out of control.
The first step in creating a control chart is to calculate the control limits. In a normal distribution, control limits are set at +/- 3 standard deviations from the mean.
For this process, the mean is 10.6 hits per minute and the standard deviation is 0.49 hits.
The control limits would be:
Upper control limit (UCL) = 10.6 + (3 * 0.49) = 11.57 hits
Lower control limit (LCL) = 10.6 - (3 * 0.49) = 9.63 hits
Next, we compare the data point of 11.8 hits to the control limits.
If the data point falls outside of the control limits, the process is considered out of control.
If the data point falls within the control limits, the process is considered in control.
In this case, the data point of 11.8 hits is outside of the control limits and is higher than the upper control limit of 11.57 hits.
This means the process is considered out of control.
For more questions on control chart analysis
https://brainly.com/question/14917364
#SPJ4
HELP NOwwwwWWWW ILL GIVE BRAINLIEST
line A is a perpendicular to line B. if the slope of line A is 3/7 what is the slope of line b?
Answers
Answer: -7/3
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other.
James calculated the height of a cylinder that has a volume of 324 pi cubic inches and a radius of 12 inches. His work is shown below. V = B h Step 1: 324 pi = pi 12 squared h Step 2: 324 pi = 24 pi h Step 3: StartFraction 324 pi over 24 pi EndFraction = StartFraction 24 pi over 24 pi EndFraction h Step 4: h = 13.5 pi inches What is the first error that James made when calculating the height of the cylinder? In step 1, he substituted into the volume formula incorrectly. In step 2, he calculated 12 squared incorrectly. It should be 144 rather than 24. In step 4, the Pi should have canceled, making the correct answer 13.5 cm. James calculated the height of the cylinder correctly.
Answers
Answer:
I believe the answer is B let me know if it's wrong
Answer:
(B) In step 2, he calculated 12 squared incorrectly. It should be 144 rather than 24.
Instructions and Question in picture
Answers
Answer:
2
Step-by-step explanation:
Standard form means the terms are in descending order according to the power of the x.
Therefore, 2x³ would be first, as 3 is the highest power, followed by 3x² + 7x - 6.
A coefficient is the number in front of the x. The leading coefficient is the number in front of the highest degree x.
Now, looking at our equation, 2x³ + 3x² + 7x - 6, we see that 2x³ is our highest degree term, which makes 2 our leading coefficient.
Please help me with my algebra homework.
Solve log x = 3
a. x=3
b. x=30
c. x=1,000
d.x=10,000
Answers
Answer:
c. x=1,000
Step-by-step explanation:
log x = 3
Imagine that it's log10 x = 3
So, x = 10^3 (10 to the third power)
x = 10 * 10 * 10
x = 1,000
Emily has 6 pages of homework to do. If she can finish 3/8 a page in one
hour, how many hours will her homework take?
Answers
Answer:
16 hours
Step-by-step explanation:
To make it easier, we can put 3/8 as 37.5, and 6 as 600.
37.5 / 600 = 16
16 hours of homework.
When rounded to the hundreds place, which of the numbers below round to 456,700?
A) 456,605
B) 456,739
C) 456,798
D) 456,698
E) 45,673
Answers
Answer:
If you can only pick one option I'd choose D.)
Step-by-step explanation:
Option D is only two numbers away from 456,700
The second closest number would be option B.)
Answer:
\(D) . \: 456,698 = 456,700 \: to \: the \: hundreds \: place.\)
how does the sample size and percentage of confidence influence the width of a confidence interval?
Answers
As a result, the width of the confidence interval will rise as the sample size is reduced.
Define confidence interval.An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.
Given,
What causes a confidence interval's width to grow?
The confidence interval widens as the confidence level does. The only option to get more accurate population estimates, assuming the confidence level is fixed, is to reduce sampling error. The standard error statistic assesses sampling error.
When sample size is reduced, what happens to the width of the confidence interval?
As a result, the width of the confidence interval will rise as the sample size is reduced.
To learn more about confidence interval, visit:
https://brainly.com/question/24131141
#SPJ4
Find the slope of the line that passes through A(–2, –1), B(–1, 1)
A)1/2
B)-1/2
C)-2/1
D)2/1
Answers
-x/5-8=12
Show work
And check
Answers
Answer:
\(\huge\boxed{\sf x = -100}\)
Step-by-step explanation:
Given equation:\(\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}\)
given AB is congruent to AC and AL and AM trisect angle BAC. Prove AL is congruent to AM.
Answers
Explanation:
You want to show AL≅AM in the given figure.
Statement . . . . Reason1. AB≅AC . . . . given
2. ∠1≅∠3 . . . . given
3. ∆ABC is isosceles . . . . definition of isosceles triangle
4. ∠B≅∠C . . . . base angles are congruent in an isosceles triangle
5. ΔLBA≅ΔMCA . . . . ASA congruence postulate
6. AL≅AM . . . . CPCTC
What's 16 to the fifth power
Answers
Answer:
1048576
Step-by-step explanation:
1.048576 × \(10^6\)
An isosceles triangle in which the two equal sides, labeled a, are longer than the base, labeled b.
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
cm
Answers
If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.
Let's solve the problem step by step:
1. Identify the given information:
- The triangle is isosceles, meaning it has two equal sides.
- The two equal sides, labeled "a," are longer than the base, labeled "b."
- The perimeter of the triangle is 15.7 centimeters.
- One of the longer sides is 6.3 centimeters.
2. Set up the equation based on the given information:
Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:
2a + b = 15.7
3. Substitute the known value into the equation:
One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:
2(6.3) + b = 15.7
4. Simplify and solve the equation:
12.6 + b = 15.7
Subtract 12.6 from both sides:
b = 15.7 - 12.6
b = 3.1
5. Interpret the result:
The length of the base, labeled "b," is found to be 3.1 centimeters.
Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.
For more questions on Isosceles .
https://brainly.com/question/29793403
#SPJ8