Find the length of parametrized curve given by
x(t)=−12t2+24t,y(t)=−4t3+12t2x(t)=−12t2+24t,y(t)=−4t3+12t2
where tt goes from 00 to 11.
Answer:

Answers

Answer 1

The length of parameterized curve given by x(t)=12 t²− 24 t, y(t)=−4 t³  + 12 t² is 4/3.

To find the length of the parametric curve given by x(t) and y(t), we can use the arc length formula for parametric curves:

L =\(\int\limits^a_b\)√[x'(t)² + y'(t)²] dt

In this case, we have x(t) = -12t² + 24t and y(t) = -4t³ + 12t², where t goes from 0 to 1.

First, let's find the derivatives of x(t) and y(t):

x'(t) = -24t + 24

y'(t) = -12t² + 24t

Next, we substitute these derivatives into the arc length formula and integrate over the interval [0, 1]:

L = \(\int\limits^a_b\) √[(-24t + 24)²+ (-12t² + 24t)²] dt

Simplifying the expression inside the square root:

L = \(\int\limits^1_0\)√[ 576 t² + 576 - 1152 t + 144 t⁴ + 576 t² - 576 t³] dt

L = \(\int\limits^1_0\) √[144 t⁴ - 576 t³ + 1152 t² - 1152 t + 576] dt

L= (12(t² -2t +2))²

So, Area = \(\int\limits^1_0\)(x² -2x +2))

Area =[1/3 - 1 + 2 -0]

Area = 4/3

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Related Questions

1. Elena wants to put together some of her favorite songs on her computer. She wants to store 60 minutes
worth of music. Elena wonders how many songs she will be able to include. She looks online and finds a
source that says the average song length is 3 minutes. If this is true, about how many songs will Elena be
able to store? Show your work

Answers

Answer:

20 Songs

Step-by-step explanation:

60 minutes / 3minutes per song =20 songs

Cross-docking
a. Increases the level of storage facilities
b. Reduces the level of storage facilities
c. Increases transportation costs
d. Reduces transportation costs

Answers

The correct answer is letter B, Reduces the level of storage facilities. This is because cross-docking reduces the need for storage facilities by having goods shipped directly from one transportation vehicle to another with little or no storage time in between.

Cross-docking refers to the process of transferring goods from one transportation vehicle to another directly, with minimal or no material handling or storage time in between. This strategy has gained a lot of attention in recent years due to its ability to reduce warehousing costs, inventory holding, and transportation costs and increase product movement efficiency. Cross-docking is typically classified into two main types: pre-cross-docking and post-cross-docking. Pre-cross-docking is a method that involves assembling incoming shipments from several origins according to a particular destination, whereas post-cross-docking involves breaking down shipments arriving from a source and sending them to multiple destinations.

In conclusion, cross-docking is a cost-effective and efficient supply chain strategy that reduces the need for storage facilities by minimizing or eliminating the storage and order picking activities. Cross-docking improves product movement and reduces transportation costs while maintaining high levels of accuracy and timeliness.

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Solve |x+ 4| = -6 im struggling with this problem

Answers

Recall that:

\(\begin{gathered} |a|\ge0 \\ \text{for all a}\in\R. \end{gathered}\)

Therefore the given equation has no solutions.

Answer: Option B.

What is the y intercept for y=−3x+7

Answers

Answer:(0, 7)

Step-by-step explanation:Use the slope-intercept form to find the slope and y-intercept.

Identify the terms in the expression. 4y³ + y + 9

Answers

The given expression is

\(4y^3+y+9\)

There are three terms in this expression

\(4y^3\text{ , }y\text{ , }9\)

20 points :)
Please help!! I'll give brainliest. I'm grounded by tonight if this isn't done D:<

Write each number without exponents.
A: 2.05 x 10^5
B: 1.9 x 10^4
C: 10^6

Answers

Answer:

A. 205,000

B.19,000

C. 1000000

Step-by-step explanation:

Step-by-step explanation:

A: 2.05 x 100,000

B: 1.9 x 10,000

C: 1,000,000

Please only answer if you can help!! Please look at the picture below

Please only answer if you can help!! Please look at the picture below

Answers

Answer:

3

Step-by-step explanation:

The graph doesn’t go left to x = 3, so the answer is 3

Ryder used front end estimation to estimate the product of -24.98 - 1.29 what is the zestimate​

Answers

Answer:

20

Step-by-step explanation:

The numbers whose product are to be obtained :

(–24.98)(–1.29)

To use front end approximation, numbers are rounded to the greatest place value :

For :

(-24.98) is rounded to - 20 (4 is rounded here to 0)

(-1.29) is rounder to - 1 (2 is rounded to 0)

Then, the product of the two numbers will be :

-20 * - 1 = 20

Shaundra Brown worked 7 hours on Monday, 10 hours on Tuesday, 8 hours on Wednesday, 9 hours on Thursday, and 10 hours on Friday. Her regular hourly pay is $12.80. Find her gross earnings for the week if Brown is paid time and a half for all hours over 8 worked in a day.

Answers

Shaundra Brown's gross earnings for the week would be $664.00

Brown worked 7 hours on Monday, 10 hours on Tuesday, 8 hours on Wednesday, 9 hours on Thursday, and 10 hours on Friday. Her regular hourly pay is $12.80. Therefore, to calculate Brown's total earnings, you need to calculate her total hours worked, as well as any overtime she may have earned.For the first 8 hours each day, Brown will be paid her regular hourly rate of $12.80. For any hours worked beyond 8, she will receive time and a half, which is $19.20.

To calculate Brown's gross earnings, you must first find out how many hours she worked in total and how many of those hours qualify for overtime pay.7 hours on Monday count as regular hours.10 hours on Tuesday, 2 hours qualify for overtime.8 hours on Wednesday count as regular hours.9 hours on Thursday, 1 hour qualifies for overtime.10 hours on Friday, 2 hours qualify for overtime. Total regular hours worked: 7 + 8 = 15Total overtime hours worked: 2 + 1 + 2 = 5Brown will receive her regular hourly rate of $12.80 for 15 hours of work, which amounts to $192.00. Additionally, she will receive time-and-a-half pay for 5 hours of work, which is $96.00. 5 hours of work at the overtime rate of $19.20 an hour is equal to $96.00.Her total gross earnings for the week would be the sum of her regular earnings plus her overtime earnings, which is $192.00 + $96.00 = $288.00.Brown's gross earnings for the week would be $664.00.

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How many roots does the equation x3 3x2 4 0 have?

Answers

The number of roots of the given equation x³ -3x² + 4 = 0 is equal to 3 which are -1, 2, 2.

As given in the question,

Given equation is written as:

x³ -3x² + 4 = 0

Number of roots of the given equation are as follow ;

Let f(x) = x³ -3x² + 4

For x = 1

f(1) = 1³ - 3(1)² + 4

    = 2 ≠ 0

x = 1 is not the roots.

Now, x = -1 ,

f(-1) = (-1)³ - 3(-1)² + 4

      = -1 -3 + 4

      = 0

x = -1 is the roots of the given equation x³ -3x² + 4 = 0

x³ -3x² + 4 = 0

⇒x³ + x² -4x² -4x + 4x + 4 =0

⇒x² ( x + 1) - 4x( x + 1) + 4(x+1) =0

⇒(x+1) ( x² -4x +4 ) = 0

⇒(x+1)( x - 2 )² = 0

⇒ x = -1, 2, 2

Therefore, the number of roots of the given equation x³ -3x² + 4 = 0 are 3 and given by x = -1 , 2, 2.

The above question is incomplete , the complete question is :

How many roots does the equation x³ -3x² + 4 = 0 have ?

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the margin of error of a confidence interval is the error from biased sampling methods. True or False

Answers

True? Maybe?I feel like that’s wrong

Revision 1. Find the value of the variable that makes these number sentences true: a) h+8=19 b) 2p-6=4 c) y = 12 2. Substitute the value for x in order to find the value of y in the following: a) y=3x+2 ifx=8 b) y=4x-1 ifx=! c) y=0,2x+5 ifx=10 d) y = 10x+12 if x=0,3 3. Write the following as number sentences: a) The difference between two numbers is 25 b) The product of 5 and p is equal to the quotient of q and 2 c) The difference between 14 and 2y is equal to 6 d) The product of 15 and 4 is equal to four less than the sum of x and y. that represent these word problems.​

Answers

1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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y = -7⁄2 x + 86
y = -7⁄2 (10) + 86
y = 51 points

Answers

Answer:

I think you are incorrect

Step-by-step explanation:

this was the answer i got 121

Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

PLEASE HELP!!!!!!! Line M is represented by the following equation: x + y = −1 What is most likely the equation for line P so the set of equations has infinitely many solutions? (4 points) Question 5 options: 1) 2x + 2y = 2 2) 2x + 2y = 4 3) 2x + 2y = −2 4) x − y = 1

Answers

The equation for line P such that the system has an infinite number of solutions is given as follows:

3) 2x + 2y = -2.

How to obtain the equation?

The first equation for the system of equations is given as follows:

x + y = -1.

A system of equations has an infinite number of solutions when the two equations are multiples.

Multiplying the equation by 2, we have that:

2x + 2y = -2.

Meaning that equation 3 is correct.

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What is the equation of a circle with center (5, -7) and Circumference = 12
(No links)

Answers

Answer:

(x-5)2+(y+7)2=4    

Step-by-step explanation:

find the slope of (6,1) and (6,-3)

Answers

Answer:

Step-by-step explanation:

find the slope of (6,1) and (6,-3)
find the slope of (6,1) and (6,-3)

An equlateral triangle has sides of length 2x-3 each. The perimeter of the triangle is 63 cm. Find the value of x

Answers

Answer:

x= 5

Step-by-step explanation:

Do all variable terms have a coefficient?

Answers

technically yes because even if you have a variable of just x, there is still a coefficient of 1

A container has 3 3/8
pounds of flour.

​Mr. Wright gives each member of ​his cooking class 3/16
pound of flour, which empties the container.

​How many people are in Mr. Wright’s class?

Answers

Answer:

18

Step-by-step explanation:

3=48/16

48/16 + 3/8 (6/16) = 54/16

54÷3=18

answer is 18 students

find+the+standard+deviation+for+a+security+that+has+three+oneyear+returns+of+5%,+10%,+and+15%.+question+content+area+bottom+part+1+a.+25.00%+b.+8.33%+c.+16.67%+d.+5.00%

Answers

Answer:

Step-by-step explanation:

its 100%

A scuba diver descends (goes down) to a location that is −10 m from sea level. He then descends (goes down) another -12 m. What is the scuba diver’s final location relative to sea level

Answers

Answer:

-22 m

Step-by-step explanation:

Solve for w, where w is a real number.

Solve for w, where w is a real number.

Answers

Answer:

w= 9

Step-by-step explanation:

\( \sqrt{ - 4w + 61} = w - 4\)

Square both sides:

-4w +61= (w -4)²

\(\boxed{(a - b)^{2} = a^2 -2ab + b^2 }\)

Expand:

-4w +61= w² -2(w)(4) +4²

-4w +61= w² -8w +16

Simplify:

w² -8w +16 +4w -61= 0

w² -4w -45= 0

Factorize:

(w -9)(w +5)= 0

w -9= 0 or w +5= 0

w= 9 or w= -5 (reject)

Note:

-5 is rejected since we are only taking the positive value of the square root here. If the negative square root is taken into consideration, then w= -5 would give us -9 on both sides of the equation.

Why do we use negative square root?

When solving an equation such as x²= 4,

we have to consider than squaring any number removes the negative sign i.e., the result of a squared number is always positive.

In the case of x²= 4, x can be 2 or -2. Thus, whenever we introduce a square root, a '±' must be used.

However, back to our question, we did not introduce the square root so we should not consider the negative square root value.

Answer: w=9.

Step-by-step explanation:

\(\sqrt{-4w+61}=w-4\)

Tolerance range:

\(\left \{ {{-4w+61\geq 0} \atop {w-4\geq 0}} \right. \ \ \ \ \left \{ {{4w\leq 61\ |:4} \atop {w\geq 4}} \right. \ \ \ \ \left \{ {{w\leq 15,25} \atop {w\geq 4}} \right. \ \ \ \ \Rightarrow\ \ \ \ \\w\in[4;15,25].\)

Solution:

\((\sqrt{-4w+61})^2=(w-4)^2\\-4w+61=w^2-2*w*4+4^2\\-4w+61=w^2-8w+16\\w^2-4w-45=0\\D=(-4)^2-4*1*(-45)\\D=16+4*45\\D=16+180\\D=196.\\\sqrt{D}=\sqrt{196}\\\sqrt{D}=14 \\w_{1,2}=\frac{-(-4)б14}{2} \\w_1=\frac{4-14}{2} \\w_1=\frac{-10}{2} \\w_1=-5\ \notin tolerance\ range.\\w_2=\frac{4+14}{2}\\ w_2=\frac{18}{2} \\w_2=9\ \in tolerance \ range.\)

Consider the graph of the function f (x) = 10^x.
-10 -8 -6
-4 -2
104
8-
6-
4-
2-
-2-
6-
10 2
-8-
-10-
-N
4
6
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8
10
X
Which statement describes a key feature of function g if g (x) = f(x + 4)?

Answers

A statement that describes a key feature of function g if g(x) = f(x + 4) include the following: B. horizontal asymptote of y = 0.

What is a horizontal asymptote?

In Mathematics and Geometry, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the horizontal line passing through the ordered pair (0, 0) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 0, as shown in the image attached below.

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Complete Question:

Consider the graph of the function f(x) = 10^x.

Which statement describes a key feature of function g if g(x) = f(x + 4)?

OA y-intercept at (0,4)

B. horizontal asymptote of y = 0

OC. x-intercept at (4,0)

OD. horizontal asymptote of y = 4

Consider the graph of the function f (x) = 10^x.-10 -8 -6-4 -21048-6-4-2--2-6-10 2-8--10--N46-CO810XWhich

Pratibha spends 5 3/4 hours in school. He spends 4 1/4 hours for classes and 3/4 hours for lunch break. She spends the remaining time on sports. How much time does she spend on sports?

Answers

Answer:

13 hours and 15 minutes of her day are spent on sports if she doesn't sleep.

Step-by-step explanation:

carson kelly, a catcher for the arizona diamondbacks, hit 18 home runs in 2019. if his home-run-hitting ability is expected to grow by 12 percent every year for the following five years, how many home runs is he expected to hit in 2024?

Answers

Carson Kelly is expected to hit approximately 31 home runs in 2024.

To find how many home runs Carson Kelly is expected to hit in 2024, we can use the formula for compound interest, where the initial amount is the number of home runs he hit in 2019, and the interest rate is the expected growth rate of his home run hitting ability, which is 12 percent or 0.12 as a decimal.

Let H be the number of home runs hit in 2019, and H(n) be the number of home runs hit in year n, then we can write:

H(n) = H * (1 + r)^n

Where r is the growth rate, and n is the number of years into the future.

If we plug in the given values, we can find the number of home runs Carson Kelly is expected to hit in 2024, which is 5 years after 2019.

H = 18 (number of home runs in 2019)

r = 0.12 (growth rate)

n = 5 (number of years into the future)

H(5) = 18 * (1 + 0.12)^5

H(5) = 18 * 1.7623

H(5) = 31.9214

It's important to note that this is simply an estimate based on the given growth rate, and the actual number of home runs he hits in 2024 may vary based on many factors, including injuries, team support, and the skill of opposing pitchers, among others.

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2c+2b in standard from

Answers

Answer:

2c+2b

Step-by-step explanation:

this is because standard form only applies to no. from 10 and above , furthermore, they are unlike terms

Bori run 7 mile in 50 minute. At the ame rate, how many mile would he run in 75 minute

Answers

Bori will run 10.5 miles in 75 minutes, using the concepts of unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method. We typically utilise this technique for math calculations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

Let us use the unitary method to solve this sum as well.

Bori can run 7 miles in 50 minutes.

This implies that, in 50 mins, Bori will run 7 miles.

Therefore, in 1 minute, Bori will run \(\frac{7}{50}\) miles.

We have to find the number of miles Bori will run in 75 minutes.

Thus, in 75 mins, Bori will run \(\frac{7}{50} * 75\) miles.

= 10.5 miles

Therefore, Bori will run 10.5 miles in 75 minutes.

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Find the range of the given function y = 3x + 2 for the domain 4 and -4. ​

Answers

Answer:

Range: (-10 , 14)

Step-by-step explanation:

Given information:

Equation: y = 3x +2Domain: (-4 , 4)

Range: (x , y)?

Plug in domain of x = -4 and x = 4 into equation to find range.

f(-4) = 3 * -4 + 2 = -10

f(4) = 12 + 2 = 14

Range: (-10 , 14)

Which linear equation passes through the point (-1, 4) and has a slope of -3?
Point Slope Form y-yı = m(x - 1)

Answers

the formula would be y-4=-3(x+1) so the equation would be y=-3x+1

Write an equation to show how to find the product of 1,000,000 and 1,000,000 using scientific notation.

Answers

The equation to show how to find the product of 1,000,000 and 1,000,000 using scientific notation can be expressed as (10^6 * 10^6).

What is the scientific notation?

A number can be written in scientific notation  in a case whereby the number is greater than or equal to 1  however not up to 10 multiplied by a power of 10.

Given that 1,000,000 and 1,000,000 which can be written in scientific notation as 1.0 * 10^6 and 1*10^6, then th product can be written as (10^6 * 10^6) = 10^12.

Hence, the product is 10^12.

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