Explain the Fundamental Theorem of Calculus Part 1 (the antiderivative part) and Part 2 (the evaluation part). Then compare each part and specify when one part would be used over the other. Give a real-world example that involves Part 2 of the Fundamental Theorem of Calculus.
I already have an explanation for each separate part but I need help with examples of comparing the two parts, when each part should be used over the other, and a real-world example.
Thanks!

The actual length of the tree based on the information is 19 inches.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches.

The actual length will be:

= 4.75 × 4

= 19 inches

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Complete question

Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches. What is the actual length of the tree?

The blanks in the equation are filled as below

5 1/8 = 4 + 1 + 1/8 = 4 + 1/8 8 + 1/8 = 5 1/8

To fill the blanks the equation is written completely in figures

5 1/8 = 4 + 1 + 1/8 = 4 +   8 + 1/8 =  

From the knowledge of equality to maintains a true equation the last blank should be equal to 5 1/8.

With this information, we use addition operation to solve for the first blank as follows.

let the first blank be x

4 +   8 + 1/8 = 5 1/8

4 + x * 8 + 1/8 = 5 1/8

4 + 8x + 1/8 = 5 1/8

collection like terms

8x = 5 1/8 - 4 - 1/8

8x = 1

divide both sides by 8

x = 1/8

the blanks are 1/8 and 5 1/8

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If you solve 3x - 2y = -5 for slope-intercept form, you'd have:

     y = 3/2 x + 5/2

If you solve 3x - 2y = 8 for slope-intercept form, you'd have:

     y = 3/2 x - 4

Since the slopes are the same, but the y-intercepts are different, these lines are parallel.

The change in dollars at the end of the week is - $5

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

Amount spent = $45

Amount gained = $55

Amount spent on gas = $15

The change is then calculated as

Change = Amount gained - Amount spent - Amount spent on gas

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

Change = 55 - 45 - 15

Evaluate

Change = -5

Hence, the change is a deficit of $5

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Answer: [tex]\triangle TUS \cong \triangle QRP[/tex]

Step-by-step explanation:

When naming congruent triangles, corresponding vertices must have the same positions in the names of the triangles.

the value of theta in the given complex expression is equal to 16°.

Given, a number. [tex]rcis\theta, is[/tex] expressed by.

cis75° + cis83° + cis91°+.... + cis147°.

we have to find the value of angle in degrees.

The function cisA is a shorthand way of writing the equivalent expression cisA=cosA+i sinA

By definition: CisA=CosA+iSinA

This form simplifies complex arithmetic and allows for the study of complex analysis, as well as reduces the workload in writing the expressions.

now, we have to find the sum of the given expressions.

[tex]cis75+cis83+cis91+...+cis147 as, cis\theta=e^{i\theta}[/tex]

[tex]e^{75i}+e^{83i}+e^{91}+....+e^{147i}\\\\e^{\frac{75\pi}{180} }+e^{\frac{83\pi}{180} }+.....+e^{\frac{147\pi}{180} }[/tex]

on using geometric sum of the series we get,

[tex]Sum=\frac{e^{\frac{75i\pi}{180}}(1-e^{\frac{72i\pi}{180} ) }}{(1-e^{\frac{8i\pi}{180} })}\\ \\\theta=16[/tex]

the value of theta of the angle be 16 degree.

the complete question is.

The number cis 75 + cis 83 + cis91 +...+ cis 147 is expressed in the form r cis(theta), where 0 <= theta < 360.

Find theta in degrees.

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Expression that can be used to find -6.3 x -4.2 are

(1): -4.7 - 2.3x + 0.5 - 4x

(2):-5.3x-4.2-x

(3):-3.4-6.3x-0.8

Expression can be defined  as a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction and multiplication

By Collecting like terms and adding the answer I get -6.3x - 4.2

(1):-4.7-2.3x+0.5-4x

Collect like terms

-2.3x-4x-4.7+0.5

-6.3x-4.2

(2):-5.3x-4.2-x

Collect like terms

-5.3x-x-4.2

-6.3x-4.2

(3): -3.4-6.3x-0.8

Collect like terms

-6.3x-3.4-0.8

-6.3x-4.2

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The option are:

-4.7 - 2.3x + 0.5 - 4x

-5.3x - 4.2 - x

-3.4 - 6.3x - 0.8

-6.2x - 4.2

-4.2x - 6.3

-3.7 - 5.3x + 0.5

multiple choice

Answer:7

Step-by-step explanation:

Answer:  ≈ 174.01

Thus, The Sky Scraper  ≈  174.01

Step-by-step explanation:

From his eye, which stands 1.55 meters above the ground, Tyler measures the angle of elevation to the top of a prominent skyscraper to be 57∘

∘. If he is standing at a horizontal distance of 112 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

1 - Draw Diagrams, Label Knowns:

Unknowns: X

2 - Identify: OPPOSITE, ADJACENT, HYPOTENUSE

3 -  WHAT FUNCTION USES THE OPPOSITE AND THE ADJACENT?

SOH - CAH - TOA

NOW SHOWING WORK:

tan 57 = opposite/adjacent =  x/112

tan 57 = x/112

tan 57/1  = x/112

112 tan 57 = x         ( Cross Multiply)

x = 172.464875    (Now, type into the calculator)

So, Now we ADD:

1.55, the distance from the ground to his eye.

172.464875  +   1.55  =  174.014875

≈ 174.01     (Round to The Nearest HUNDREDTH)

Thus, the Sky Scraper is ≈ 174.01 meters tall.

So, your answer would be :  

Sky Scraper  ≈  174.01

Hope I have explained it and helped you in your studies!

The height of the skyscraper is given by H = 174.01 m

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

We can start by drawing a right triangle, where the horizontal distance from Tyler to the base of the skyscraper is one leg, the height of the skyscraper is the other leg, and the line of sight from Tyler's eye to the top of the skyscraper is the hypotenuse.

Then we can use trigonometry to solve for the height of the skyscraper.

Let the height above the ground from his eye = 1.55 m

Now , the angle of elevation θ = 57°

The horizontal distance from the base of the skyscraper = 112 m

Now , from the trigonometric relations ,

tan θ = opposite / adjacent

So , tan 57° = x / 112

Multiply by 112 on both sides , we get

x = 172.46 m

Now , the total height of the skyscraper = 172.46m + 1.55 m

So , height H = 174.01 m

Hence , the skyscraper has a height of 174.01 m

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The three true statements are:

The standard form of the equation is (x – 1)² + y² = 3.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is the center of the circle?

A circle is named by the point in the center. A radius is a line segment from the center of the circle to the edge. A diameter is a line segment that passes through the center of a circle.

The true statements are:

The standard form of the equation is (x – 1)² + y² = 3.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Given an equation of x2 + y2 – 2x – 8 = 0, we can make the following observations:

We can complete the square to get the equation in standard form. (x – 1)² + y² = 3². This is true statement.

The center of the circle is (1,0) which is on the x-axis, this statement is true.

The radius is 3 units, which is the same as the radius of the circle x² + y² = 9 (3²). This statement is true.

The center of the circle does not lie on the y-axis as its x-coordinate is not 0.

Hence, The three true statements are:

The standard form of the equation is (x – 1)² + y² = 3.

The center of the circle lies on the x-axis.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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There were 50 single tickets sold and 40 couples tickets were sold.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.

Let's call the number of single tickets sold "x". Then the number of couple tickets sold would be "y".

We know the total number of attendees is 130, so we can write the equation:

x + 2y = 130

We also know that the total revenue from the ticket sales is $24,000, so we can write another equation using the cost of the tickets:

200x + 350y = 24,000

We now have a system of two equations that we can solve for x and y then we get the values are:

x = 50 and y = 40

So, 50 single tickets were sold and 40 couples tickets were sold.

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Answer:

63

Step-by-step explanation:

the value of the difference between the terms increases by 4 as the series continues.

basically, this shows that the difference between 3 and 12 is 9, the difference between 12 and 25 is 13 (which is 4 more than 9), the difference between 25 and 42 is 17 (which is 4 more than 12), and so on.

using this pattern, all we have to do is find the next difference- the one between 42 and the missing term.

to do this, we take the previous difference, 17, and add 4. this gives us 21.

we then add 21 to 42 to get the next term: 63.

hope this helped, good luck!

Answer:m=-5/4

Step-by-step explanation: The formula for finding slope is y1-y2 / x1-x2 so when plugging in these coordinates, you get -3-(-8)/-6-(-2). When simplified -3-(-8) is 5 and -6-(-2) is -4, so the answer is -5/4. You can also switch the numbers so its -8-(-3) / -2-(-6) and still get the same answer.

The least certain measurement determines the certainty of the answer.

What guidelines apply when rounding sig figs?

(1) The final digit that is preserved is raised by one if the digit to be eliminated is greater than 5. As an illustration, 12.6 is rounded to 13.

                                      (2) The last digit that remains is left alone if the digit to be dropped is less than 5. As an illustration, 12.4 is rounded to 12.

Which of the following statements best describes the significant figures rule?

Use the following 3 principles to calculate how many significant figures are present in a number: The significance of non-zero digits is constant.

                                   A significant zero is one that comes in between two significant digits. ONLY the decimal part has any significance when there is a final zero or trailing zeros.

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Answer:

Step-by-step explanation:

The probability that ŕose will choose a science book first is 5/8 and the probability of the adventure book is 3/8

The rate of change of a function at a point is given by its derivative. To compare the rate of change of f(x) and g(x) at different points, we need to find the derivative of both functions and compare them.as explained below :

The derivative of f(x) = e^x is f'(x) = e^x

The derivative of g(x) = x^4 is g'(x) = 4x^3

Now we need to compare the two derivatives to find on which intervals the rate of change of f(x) is greater than the rate of change of g(x). To do this, we will find the point of intersection between the two functions and compare them.

e^x = 4x^3

Taking the natural logarithm of both sides we get:

x = ln(4x^3) / ln(e)

Approximating we get x ≈ 0.816 and x ≈ 1.430 and x ≈ 8.613

For x < 0.816, e^x < 4x^3, so the rate of change of f(x) is smaller than the rate of change of g(x)

For x > 8.613, e^x > 4x^3, so the rate of change of f(x) is greater than the rate of change of g(x)

Between 0.816 < x < 1.430 and 1.430 < x < 8.613, e^x = 4x^3, so the rate of change of f(x) is equal to the rate of change of g(x).

So the answer is (D) (0.816, 1.430) and (8.613)

Note that the answer (B) (0.831) and (&.384) is not possible as the point of intersection is a number and not an interval and the answer (A) (0.831, 7.384) is not correct as the point of intersection is 1.430 and 8.613 not 0.831 and 7.384

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The number of beads used for Michelle necklace is 70.

Michelle made a bead necklace that was 13 inches long.  The length of the necklace, in inches, is equal to 3 added to one-seventh the number of beads, b.

The number of beads Michelle used for her necklace can be calculated as follows:

number of beads she used for her necklace  = b

Therefore,

13 = 3 + 1 / 7 b

13 - 3 = 1 / 7 b

10 = 1 / 7 b

cross multiply

b = 10 × 7

b = 70

Therefore,

number of beads she used for her necklace  = 70

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Answer:

19(42 + 58)

Step-by-step explanation:

19(100)

1900

Population Mean is the statistical indicator to its designation or nomenclature.

Therefore,

The formula for the population mean, which is the population's average score on a certain variable, is:  μ = ( Σ Xi ) / N. The population mean is represented by the symbol "."

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Yes, BD is the bisector of ∠ABC.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is that ABC is straight angle. BD is drawn so that two adjacent angles are created. It is given that  m ∠ABD = 22x - 9 and m∠ CBD = 4x + 7.

For BD to be the bisector of ∠ABC, ∠ABD and m∠ CBD should be equal. So  we can write -

22x - 9 = 4x + 7

22x - 4x = 16

18x = 16

x = 8/9

Now, we can write -

m ∠ABD = 22x - 9 = 22 x 8/9 - 9 = 10.55°

m ∠ABD = 10.55°                                                    ...... (1)

m ∠CBD = 4x + 7 = 4 x 8/9 + 7 = 10.55°

m ∠CBD = 10.55°                                                    ...... (2)    

m ∠ABD = m ∠CBD                                                

Yes, BD is the bisector of ∠ABC.

Therefore, yes, BD is the bisector of ∠ABC.

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9 students preferred learning only through videos.

Inclusion-exclusion is a principle used in counting to find the total number of elements in a union of sets by subtracting the elements that are counted multiple times and adding back in the elements that are not counted at all.

The number of students who preferred learning only through videos is 17.

This can be found by using the principle of inclusion-exclusion:

35 students liked to learn through videos

14 students liked to learn through listening and videos

5 students liked all three channels

So, 35 - 14 + 5 = 26 students liked to learn through videos and listening

Therefore, 35 - 26 = 9 students preferred learning only through videos.

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Answer:

Length of each side = 3.055

Step-by-step explanation:

The relationship between altitude h and side a of an equilateral triangle is

[tex]h = \dfrac{\sqrt{3} }{2} a\\\\\\\rightarrow a = \dfrac{ 2h}{{\sqrt{3} }}\\\\[/tex]

Given h = √7.

we get

[tex]a = \dfrac{2\sqrt{7} }{\sqrt{3} }\\\\a = 2 \sqrt{\dfrac{7}{3}}\\\\a = 2\times 1.5275\\\\a = 3.055\\\\[/tex]

Due to weaker aggregate demand, the negative demand shock will cause the aggregate demand curve to move to the left.

Result: A lower output and price level.

Part B:

Explanation of part B

Result of negative supply shock , aggregate demand falls cause the lower demand for the money . This will lead towards the left shift in money demand.(MD 1 TO MD 2(R1 TO R2)

Part c:

Interest rate and bond price are related inversely . Due to negative demand shock the interest rate falls down. vice-versa bond price will rise.

Part D:

Due to fall in the interest rate central banks will follow contractionary fiscal policy which will increase interest rate and reduce the money supply.

Part E :

If the central banks need to increase the money supply by $80 billion. Central banks need to buy securities in exchange of cash .This will Raise the money supply.

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The probability of a random variable X with a uniform distribution being greater than 0.49 can be calculated using the formula P(X > 0.49) = 1 - P(X ≤ 0.49).

Since X has a uniform distribution, it means that the probability of any number between 0 and 1 occurring is the same. Therefore, P(X ≤ 0.49) = 0.49.

The probability of X being greater than 0.49 can be calculated using the formula for uniform distributions, which is P(X>a) = 1 - P(X≤a). In this case, P(X>0.49) = 1 - P(X≤0.49). The probability of X being less than or equal to 0.49 can be calculated by multiplying the probability of each individual outcome (since they are all equally likely) by the number of outcomes that satisfy the condition .Substituting this into the formula to calculate P(X > 0.49), we get P(X > 0.49) = 1 - 0.49 = 0.51. Therefore, the probability of a random number generated being greater than 0.49 is 0.51.

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The level curves of the function h(x,y) = 2x-y at c = 0, -2, 2 are y = 2x, y = 2x + 2, y = 2x - 2 respectively.

A level curve (also called a contour line or an isocline) of a function is a curve that represents all the points where the function has a constant value. To find the level curve of a function at a given value of c, we need to set the function equal to c and solve for the variables.

For h(x,y) = 2x-y, we can find the level curves at c = 0, -2, 2 by setting the function equal to c and solving for x and y:

The level curves of h(x,y) = 2x-y at c = 0, -2, 2 are the lines y = 2x, y = 2x + 2, y = 2x - 2 respectively. Each line represents a different value of c and separates the domain of x and y into different regions where the function takes on that constant value.

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The TRUE statements about the inequality y ≤ 150x - 3100 are:

Inequality refers to a mathematical statement claiming the inequality of two or more mathematical expressions.

The following types and inequality symbols represent inequalities:

Check:

Ordered pairs (40, 2900)

y ≤ 150x - 3100

y ≤ 150(40) - 3100

y ≤ 6,000 - 3100

y ≤ 2900

Thus, the true statements about this inequality are Options A and E.

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Answer:

x + 2  (Choice D)

Step-by-step explanation:

The two polynomials are
P1 = 4x² + 5x - 4  

and

P2 = 4x² + 4x - 2

P1 - P2

==>  (4x² + 5x - 4 ) -  (4x² + 4x - 2)

Expanding brackets we get

==> 4x² + 5x - 4 - 4x² - 4x + 2        (signs inside the second parentheses are    

                                                 reversed because of the - sign preceding it)

Group similar terms and add the coefficients

==> (4x² - 4x²) +(5x - 4x) +(-4 + 2)

==> 0 + x + 2

==> x + 2  (Choice D)

Answer:

h = 18 in.

Step-by-step explanation:

Both safes are in the shape of a rectangular prism

The volume of a rectangular prism = L X w X H

where L = length, W = width and H = height

Safe A has volume 18 x 15 x 24

Safe B has volume 20 x 18 x h

Both volumes are equal and we have to find h

Equating both expressions

20 x 18 x h = 18 x 15 x 24

Dividing by 18 on both sides will get rid of the 18 in the product

(20 x 18 x h)/18 = (18 x 15 x 24)/18

20h = 15 x 24

20h = 360

h = 360/20

h = 18 in.

Answer:

52°

Step-by-step explanation:

The angle of depression is 90 - angle of elevation

So angle of depression = 90 - 38 = 52°