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The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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Answer:

d) 1/12

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let L represent the length of the triangle.

Let W represent the width of the triangle.

The length of a rectangle is four more than three times the width. This means that

L = 3W + 4

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

If the perimeter of this rectangle is at least 70 square centimeters, an inequality that can be solved to find the width of the rectangle is

2(L + W) ≥ 70

L + W ≥ 70/2

L + W ≥ 35

Answer:

6w +8 ≥70

Step-by-step explanation:

Let w be the width

The length is then 3w+4 ("the length is 4 more than 3 times the width")

Since a rectangle has opposite sides equal, the perimeter would be 2(l+w) or 2(w+3w+4) which would be 6w +8.  If the perimeter is at least 70, that is, 70 or more, the inequality would be

  6w + 8 ≥ 70.  

The units, however, would not be SQUARE centimeters, just centimeters.  If the question were asking for area, the units would be square units, but since perimeter is a linear measurement,  the units would have to be linear.

Answer:

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Step-by-step explanation:

The resulting differential function is f'(x) = 2x and g'(x) = 2x² + 1

The term function in statistics refers the expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here we have given that let f and g be functions that are differentiable for all real numbers.

And we have to find the solution for the function.

Let us consider f(x) =  x² and g(x) = x³ + 1

Then the differentiation function is calculated as,

As per the law of differentiation, it can be written like the following,

=> f'(x) = x² dx

Then it can be written as the following after differentiation

=> f'(x) = 2x

Similarly, the g(x) is differentiated like the following,

=> g'(x) = x³ + 1 dx

=> g'(x) = 2x² + 1

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The total cost of all the items he wants to buy with the applied discount and before tax is $9.9.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Bashir has a loyalty card good for a 10% discount at his local hardware store.

So, Each good he buys at (100 - 10)% = 90% of the value before tax.

He wants to buy some items that cost $11  before the discount and tax.

Therefore the amount he has to pay is,

= (90/100)×11.

= $9.9

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Answer:

3

Step-by-step explanation:

It depends on the denominator

For 3 where comparing 16 to 24

Of course its going to be 16

Hope this helps!

Answer:

the last one: 490mm²

Step-by-step explanation:

the circles are around 113mm and

the 7mm face is 263mm so I think the last one makes the most sense as

263+113+113= 489 wich is very close

Answer:

Surface area is the total amount of space that all of the surfaces of an object take up. It is the sum of the area of all the surfaces of that object. Finding the surface area of a three-dimensional shape is moderately easy as long as you know the correct formula.

Step-by-step explanation:

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Answer:

Solving gives us the result, x = 2, y = -1

Step-by-step explanation:

The system of equations is,

y = 2x-5

y=-2x+3

equating the two equations, we get,

(since y = y)

\(2x-5 = -2x + 3\\4x -5 = 3\\4x = 3+5\\4x=8\\x=8/4\\x=2\)

and then since y = 2x-5

\(y=2(2)-5\\y=-1\)

so, x =2, y = -1

Answer:

A

Step-by-step explanation:

The lines cross or touch the X-Axis 4 times which means that there are 4 solutions.

Answer:

29 degrees

Step-by-step explanation:

Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees

Answer:d

Step-by-step explanation:

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Answer:

Step-by-step explanation:

i cant see the answer

Answer:

Hanna is 8 years old.

Step-by-step explanation:

Hanna = x

Tina = 4x

Sum = 40.

Hanna =?

Hanna + Tina = 40

4x + x = 40

5x = 40

x = 40/5

x = 8.

Hanna is 8 years old.

Answer: 3N+6

Step-by-step explanation:

Answer:

A: 219.84

B: 219.84 x 36 = 7914.21

C: 7914.21 - 7000 = 914.24

Step-by-step explanation:

When Carly took a $7,000, 3-year loan with an APR of 3.15%, then

Monthly payments can be referred to or considered as the monthly amount paid towards the partial repayment of a loan or an advance taken at a predetermined interest rate and time period.

Compounded Annuity = 7000(1+0.0315)^3

Compounded Annuity = $7,682.55.

Now, the amount of monthly payments for 3 years, or 36 months will be

Monthly payments = 7682.55 / 36

Monthly payments = $213.40

Finance Charge = Annuity – Principal

Finance Charge = 7682.55-7000

Finance Charge = $682.55

Therefore, the significance regarding monthly payments and the amounts of finance charge for the given condition has been aforementioned.

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Explanation:

The constant of proportionality is the same as the slope for equations of the form y = kx.

To find the value of k, we divide the y over x values.

k = y/x = 12/8 = 1.5

or

k = y/x = 6/4 = 1.5

Either way the answer is 1.5

This means Ziah ran at a rate of 1.5 city blocks per minute.

The value of each variable is:

x = 11 units

y = 11√2 units

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We can find the value of each variable using trigonometric ratios:

tan 45° = x/11 (tan = opposite/adjacent)

1 = x/11

x = 11 units

sin 45° =  9/y (sine = opposite/hypotenuse)

(√2)/2 = 11/y

y = 11/ (√2)/2

y = 11√2 units

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Answer: 1.2

Step-by-step explanation:

12/16 = 0.75

0.75 X 4/3 = 1

1/ (5/6) = 1.2

Answer:

I believe it is 1.2

Step-by-step explanation:

12/16x4/3

12x4=48

16x3=48

48/48=1

1 divided by 5/6=1.2

hope this helps :)

Of the fifth grade students, \(\frac{15}{20}\)  went to the book fair. Of the student who went to the book fair, \(\frac{6}{8}\) bought at least one book. The fraction of fifth grade students who bought at least one book is  \(\frac{9}{16}\)  that is  \(\frac{15}{20}\) x  \(\frac{6}{8}\)  of total(Option B)

What is a fraction?

Fraction is a type of number which represents a part of a whole thing. It is represented in two parts containing numerator which represents parts selected and the denominator which represents the total parts in which whole is divided.

Let the total students of grade fifth= s

Given that number of students who went to book fair=  \(\frac{15}{20}\)  of total

                                                                                        = \(\frac{15}{20}\)   x s

                                                                                         =\(\frac{15s}{20}\)

Given that numebr of students who bought at least one book=  \(\frac{6}{8}\)  of who went to fair

                                                                                        = \(\frac{6}{8}\)  x \(\frac{15s}{20}\)

                                                                                        = \(\frac{15}{20}\) x  \(\frac{6}{8}\)  of total

The correct answer will be option B.

On simplifying, fraction of grade fifth who bought at least one book

                                                                                        =\(\frac{3}{8}\) × \(\frac{15s}{10}\)

                                                                                        =\(\frac{45s}{80}\)

                                                                                        =\(\frac{9 s}{16}\)

                                                                                        = \(\frac{9}{16}\) of total

∴ The fraction of students who bought atleast one book is  \(\frac{9}{16}\)

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For complete question refer to the figure below:

Answer:

Therefore, 512/128 simplified to lowest terms is 4/1.

Step-by-step explanation:

Reduce 512/128 to lowest terms

The simplest form of  

512

128

is  

4

1

.

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 512 and 128 is 128

Divide both the numerator and denominator by the GCD

512 ÷ 128

128 ÷ 128

Reduced fraction:  

4

1

Therefore, 512/128 simplified to lowest terms is 4/1.

Answer:

Step-by-step explanation:

The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32F = [ C × (9/5) + 32 ] Given that, C = 25F = 25 × (9/5) + 32F = 45 + 32F = 77Thus, 25° C is equivalent to 77° F.

Answer:

w=15

Step-by-step explanation:

4w+13×5 = 25×5

4w =125-65

4w =60

w=15

The likelihood of randomly selecting a chocolate chip cookie from the batch would be likely. That is option A

Probability is defined as the possibility of an outcome of an event which may likely or unlikely occur.

The batch contains the following content:

The chocolate chip makes up 68% of the batch and this shows a higher quantity than other content. Therefore, likelihood of randomly selecting a chocolate chip cookie from the batch would be likely.

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Answer:

D

Step-by-step explanation:

The greatest common factor of 12 and 24 is 12. The only option which accounts for this is D.

The days it would take to complete the building is 104 22/25 days.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.

A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.

The first step is to determine the total height of the office bulding = height of each floor x total number of floors

15 x 10 2/5

15 x 52/5 = 780 /5 = 156

The next step is to determine the floors left to complete the office building :

156 - 24 9/10 = 131 1/10 feet

The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :

1311/10 ÷ 1 1/4

1311 / 110 ÷ 5/4

1311 / 10 x 4/5 = 104 days 44/50

104 22/25 days

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Answer:

Step-by-step explanation:

2x+3x+8-3x-2 = 2x + 6

The given inequality : 4 - 2x > 7 - 3x

Simplify:

Add 3x on both side :

4 - 2x + 3x > 7 - 3x + 3x

4 + x > 7

Subtract 4 on both side :

4 + x - 4 > 7 - 4

x > 3

Answer : x > 3

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.