Which term refers to slope?

The area of the region that lies inside the circle r=3sinΘ and outside the cardioid r=1+sinΘ is 0.6323

To find the area of a region in polar coordinates, we can integrate 1/2 r² dΘ over the desired interval of Θ. The factor of 1/2 is included because the area element in polar coordinates is 1/2 r² dΘ, as opposed to the dx dy element in Cartesian coordinates.

First, we need to find the points of intersection between the circle and the cardioid. To do this, we set the two equations equal to each other:

3sinΘ = 1+sinΘ

2sinΘ = 1

sinΘ = 1/2

Θ = π/6 or 5π/6

Now we can set up our integral. We want to integrate 1/2 r² dΘ over the interval π/6 ≤ Θ ≤ 5π/6. We will break this up into two integrals, one for the area inside the circle and one for the area inside the cardioid but outside the circle.

For the area inside the circle, we integrate from 0 to π/6 and from 5π/6 to π:

∫[0 to π/6,5π/6 to π] (1/2) (3sinΘ)² dΘ

= (9/2) ∫[0 to π/6,5π/6 to π] sin²Θ dΘ

Using the double angle identity, sin²Θ = (1-cos2Θ)/2, we can simplify this to:

(9/4) ∫[0 to π/6,5π/6 to π] (1-cos2Θ) dΘ

= (9/4) [Θ - (1/2)sin2Θ] [π/6 to 5π/6]

= (9/4) [(5π/6 - π/6) - (1/2)(sin(5π/3)-sin(π/3))]

= (1/2) [(2/3) + (√(3)/2) - (-√(3)/2 - 2/3) + (1/3)(-2-√(3))] - (9/2) [(2/3) - (1/2)(-√(3)-√(3)/2)]

= (1/2) [(4/3) - (1/3)√(3)] - (9/2) [(2/3) + (√(3)/2)]

= -19/24 - (15/4)√(3)

Finally, we can add the two areas together to get the total area:

Total area = area inside circle - area inside cardioid but outside circle

= (9/8) + (9/4)√(3) - (-19/24) - (15/4)√(3)

= 2/3 - (3/4)√(3) = 0.6323

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Answer:

B

Step-by-step explanation:

statistical should have data and numbers that can calculate

ex Mean, Med, Mode

Answer:

A) How may students are in your math class?

This is because statistics are collecting How Many of something there is. If a question said: "How many people in your class are 5'2" that would be statistical.

Answer:

To find the area of the shaded sector, we need to first find the area of the entire circle and then multiply it by the fraction of the circle that the sector represents.

The formula for the area of a circle is:

A = πr²

where A is the area and r is the radius.

In this case, the radius is given as 15 ft, so we can plug it into the formula:

A = π(15)²

A = 225π

The area of the entire circle is 225π square feet.

The sector is 332 degrees out of 360 degrees, so the fraction of the circle that the sector represents is:

332/360 = 0.9222

To find the area of the shaded sector, we multiply the area of the entire circle by this fraction:

Area of sector = 0.9222 x 225π

Area of sector = 651.89 square feet (rounded to the nearest hundredth)

Therefore, the area of the shaded sector is approximately 651.89 square feet.

Step-by-step explanation:

The area of the shaded sector is approximately 651.89 square feet.

What is circle?

The circle is a geometric shape in two dimensions, defined as the set of all points in a plane that are equidistant from a given point, called the center. The distance between any point on the circle and the center is called the radius of the circle.

To find the area of the shaded sector, we need to first find the area of the entire circle and then multiply it by the fraction of the circle that the sector represents.

The formula for the area of a circle is:

A = πr²

where A is the area and r is the radius.

In this case, the radius is given as 15 ft, so we can plug it into the formula:

A = π(15)²

A = 225π

The area of the entire circle is 225π square feet.

The sector is 332 degrees out of 360 degrees, so the fraction of the circle that the sector represents is:

332/360 = 0.9222

To find the area of the shaded sector, we multiply the area of the entire circle by this fraction:

Area of sector = 0.9222 x 225π

Area of sector = 651.89 square feet (rounded to the nearest hundredth)

Therefore, the area of the shaded sector is approximately 651.89 square feet.

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Answer: -1

Step-by-step explanation: Plug 1 in as x. You get h(1)=-3(1)+2. If you solve this, it is h(1)=-3+2, or h(1)=-1

Answer:

\( \sf \: h(1) = - 1\)

Step-by-step explanation:

Given equation,

→ h(x) = -3x + 2

Now the value of h(1) will be,

→ h(x) = -3x + 2

→ h(1) = -3(1) + 2

→ h(1) = -3 + 2

→ [ h(1) = -1 ]

Hence, the value of h(1) is -1.

The system defined by the impulse response h(n) = 28(n+3) + 28n + 28(n-3) can be represented as h(n) = 28δ(n+3) + 28δ(n) + 28δ(n-3), where δ(n) denotes the unit impulse function.

In terms of causality, we can determine whether the system is causal by examining the impulse response. If the impulse response h(n) is non-zero only for n ≥ 0, then the system is causal. In this case, since the impulse response h(n) is non-zero for n = -3, 0, and 3, the system is not causal.

To determine the stability of the system, we need to examine the summation of the absolute values of the impulse response. If the summation is finite, the system is stable. In this case, we can calculate the summation as ∑|h(n)| = 28 + 28 + 28 = 84, which is finite. Therefore, the system is stable.

However, since the impulse response is given in the time domain and not in a closed-form expression, it is not possible to directly determine the frequency response without further manipulation or additional information.

Given the absence of specific frequency domain information or a closed-form expression for the frequency response, it is not possible to accurately represent the module and phase of the system H(e^ω) without further calculations or additional details about the system.

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Answer:

A is the correct one

Step-by-step explanation:

Differentiation is a process of finding the rate of change of a function with respect to its independent variable. The notation used to denote the derivative of a function f(x) with respect to x is f′(x) or dy/dx or y′.  

We have to differentiate the given expressions:(a) y = x2xDifferentiating both sides with respect to x, we gety' = [(x2x)lnx]'(x2x)'

= (xlnx)'x2x

= (1 + ln x)x2x

Hence, the derivative of y = x2x is

y' = (1 + ln x)x2x.

(b) f(x) = ∫2sinx​(t2 − 1)dt Given function is in definite integral form, i.e., the function has a limit. We have to use the Leibniz rule of differentiation to differentiate the integral functions using limit. Using Leibniz rule, we have f′(x) = ddx​{F(x,2sinx) }F(x,y)

= ∫g(x,y)dy( limits of integration are constants )

Where F(x, y) is a function of two variables.

∫2sinx​(t2 − 1)dt

= F(x,2sinx)

Lower limit, a = 0 and

upper limit, b = 2sinx

∴ F(x, 2sinx) = ∫2sinx​(t2 − 1)dtd

Fdx​=∂F∂x​+∂F∂y​⋅

dydx​=∂F∂x​+g(x,y)f′(x)

=dFdx​

=∂F∂x​+g(x,y)

∴ f′(x) = ∂F∂x​+g(x,y)

f′(x) = (2sinx2 − 1)× d(2sinx)

dx= (4sin3x)×2

=8sin3x

Hence, the derivative of f(x) = ∫2sinx​(t2 − 1)dt is

f′(x) = 8sin3x.

We have to use the Leibniz rule of differentiation to differentiate the integral functions using limit. Using Leibniz rule, we have f′(x) = ddx​{F(x,2sinx) }F(x,y) .Differentiation is a process of finding the rate of change of a function with respect to its independent variable.

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Answer:

25%

Step-by-step explanation:

25 - 20 = 5

20/4 = 5

100 / 4 = 25

Answer:

20+25%=25% Ali Has increased 25%

Answer: 120 degrees, the total is 720 degrees, so that divided by 6 is 120

Option A is correct. Use HL to prove two triangles are congruent.

Given:

In triangle ABC and triangle DEF as shown in figure below.

AB≅DE   [leg]                 [Given]

AC≅DF    [Hypotenuse side]      [Given]

∠B = ∠D = 90°

HL(Hypotenuse -Leg) postulates states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Then, by HL postulates;

ΔABC ≅ ΔDEF.

Therefore, the method you use to prove the two triangle congruent is, HL.

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Answer:

87.22 hopee helps

Step-by-step explanation:

Ax

B

Step-by-step explanation:

.....

...

..

Answer:

Pumpkin: 6

Hat: 5

Cauldron: 12

Ghost: 2

Double check those just in case, but those are the answers.

Therefore , the solution of the given problem of arithmetic mean comes out to be  2.5 to 12.5 there are three arithmetic means: 5, 7.5, and 10.

The typical values of a list, often known sequence as the organization's goals, are calculated by adding up all of the values on the list. Afterwards, these average figures are corrected using the percentage of list elements with the highest density. Growth patterns in mathematics are comparable. The true average of the numbers 5, 7, and 9 is 4, and by adding three, the number 21 becomes seven.

Here,

The following formula can be used to determine an arithmetic sequence's nth term:

=> an = a1 + d(n - 1)

The first term is known to be a1 = 2.5, and the fifth term is known to be a5 = 12.5. We can find d by using the above formula:

=> a5 = a1 + d(5 - 1) (5 - 1)

=> 12.5 = 2.5 + 4d

=> 10 = 4d

=> d = 2.5

Hence, 2.5 is the typical difference between two successive words.

The second, third, and fourth terms are the three arithmetic means. As a result, we have:

=> a1 = 2.5

=> a2 = a1 + d = 2.5 + 2.5 = 5

=> a3 = a2 + d = 5 + 2.5 = 7.5

=> a4 = a3 + d = 7.5 + 2.5 = 10

In this range of 2.5 to 12.5 there are three arithmetic means: 5, 7.5, and 10.

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Answer: 4. 1,541  5. 2,838 6. 5,538

Step-by-step explanation:

Answer:

BA ≈ 1.88

General Formulas and Concepts:

Pre-Algebra

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use trig to find the missing length

Step 2: Identify Variables

POV from angle C

Angle = 28°

Adjacent = BA

Hypotenuse = 4

Step 3: Solve for BA

Answer:

hope this helps

Step-by-step explanation:

Answer:

you have to graph it urself, but what you have to do is but the starting point at -3, and go down 3 on the y-axis, and up 2 on the x-axis. you can also go up 3 on the x-axis, and 2 down on the y-axis. i hope this explained it and helped you :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The units MUST be the same before they can be compared.

So 5 inches = 10 feet

1 foot = 12 inches

10 feet = 12*10 = 120 inches.

Scale = 1 : 120/5

Scale = 1 : 24

So 1 inch on the drawing represents 24 inches in reality.

Answer:

17

Step-by-step explanation:

34/2=17

Answer: the polygon sides is 15

If the measure of one exterior angle of a regular polygon is 24, Number of sides of polygon with each angle of 24 is 15 sides.

Solution:

Given:

Using the formula;

The z-score for 80% confidence interval is given by 1.28

Hence,

Hence, the point estimate with its margin of error to one decimal place is;

Answer:

D)  y = 7x + 1

Step-by-step explanation:

Slope-incercept form is y = mx + b in which m = slope and b = y-incercept

The line crosses through (0,1), which means the y-intercept is 1

Plug the given numbers into that formula:

y = 7x + 1

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

In the Histogram the horizontal line (dimension) represents the value of the selected collection plan element. The vertical line (dimension) represents the count or sum of occurrences of the primary collection element on the horizontal line.

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Answer:

(x^3 + 3x^2 - 2x + 7)/x- 2

Expand the numerator in the above expression

(x^3 + 5x^2 - 2x^2 + 8x - 10x - 16 + 23)/(x - 2)

Rearrange the terms of the numerator in the above expression

(x^3 + 5x^2 + 8x - 2x^2 - 10x - 16 + 23)/(x- 2)

Factorize the numerator in the above expression

[x(x^2 + 5x + 8) - 2(x^2 + 5x + 8) + 23]/(x - 2)

Factor out x^2 + 5x + 8

[(x -2)(x^2 + 5x + 8) + 23]/(x - 2)

Split the fractions

(x -2)(x^2 + 5x + 8)/(x - 2) + 23/(x - 2)

Divide the common factors

(x^2 + 5x + 8) + 23/(x - 2) hope this help btw your welcome

Answer:

The answer is really option A. x^2 - x +2-5/x-1

Step-by-step explanation:

I just took the test and got it right :)

The required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.

In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows some root properties to be inferred without having to compute them.

It is essentially a polynomial function of the coefficients of the initial polynomial.

So, we have the quadratic equation:

ax- bx +c= 0

We know that the discriminant formula is as follows:

Discriminate = b² - 4c

Now, get the discriminant:

D = b² - 4c

Therefore, the required discriminant of the quadratic equation ax-bx+c= 0 is D = b² - 4c.

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Answer:

Last Option: y=2x-2

78 sit ups in 2 minutes

so

= 78 : 2 sits in 1 minute = 39 sits up per minute

x 5 = 195 sit ups in 5 minutes

Answer:  39 situps per time

Step-by-step explanation:

Answer:

c = -22, 22

Step-by-step explanation:

\( {(x - 11)}^{2} = {x}^{2} - 22x + 121\)

\( {(x + 11)}^{2} = {x}^{2} + 22x + 121\)