xplain in words and write mathematically how the fundamental theorem of calculus is used to evaluate definite integrals.

The rate at which the water flow from the given volume is 21.72 in³/sec

To find the rate at which water is being drained from the container, we first need to find the rate at which the water level is falling and then use that to calculate the volume of water being drained per unit of time.

We know that the surface level is falling at a rate of 0.9 inches per second and that the container has the shape of an inverted right circular cone. The volume of a cone is given by the formula:

V = (1/3) * π * r^2 * h

Where V is the volume, π is pi (approximately 3.14), r is the radius of the base, and h is the height of the cone.

We can use this formula to find the volume of the container when the water level is 8 inches. The radius at this point is 6 * (8/10) = 4.8 inches and the height is 8 inches.

V = (1/3) * π * (4.8 inches)^2 * 8 inches = 193.02 inches³

Now that we know the volume of the container when the water level is 8 inches, we can use the rate at which the water level is falling (0.9 inches per second) to find the rate at which the water is being drained.

The rate at which water is being drained = rate of change of volume / rate of change of height = dV/dt = dV/dh * dh/dt = -dV/dh * dH/dt

Where dV/dh is the derivative of volume with respect to height, dH/dt is the rate of change of height.

-dV/dh = -(1/3) * π * (4.8 inches)^2 = -24.13 in³

dH/dt = -0.9 inches/sec

The rate at which water is being drained = -dV/dh * dH/dt = -24.13 * -0.9 inches/sec = 21.72 in³/sec

So the rate at which water is being drained from the container is 21.72 in³/sec

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Answer:

59.036

Step-by-step explanation:

tanΘ = opposite/adjacent

Θ =tan⁻¹(opposite/adjacent)

tan⁻¹(10/6) - 59.03624347

728 kilograms of sugar is used in this month.

percentage, a relative value indicating hundredth parts of any quantity.

Given that a bakery used 30% more sugar this month than last month.

Let us convert 30% to decimal.

Divide 30 by 100

30/100=0.3

the bakery used 560 kilograms of sugar last month we have to find the amount of sugar used this month.

Now multiply 30% of 560

0.3×560

168.

So now 560+168=728 is the amount of sugar used this month.

Hence, 728 kilograms of sugar is used in this month.

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They move off together with a speed of 1/3 v,The mass of the boxcar is m/3 (V₁ - V₂)².

A body's mass is an inherent quality. Prior to the discovery of the atom and particle physics, it was widely considered to be tied to the amount of matter in a physical body.

in Kinetic energy 4 system, the

K = Kf-Ki

K = 1 (Mcar + Mtruck) Vp ² + mcarv₁_ J 2 2 + Mtruck V2 2 2

K = +(m+2m) (V₁+2√2)² +mv₁² - 1 x 2m v₂ ² 2 2 9

K m (v, ² + 4 √₂ ² + AV₁ V2 ) - { mv, ² - tn v₂ 2 2 6

K = m (V₁²+ 4V₂² + 4 V₁ V2 -1/3V, ² - 6V, ²) /6.

K = m/6 (4V₁V2.-2V₁2-2√22)

k = + m/3 (V₁ - V₂)²

They move off together with a speed of 1/3 v, The mass of the boxcar is m/3 (V₁ - V₂)².

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Answer:

Step-by-step explanation:

36

(

x

+

3

)

2

(

x

−

3

)

2

The Numerical Expressions answers are shown below:

Integers come in three types:

Given:

1. 7-6+ 5

= 7 -1

= 6

So, the value of 7-6+ 5 is 6.

2. 31 +19 -8

= 31 + 11

= 42

So, the value of 31 +19 -8 is 42.

3. 64-8+21

= 56 + 21

= 77

So, the value of 64-8+21 is 77.

4. 17+34-2

= 51-2

= 49

So, the value of 17+34-2 is 49.

5. 28+ 89 -67

= 117-67

= 50

So, the value of 28+ 89 -67 is 50.

6. (8+1) x 12- 13

= 9 x 12 -13

= 108 - 13

= 95

So, the value of (8+1) x 12- 13 is 95.

7. 63/9 +8

= 7 +8

= 18

So, the value of 63/9 +8  is 18.

8. 5 x 6 -(9-4)

= 5x 6 - 5

= 30- 5

= 25

So, the value of 5 x 6 -(9-4)  is 25.

9. 13x 4 -72 /8

= 13 x 4 - 9

= 52- 9

= 43

So, the value of 13x 4 -72 /8  is 43.

10. 16/2 + 8 x 3

= 8 + 8 x 3

= 8+24

= 32

So, the value of 16/2 + 8 x 3  is 32.

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Diya could earn 72 marks out of 80 after getting the extra credits.

Teachers employ extra credit for a variety of reasons. For example, it may be felt that students who are highly capable may benefit from an additional challenge that might not be suitable as required work for all students. Extra credit may also be used as a way to allow a student to improve their grade after a weak performance earlier in a course. In both of these cases, extra credit can promote differentiated instruction by factoring in optional work in the assessment of student performance.

Given here: Diya scores 36 out of 80 on a test.

Also, her teacher gives her extra credit with which she could double her marks.

If Diya doubles her marks then her total marks would be 72

Therefore the increase in her marks is 72-36=36

She could earn another 36 credits.

Thus her score after the extra credit is equal to 72

Hence, Diya could earn 72 marks out of 80 after getting the extra credits.

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The equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.

What is the slope intercept?

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The line passing through the point (8, 4) and having a slope of 0 is a horizontal line which is parallel to the x-axis. The slope (m) of this line is 0.

The point-slope form of this line would be:

(y - 4) = 0(x - 8)

Simplifying this, we get:

y = 4

Hence, the equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.

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The quadratic function y = 7(x + 1)² + 1 in standard form is y = 7x² + 14x + 2.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The given quadratic function is -

y = 7(x + 1)² + 1

Solve the equation to get the standard form.

First solve using the formula (a + b)² = (a² + 2ab + b²) -

y = 7(x + 1)² + 1

y = 7(x² + 2x + 1) + 1

Now, open the brackets -

y = 7x² + 14x + 1 + 1

Now, add the like terms -

y = 7x² + 14x + 2

Therefore, the value is obtained as 7x² + 14x + 2.

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The additional fact that would prove that

EFGH is a square is D) IFLEH ~ LFGH.

A quadrilateral is a plane figure with four edges and four corners, also known as vertices. The quadrilateral's four vertices or corners all have angles.

If a quadrilateral is a rhombus, that means opposite sides are congruent, but it does not mean that all angles are congruent. In order to prove that EFGH is a square, we need to show that all angles are congruent. The statement "IFLEH ~ LFGH" implies that all angles in the quadrilateral are congruent, since it states that opposite angles are congruent, which is one of the defining characteristics of a square. Therefore, statement D is the correct answer.

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In a plane, intersecting lines are any two or more lines that cross each other. The point of intersection is the common point shared by all intersecting lines.

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If Anthonia and Zahra compete at the same event, the probability that Anthonia will successfully land her jump and Zahra will not land hers is 18.33%.

We describe probability as the chance or likelihood that an expected event occurs when there are many possible outcomes.

Probability lies between one and zero when it is not 100% certain or uncertain.

The probability that Anthonia lands her triple axel jump = 33.33%

The chance that Anthonia does not land her jump = 66.67% (1 - 33.33%)

The likelihood of Zahra landing her jump successfully = 45%

The odds that Zahra will not successfully land her jump = 55% (1 - 45%)

The probability that Anthonia lands successfully while Zahra does not = 18.33% (33.33% x 55%)

Thus, Anthonia has the chance of winning Zahra at 18.33%.

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Answer:

As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.

19+m=38

If you want to solve the equation, just subtract 19 from both sides.

19+m=38

m=19

The movie theater will have 50 shows in 6 days

To find the total number of shows in 6 days, we need to calculate the number of shows for each type of day (4 days per week with 7 shows per day and 2 days per week with 11 shows per day) and then add them together.

First, let's calculate the number of shows for the 4 days per week with 7 shows per day:

4 days per week x 7 shows per day = 28 shows per week

Next, let's calculate the number of shows for the 2 days per week with 11 shows per day:

2 days per week x 11 shows per day = 22 shows per week

Now, we can add the number of shows for each type of day together to find the total number of shows in 6 days:

28 shows per week + 22 shows per week = 50 shows in 6 days

We used multiplication to calculate the number of shows per week for each type of day (by multiplying the number of days by the number of shows per day) and then added the two results together to find the total number of shows in 6 days.

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Kimiyo would make $987 in a work week if she sold $4,800 worth of merchandise.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Kimiyo earns a weekly salary of $675 plus a 6.5% commission on sales at a gift shop.

She sold $4,800 worth of merchandise.

That means,

the commissioned amount = 4800 x 6.5 /100

The commissioned amount = $312

In a week,

Kimiyo's total earning is,

= $675 + $312

= $987

Therefore, $987 is the total salary.

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Since it has no impact on the result or solution of the problem, assuming that a > d does not reduce the generality of the statement. If a > d, the issue can be solved by simply swapping the values of a and d.

It makes no difference to the problem whether an is more or less than d because we are presuming that each integer is distinct. Furthermore, by supposing that a > d, the problem's variables can be arranged consistently, making it simpler to comprehend and resolve. As a result, making the assumption that a > d does not reduce the generality of the solution because the problem remains the same and the assumption may be readily changed if necessary.

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After 180 miles both the cars' tanks contain same amount of gas.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Given that, Ann and Leila are driving separate cars to New York. They begin the trip with full gas tanks.

From the given  graph,

After 360 miles Ann's car has 2 gallons of gas.

After 180 miles both the cars' tanks contain same amount of gas.

When they travelled less than 180 miles, Leila's car has more gas.

Therefore, after 180 miles both the cars' tanks contain same amount of gas.

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Answer:

honestly, I got no idea. I can tell you though - go us Desmos kid. it'll help you more than any person in this platform.

don't thank me

Step-by-step explanation:

Desmos

use Desmos

a) The z-score for a structure costing $2,300 is given as follows: -0.67.

b) The z-score for a structure costing $4,900 is given as follows: 1.5.

c) The interpretation of each z-score is given as follows:

d) The structure would have an unusual price, as the z-score has an absolute value greater than 2.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 3100, \sigma = 1200[/tex]

For item a, the z-score is then given as follows:

Z = (2300 - 3100)/1200

Z = -0.67.

For item b, the z-score is then given as follows:

Z = (4900 - 3100)/1200

Z = 1.5.

For the price of $13,000, the z-score is given as follows:

Z = (13000 - 3100)/1200

Z = 8.25.

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The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°

What exactly is the degree formula?

Yes, we can use the radian-to-degree formula to convert a negative radian to a degree. Degrees = Radians 180 / is the formula, and it may be used for both positive and negative values. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees).

These are referred to as parallels. A circle of latitude is an imaginary ring that connects all places that share a parallel. The Equator is the 0 degree latitude line. Each parallel is one degree north or south of the Equator, with 90 degrees north and 90 degrees south respectively.

Hence, The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°

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Answer:

y = (-5/4)x - 19

Step-by-step explanation:

Given information,

→ Slope(m) = -5/4

→ Point = (-8, -9)

→ y-intercept = b

The slope-intercept form is,

→ y = mx + b

Now the y-intercept will be,

→ y = mx + b

→ -9 = (-5/4)(-8) + b

→ -9 = 10 + b

→ b = -9 - 10

→ [ b = -19 ]

Then the required equation is,

→ y = mx + b

→ [ y = (-5/4)x - 19 ]

Hence, this is the equation.

Answer:

You are correct

Step-by-step explanation:

You are correct sir. They want the answer in feet, so everything on that triangle has to be converted into feet.

There are 12 inches in a foot. If we do 108/12 we get 9 feet.

Answer: To find the price of the 3-year old car, we need to determine how much less it is than the new car, which is 23% of the price of the new car.

We can start by finding the value of 23% of the price of the new car, which is: $12,400 x 0.23 = $2,832

Now we know that the price of the 3-year old car is $2,832 less than the price of the new car. To find the price of the 3-year old car, we subtract $2,832 from the price of the new car: $12,400 - $2,832 = $9,568

So the price of the 3-year old car is $9,568.

Step-by-step explanation:

Answer:

1.44

Step-by-step explanation:

11.52/8=1.44

the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.

Option (C) is CORRECT.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, that the coordinates of the vertices of a  quadrilateral composed in the first quadrant of the coordinate plane are (0,0) (a, b), (a + c, b), and (c, 0).

We are to select the most accurate classification of the quadrilateral.

Let the coordinates of the vertices of the quadrilateral be P(0,0), Q(a, b), R(a + c, b), and S(c, 0).

The lengths of the sides are calculated using the distance formula as follows :

PQ = √(a² + b²)

QR = √(a +c -a)² + (b-b)² = √c² = c

RS =  √(a² + b²)

SP = c

So, the opposite sides are equal in length.

And, the slopes of the sides are calculated as follows :

The slope of PQ(m₁) = (b-0)/(a-0)

The slope of QR(m₂) = (b-b)/(c-a-c) = 0

The slope of RS(m₃) = 0-b/(c-a-c) = 0

The slope of SP(m₄) = (0-0)/(0-c) = 0

So, the slopes of the opposite sides are equal but:

m₁ *m₂ = 0 ≠ -1

m₃ *m₄ = 0 ≠ -1

Therefore, the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.

Option (C) is CORRECT.

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The equation when making x the subject is X = -2 - 6y

To do this, we would have to take the values that are in the left hand side to the right hand side. When we do this, the signs on the left hand side would have to change

X+6y=-2

we have to take +6y to the right hand side.

When the positive sign crosses the equal sign it becomes negative

X = -2 - 6y

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X+6y=-2 show ur work make x the subject

Answer:

7/12 of salt.

1/4 + 1/3 =

1/3 + 1/4 =

4/12 + 3/12 = 7/12.

Step-by-step explanation:

Hope it helps! =D