How do I turn this limit into a definite integral? Could you go step by step please

(The xi's are "x sub i" not "x times i")

Answer:

Step-by-step explanation:

Find the asymptotes.

Vertical Asymptotes:

x

=

0

Horizontal Asymptotes:

y

=

0

No Oblique Asymptotes

The total surface area of the moon is A = 79,98,258[tex]miles^{2}[/tex]

or  A =  2.07153931 × [tex]10^{13} m^{2}[/tex]

as per given in the question,

the radius of the moon ( r) is 798 miles

to find the area of the total surface area of the cylinder

Area (A) = [tex]4\pi r^{2}[/tex]  where r is radius of the sphere,

by substituting the radius in total surface area formula area,

A = [tex]4\pi (798) ^{2}[/tex]

                                    ( let [tex]\pi =3.14[/tex])

A = [tex]4\times3.14\times798\times798[/tex]

A = [tex]12.56\times63684[/tex]

A = 79,98,258.24

                               ( by rounding to the nearest whole number we get )

A = 79,98,258[tex]miles^{2}[/tex]

or we can write in

A =  2.07153931 × [tex]10^{13} m^{2}[/tex]

                                              ( in terms of meters)

the total surface are of the sphere is A = 79,98,258[tex]miles^{2}[/tex]

A =  2.07153931 × [tex]10^{13} m^{2}[/tex]

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The probability that the next customer pays with a debit card or a credit card will be 0.28.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Jacob claims an independent venture selling bagels. He realizes that somewhat recently 108 clients paid cash, 24 clients utilized a charge debit card, and 18 clients utilized a credit card.

The total number of events is given as,

Total event = 108 + 24 + 18

Total event = 150

The probability that the next customer pays with a debit card or a credit card is written as,

P = (24 / 150) + (18 / 150)

P = 42 / 150

P = 0.28

The likelihood that the following client pays with a check card or a Visa will be 0.28.

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Answer:

Step-by-step explanation:0.28

Answer:

120 degrees

Step-by-step explanation:

sum of all three angles of any triangle is 180

X+30+30=180

x+60=180

 -60. -60

x=120

Hopes this helps

Answer: 30%

Step-by-step explanation:

Answer: hi

Step-by-step explanation:

The image of y which is g(x) is 3x² + 60x + 82.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, y = 3x² - 24x + 2.

Now, g(x) is an image of y after a translation left 5 units and up 5 units.

∴ g(x) =  3(x + 5)² + 2 + 5.

g(x) = 3(x² + 20x + 25) + 7.

g(x) = 3x² + 60x + 75 + 7.

g(x) = 3x² + 60x + 82.

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cx + cy = a² + b² is the next step to prove the theorem.

Given,

The given Pythagorean theorem was created by Todd.

With leg lengths a and b and a hypotenuse length of c, he drew right

ΔABC. The hypotenuse was then drawn with altitude C Z.

He finds that the equations c/a=a/x and c/b=b/y. He then discovers that c x=a² and c y=b².

We have to find the next step to prove the theorem;

Here,

The next step is to add cx and cy

That is,

cx + cy = a² + b²

Then,

c(x + y) =  a² + b²

c² =  a² + b²

Therefore,

The next step to prove the theorem is cx + cy = a² + b²

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Answer:

Yes it is true.............

Answer:

-----------------------------------

From the picture we see this is a reflection across the y-axis.

From the coordinates we see all x-coordinates have changed to opposite and all y-coordinates remained as is.

The rule for such reflection is:

This is the option B.

Answer:

B) (x, y) → (–x, y)

Hope This Helps <33

--Jax

Answer: x = 7

Step-by-step explanation:

15(x+2) = R because they are equal angles.

set 135 = 15(x=2) because they are opposite each other so they equal each other

[tex]\frac{135}{15} =\frac{15(x+2)}{15} \\9 = x+2\\x=7[/tex]

Answer: number 3

Step-by-step explanation:

Answer: 3/20

Step-by-step explanation:

     With our fraction, we will have officer members over total number of members. Three is a prime number, so this fraction cannot be simplified any more. This gives us the fraction;

             3/20

Multiply the width by the length:

14 • 16 = 224

Its area is 224.

Answer:

6

Step-by-step explanation:

Answer:

x = 56

y = 124

z = 56

Step-by-step explanation:

The 124° angle and y° are vertical angles. vertical angles are congruent. they have equal measures.

y = 124

Angles 124° and x° form a linear pair. Angles in a linear pair are supplementary. Their measures add to 180°.

124 + x = 180

x = 180 - 24

x = 56

Angles x° and z° are vertical angles.

z = x = 56

Answer:

x = 56

y = 124

z = 56

40 percent of Marley's attempts were strikes, when  Marley rolled 28 strikes out of 70 attempts.

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage. A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.

Given,

28 strikes rolled by Marley

Total attempts = 70

For percentage,

28/ 70 × 100%

0.4 × 100%

40%

40 percent of Marley's attempts were strikes, when Marley rolled 28 strikes out of 70 attempts.

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3(x-4)+5=2(x-3)+4

3x-12+5=2x-6+4

3x-7=2x-2

x-7=-2

x=5

Here is the two column proof:

     Statement                                        Reason                                              

Answer:

Below

Step-by-step explanation:

180° rotation (clockwise  OR counterclockwise)

Reflection across y axis would put the diagram in Q IV

90 degree rotation CCW   would also be in Q IV

Translation R and up would  be more centered around the origin

Answer:

b. 0.08x + 20

Step-by-step explanation:

its B because the price goes up $40 every 500 KW's so

40 divided by 500 = 0.08

The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

From the graph we have, (500, 60), (1000, 100), (1500, 140) and (2000, 180).

We know that, slope of a line is Slope=(y2-y1)/(x2-x1)

= (100-60)/500

= 40/500

= 0.08

Substitute m=0.08 and (x, y)=(500, 60) in y=mx+c, we get

60=0.08(500)+c

60=40+c

c=20

Substitute m=0.08 and c=20 in y=mx+c, we get

y=0.08x+20

The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.

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Answer:

7.62 units C

Answer: I believe it would be 55 but It would help if it says what kind of triangle it is.

Step-by-step explanation:

Answer:

The answer is 91°

Step-by-step explanation:

In any triangle, the sum of all angles is equal to 180°

So,

35° + 54° + x = 180°

x = 180 - 89

x = 91°

Thus, The third angle is 91°

The vertex and range of y = |x + 1| + 3 will be (−1, 3); 3 ≤ y < ∞ respectively.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

You may get the vertex of y = |x + 1| + 3 as follows.

Where the absolute values are zeros are the vertex points of the absolute value function.

|x + 1| = 0

x + 1 = 0

x = -1

Substitute the value into an original function,

y = |-1 + 1| + 3

y= 0 + 3

y = 3

As a result, the vertex is at (-1, 3)

Remember that the domain is specified in the range of (-∞, ∞) while determining the range.

Given that |x + 1| ≥ 0 , (absolute value is always 0 or positive)

The result of adding 3 to the inequality's two sides is

|x + 1| + 3 ≥ 3

But since |x+1| + 3 is identical to f(x) = y, we have y = f(x) 3, which means that the range is specified for all values larger than 3.

So the range is 3 ≤ y < ∞

Thus,the vertex and range of y = |x + 1| + 3 will be (−1, 3); 3 ≤ y < ∞ respectively.

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The time the Road Runner been running is 7.3 minutes

From the question, we have the following parameters that can be used in our computation:

Roadrunner speed = 72mph

Time for repair = 15 minutes

Speed = 220mph

Represent the time the Road Runner been running with x

The speed is calculated using

Speed = Distance/Time

So, we have the following representations

Roadrunner speed = Distance/Time

Wile Coyote speed = Distance/Time

This gives

72 = Distance/(15 + x) -- for the roadrunner

220 = Distance/x for the Wile Coyote

So, we have

Distance = 72(15 + x)

Distance = 220x

Substitute the known values in the above equation, so, we have the following representation

220x = 72(15 + x)

Open the brackets

220x = 1080 + 72x

Evaluate the like terms

148x = 1080

So, we have

x = 7.3

Hence, the minutes is 7.3 minutes

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Answer:

the answer is  87!

Answer: 6561

Step-by-step explanation: 6+3=9

9^4 = 9*9*9*9 = 81 * 81 = 6561

The Number of kids in the fair is x + 12

A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

According to the given information

Let x be the variable

Let the number of adults in the fair = x

Number of kids in the fair is 12 more than the adults

So

Number of kids in the fair = 12 + Number of adults in the fair

                                           = 12+x

Hence

The Number of kids in the fair is x + 12

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Answer: 5x= 25

Step-by-step explanation:

Answer:  The correct answer is A. 5x = 25

Step-by-step explanation:

Add the equations:

2x - 3y = -1

3x + 3y = 26

Add the like terms:

2x + 3x = 5x

3y + -3y = 0

26 + -1 = 25

The resulting equation:

5x = 25

Answer:

We can use the point-slope formula to find the equation of the tangent line. The point-slope formula is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line. To find the equation of the tangent line, we need to find the slope of the line and a point on the line.

To find the slope of the line, we can use the definition of derivative. The derivative of a function f(x) at a point x0 is defined as:

f'(x0) = lim(h->0) (f(x0 + h) - f(x0))/h

In our case, the function f(x) is given by f(x) = x^2 - 5, and the point x0 is -2, so we have:

f'(-2) = lim(h->0) (f(-2 + h) - f(-2))/h

Substituting the value of the function f(x) = x^2 - 5, we get:

f'(-2) = lim(h->0) (((-2 + h)^2 - 5) - ((-2)^2 - 5))/h

Simplifying the expression, we get:

f'(-2) = lim(h->0) (h^2 - 4h)/h

Since the limit is defined as h approaches 0, we can drop the h from the denominator since it will become insignificant in the limit:

f'(-2) = lim(h->0) (h^2 - 4h)

Now we can evaluate the limit as h approaches 0:

f'(-2) = lim(h->0) h^2 - 4h

In the limit, h^2 becomes 0, so we are left with:

f'(-2) = lim(h->0) - 4h

Since the limit is defined as h approaches 0, the value of the limit is simply -4 times 0, which is 0. Therefore, the slope of the tangent line is 0.

Now that we know the slope of the tangent line, we need to find a point on the line. We are told that the line passes through the point (-2, f(-2)) on the function f(x) = x^2 - 5. Substituting the value of the function, we get:

(-2, f(-2)) = (-2, (-2)^2 - 5) = (-2, -9)

So the point on the line is (-2, -9).

We now have the slope and a point on the line, so we can use the point-slope formula to find the equation of the line. Substituting the values into the point-slope formula, we get:

y - (-9) = 0(x - (-2))

Simplifying, we get:

y = -9

Therefore, the equation of the tangent line that passes through the point (-2, -9) with a slope of 0 is given by y = -9.

n+23=33 - This equation shows this relationship.

Let, one number be = n

another number is =23

The sum of two numbers is = 33

The sum is the result of adding two or more numbers in mathematics. It is an essential and valuable concept in mathematics. The numbers which are to be added are called addends.

In short, some can be defined as a way by which all things can be put together. We can show an equation of a sum horizontally or vertically.

Horizontal Addition :

     59+37=96

Vertical addition:

    59

   +37

   = 96

Therefore, the equation is:  n+23 =33

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