Approximately what portion of the circle is shaded blue?

A. 2/5
B. 2/3
C. 1/3

To find the volume of the solid, you need to calculate the area of each cross-section and then multiply that by the thickness of the section (which is the distance along the y-axis).

(a) Squares: The cross-sections are squares with sides of length y. The area of a square is side^2, so the area of each square is y^2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the square cross-sections is y^2 * y

(b) Semicircles: The cross-sections are semicircles with radii of length y. The area of a semicircle is (pi * r^2) / 2 , so the area of each semicircle is (pi * y^2) / 2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semicircular cross-sections is (pi * y^2) / 2 * y

(c) Equilateral triangles: The cross-sections are equilateral triangles with side length of y. The area of an equilateral triangle is (s^2 * √3)/4. so the area of each equilateral triangle is (y^2 * √3) / 4. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the equilateral triangle cross-sections is (y^2 * √3) / 4 * y

(d) Semi-ellipses: The cross-sections are semi-ellipses whose heights are twice the lengths of their bases. The area of a semi-ellipse is πab/2, where a and b are the lengths of the semi-major and semi-minor axes respectively. Therefore the area of each semi-ellipse will be (πy^2)/2. The thickness of the section is the distance along the y-axis, which is the difference between y and 0, or simply y. So the volume of the solid for each of the semi-ellipse cross-sections is (πy^3)/2

It is important to note that this is a theoretical volume calculation, as the shape of the solid does not have a closed form representation by these functions, but rather, these are an approximation.

Also, for any of these volumes to be meaningful, we have to integrate over the range of the variable y, since it is bounded by the equations y=x, y=0 and x=1, the variable y is limited.

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The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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we have

Remember that

30=2*3*5

substitute in the expression above

The expression can't be simplified

Answer:

I need more details

Step-by-step explanation:

maybe if u just add all of the numbers together , divide or multiple

Answer:

its A im pretty sure

Step-by-step explanation:

Answer:

The 4th option i.e. 'The terms in Pattern C are 2 more than the terms in Pattern D' is correct.

Step-by-step explanation:

Given the patterns

Pattern C: 4, 5, 6, 7, 8, ...

Pattern D: 2, 3, 4, 5, 6, ...

If we carefully analyze, it is clear that terms in the pattern C are 2 more than the terms in Pattern D.

In other words, if we add 2 in each term of the Pattern D, we will get the pattern C.

For example,

Pattern D: 2, 3, 4, 5, 6, ...

Now, add 2 in each term of Pattern D

i.e.

2+2 = 4

3+2 = 5

4+2 = 6

5+2 = 7

6+2 = 8

It is clear that we get the results 4, 5, 6, 7, 8 when we add 2 in each term of Pattern D.

As 4, 5, 6, 7, 8 represent Pattern C. Therefore, we conclude that the terms in Pattern C are 2 more than the terms in Pattern D.

Hence, the 4th option i.e. 'The terms in Pattern C are 2 more than the terms in Pattern D' is correct.

Answer:

4, 5, 6, 7, 8 when we add 2 in each term of Pattern D

Step-by-step explanation:

Answer:

b=7 & c=7√2

Step-by-step explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer:

Step-by-step explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

  b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

  c = 7√2

__

Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

  c² = 7² + b²

  c² = 7² +7² = 2·7²

  c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.

To find out how many students took history and math, but not psychology, we need to first calculate how many students took history and math, and then subtract the number of students who took all three subjects.

From the given information, we know that:

24 students took history (including those who took history and math, and those who took all three subjects).

23 students took math (including those who took history and math, and those who took math and psychology).

26 students took psychology (including those who took all three subjects).

We also know that:

19 students took history but not math (including those who took history and psychology, but not math, and those who took only history).

11 students took math and psychology (including those who took only math and psychology, and those who took all three subjects).

10 students took history and psychology (including those who took only history and psychology, and those who took all three subjects).

2 students took all three subjects.

To find out how many students took history and math, we can subtract the number of students who took only history or only math from the total number of students who took history or math (including those who took history and math, math and psychology, and all three subjects):

Total number of students who took history or math = 24 + 23 - 2 = 45

Number of students who took only history or only math = 19 + (23-11) = 31

Number of students who took history and math = 45 - 31 = 14

To find out how many students took history and math, but not psychology, we need to subtract the number of students who took all three subjects (2) from the number of students who took history and math (14):

Number of students who took history and math, but not psychology = 14 - 2 = 12

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

6

Step-by-step explanation:

Foot long = 1 foot

6 / 1 = 6 foot pieces

Answer:

To maximize the profits of the company, the subscription price should be raised to $ 22.

Step-by-step explanation:

Given that a bi-monthly sports magazine has 48,000 subscribers when it charges $ 20 for a one year subscription, and for every $ 1 increase in the yearly subscription price, the magazine assumes that it will lose 2,000 subscribers resulting in the equation below, to determine, Using the equation below, how much should the magazine sell for in order to maximize revenues, the following calculations should be performed:

f (x) = (48,000 - 2,000x) (20 + x)

X = 48,000 x 20 = 960,000

X = (48,000 - 2,000x1) x (20 + 1)

X = 46,000 x 21

X = 966,000

X = (48,000 - 2,000x2) x (20 + 2)

X = 44,000 x 22

X = 968,000

X = (48,000 - 2,000x4) x (20 + 4)

X = 40,000 x 24

X = 960,000

Therefore, to maximize the profits of the company, the subscription price should be raised to $ 22.

The equation of the linear function represented by the table in slope intercept form is f(x) = 2x + 2.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Equation of the linear function in slope intercept form can be represented as y = mx + d, where m is the slope and d is the y intercept.

Slope is the change in y coordinates divided by the change in x coordinates.

y intercept is the point on the line where the line touches the Y axis.

Given points are (-2, -2), (2, 6), (6, 14) and (10, 22).

Consider the points (-2, -2) and (2, 6).

Slope, m = (6 - -2) / (2 - -2) = 8 / 4 = 2

So the equation becomes y = 2x + d

Substituting one of the points (2, 6) in the above equation,

6 = (2 × 2) + d

d = 2

So the equation is y = 2x + 2.

Hence the given linear function can be represented as f(x) = 2x + 2.

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Answer:

volume of figure = 74 cm³

The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

15

Step-by-step explanation:

Shawn: 35x - 250

Nick: 25x - 100

35x - 250 = 25x - 100

          10x = 150

              x = 15

The operation that has been performed on v to result in the vector that is shown is multiplication by -1.

The vector that is shown is (-2, -1). This can be obtained from vector v = (2, 1) by multiplying it by -1. Multiplying a vector by a negative number reverses its direction.

Multiplication of a vector by a number is performed component-wise. This means that each component of the vector is multiplied by the number. In the case of (-1) * (2, 1), each component is multiplied by -1. This results in the vector (-2, -1).

Here is the mathematical equation:

(-1) * (2, 1) = (-2, -1)

Therefore, the operation that has been performed on v to result in the vector that is shown is multiplication by -1.

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Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

you need to start from the beginning add 2 and 3

Step-by-step explanation:

The chef should assign Jill to make pasta and Betty to make panini because Jill is more efficient than betty. (option 1)

Jill is more efficient at making pasta, being able to produce 20 servings in an hour, while Betty is more efficient at making panini, being able to produce 50 in an hour. By assigning Jill to pasta and Betty to panini, the chef can maximize productivity and minimize waiting times for customers. This way, both cooks can work at their highest capacity, and the restaurant can serve both dishes quickly and efficiently.

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Complete Question:

the head chef at a local restaurant is contemplating how to divide the work between her two cooks, jill and betty. jill can make 25 panini or 20 servings of pasta each hour and betty can make 50 panini or 25 servings of pasta. which of the following should be the chef's choice?

Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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A I think

Step-by-step explanation:

sorry for not responding earlier to you last week but it was my last day of 6th and the water was not good enough to be a good time to get my hands and then I can u help around and see if you work with them and they came up to you to help us with that as a way of doing that I think I would be able even to get a good feel the

Answer:

2 by 4 inches

Step-by-step explanation:

If you divide 2 1/2 by 5/4 and 5 by 5/4, you get 2 by 4 inches.

(Edit: I fixed it)

Answer:

The scale factor is a reduction, and the new card should be 4 in x 2 in.

Step-by-step explanation:

Answer:

  I, B

Step-by-step explanation:

You want the surface area of the triangular prism and the composite cuboid+pyramid figures shown.

The surface area is the area of the two bases plus the lateral area of the rectangular faces.

  SA = bh +PH

  SA = (8 ft)(6 ft) +(8 ft +6 ft +10 ft)(12 ft) = 48 ft² +(24 ft)(12 ft) = 336 ft²

The surface area of the prism is 336 square feet. (choice I)

The surface area of this figure is the sum of the areas of the square base, the lateral area of the cuboid, and the later area of the triangular faces.

  SA = s² +4sh +2sH

  SA = (10 in)² +4(10 in)(5.6 in) + 2(10 in)(11 in)

  SA = 100 in² +224 in² +220 in² = 544 in²

The area of the pyramid figure is 544 square inches. (choice B)

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Answer:

45 > 51

Step-by-step explanation:

Answer:

2.01

Step-by-step explanation:

plug it in to the calculator boo/bro....

Step-by-step explanation:

Equation of cylinder: h*pi*r^2

The equation for a cylinder is base times height where the base is a circle of area calculated by pi*r^2. I hope this helps! :)

Answer:

m∠RTS= 15°, m∠UTS= 15°, m∠RTU= 30°

Step-by-step explanation:

Since TS bisects RTS and UTS, that means the two angles are equal to each other. So let's find x first.

x+10=2x+5, subtract x to both sides

10=x+5, subtract 5 to both sides

x=5

Since RTU is basically RTS plus UTS, let's add the two angles together

x+10+2x+5, combine like terms

3x+15

Then we can plug in 5 for x

3(5)+15

15+15

=30

So, RTU is 30 degrees

Answer:

kjndnsadnsdnasnldnkasbdkbaskbjdbLol i dont caewnsnasdHBsadHKUsadkhsdkkbhaSKHChASKUCDKJGCHakbsDKskbhaKHDHU

Step-by-step explanation:

Answer:a0 = 40 mg

a1 = 20 mg  after 28 years

a2 = 10 mg  after another 28 years

Step-by-step explanation:Set this up as

10 = 40 (1/2)t/28

and solve for t in years.

10/40 = (1/2)t/28

log(0.25) = (t/28) log(0.5)

t = 28 log(0.25) / log(0.5) years = 56 years

Answer:

40 mg

Step-by-step explanation:

10 = 40 (1/2)t/28   and solve for t in years.   10/40 = (1/2)t/28   log(0.25) = (t/28) log(0.5)   t = 28 log(0.25) / log(0.5) years = 56 years