As you ride the Ferris wheel at the park, your distance from the ground varies sinusoidally with time. You start a stopwatch, when the time reads 50 seconds, your seat is at the highest point on the wheel. Let + be the number of seconds that have elapsed since the Ferris wheel started.
You find that it takes you 110 seconds to make a complete revolution. The diameter of the wheel is 60 feet and sits 3 feet above the ground.
A. Write an equation: y=
B. Determine the time you will be 40 feet above the ground for the second time

[tex]\frac{2}{8}[/tex] fraction of the apple pie was served.

Two more pieces of the blueberry pie were served than the apple pieces.

Given that,

Both blueberry pie and apple pie were divided into 8 equal parts each.

To compute the fraction in eights of apple pie, we do a multiplication of the current fraction with 8 parts:

1 apple pie=8 pieces of apple pie

1/4 apple pie = [tex]\frac{1}{4}[/tex] * 8 pieces of apple pie = 2 pieces of apple pie.

1 blueberry pie=8 pieces of blueberry pie.

1/2 blueberry pie = [tex]\frac{1}{2}[/tex] * 8 pieces of blueberry pie = 4 pieces of apple pie.

Thus. 1/4 apple pie is 2 pieces out of 8 pieces of apple pie or written as [tex]\frac{2}{8}[/tex] a fraction of apple pie.

And they served blueberry pies are 4 pieces but served apple pies are 2 pieces, thus the count of pieces of blueberry pie is 2 more than the count of pieces of apple pie served.

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For a = 1 and a = -7, the distance between the points (2, -3) and (5, a) is equal to 5.

As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given the distance between the points  (2, -3) and (5, a)

Let us assume that  (x₁, y₁) = (2, -3)

and (x₂, y₂) = (5, a)

Let d represents the distance between points (2, -3) and (5, a)

here d = 5 units

Using above distance formula,

[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow 5 = \sqrt{(5 - 2)^2 + (a -(- 3))^2}\\\\\Rightarrow 5 = \sqrt{(3)^2 + (a+3)^2}\\\\\Rightarrow 5^2=(3)^2 + (a+3)^2\\\\\Rightarrow 25=9+(a+3)^2\\\\\Rightarrow (a+3)^2=16\\\\\Rightarrow a+3=\pm 4[/tex]

⇒  a + 3 = 4      OR   a + 3 = -4

⇒ a = 4 - 3       OR   a = -4 - 3

⇒ a  = 1       OR       a = -7

Therefore, the values of 'a' are 1, -7

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The complete question is

For what value of a the distance between the points (2, -3) and (5, a) is equal to 5?.

The value of the side b of the triangle is 33.8.

The following is a detailed explanation of the sine law: In a triangle, side "a" divided by angle sine "a" equals side "b" divided by angle sine "b" equals side "c" divided by angle sine "c." In order to determine the triangle's unknown lengths or angles, we apply the sine rule.

Given that the sides and angles are c = 21 km, a = 18 km, mB = 121°. The value of the side b will be calculated as,

b² = c² + a² -2accosB

b² = ( 21² ) + ( 18 )² - 2 x 21 x 18 x cos(121)

b² = 441 + 324 _ ( 756 x -0.5 )

b² = 441 + 324 + 378

b = √ ( 1143 )

b = 33.8

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In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4).

Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.

The midpoint formula is used to find the midpoint between two points whose coordinates are known to us. The midpoint formula is also used to find the coordinates of the endpoint if we know the coordinates of the other endpoint and the midpoint. In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4). Let us learn more about the formula of the midpoint, and different methods to find the midpoint of a line.

(3, 8 )

given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

(x+x /2  ,y+y/2  )

here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then

midpoint = (1+5/2 ,++10/2  ) = ( 6/2 , 16/2 ) = (3, 8 )

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Answer: 14.3 times 1.5 equals 55.

Step-by-step explanation: multiplication can be used to solve the equation

The dimensions of the cylinder are -

{r} = √500/πh

{h} = (500/r²)

Given is the volume of the cylinder as -

V = 500 cm³

We can write -

V = 500

So, we can write -

πr²h = 500

So, we can write -

{r} = √500/πh

{h} = (500/r²)

Therefore, the dimensions of the cylinder are -

{r} = √500/πh

{h} = (500/r²)

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{Question in english -

What are the measurements of a cylinder (height, radius) if its volume is 500 cm3}

Logarithm and exponential functions are inverse as log(ex)=x and elogx=x.

Knowing that logarithms were once a tool for multiplication when ships employed celestial navigation may be helpful to the layperson. The product of two numbers' logarithms is equal to the total of their individual logarithms. Numerous log tables were published and utilized mechanically.

In 1958, this was an excellent supplemental math topic. The slide rule converts multiplication to addition of lengths using one axis graphs of an exponential function and a graphic log table as a physical correlate. As a result, the logarithm of a product is equal to the sum of the logarithms of its components.

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Answer:

1449.28

Step-by-step explanation:

To find the principal amount that will amount to Rs. 2000 in 6 years 8 months at a 5% interest rate per annum, we can use the formula for compound interest:

A = P (1 + r/n)^(nt)

Where:

A = final amount

P = principal (the amount we are trying to find)

r = interest rate per annum (in decimal form)

n = number of times interest is compounded per year

t = time in years

So we can substitute these values into the formula and solve for P:

2000 = P (1 + 0.05)^(1 * 6.67)

2000 = P * 1.38

P = 2000/1.38

P = 1449.28

The principal amount that will amount to Rs. 2000 in 6 years 8 months at a rate of interest of 5% per annum is Rs. 1281.97.

The principal amount (P) that will amount to Rs. 2000 in 6 years 8 months at the rate of interest of 5% per annum can be calculated using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = final amount

P = principal

r = rate of interest (5% per annum = 0.05)

n = number of times the interest is compounded per year (e.g. annually, semi-annually, quarterly)

t = time in years (6.67 years = 6 years 8 months)

Let's assume n = 12 (monthly compounding)

Substituting the values into the formula, we get:

2000 = P(1 + 0.05/12)^(12*6.67)

(To solve for P, we can divide both sides of the equation by the right side of the equation)

P = 2000 / (1 + 0.05/12)^(12*6.67)

P ≈ Rs. 1281.97

Therefore, the principal amount that will amount to Rs. 2000 in 6 years 8 months at a rate of interest of 5% per annum is Rs. 1281.97

It's important to note that this calculation is based on the assumption that the interest is compounded monthly, if the interest is compounded annually or semi-annually the amount will be different.

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96 yards of the same fabric would cost 288$ and the rate of the fabric per yard is 3$

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the rate of the fabric per yard we have:

Rate = total cost / No. yards

Rate = $75 / 25 yard

Rate = $3 per yard

Calculating the amount of dollars paid for 96 yards:

Cost (96 yards) = No. yards 2 * Rate

Cost (96 yards) = 96 yards * 3$/ yard

Cost (96 yards) = 288$

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The maximum value of the linear equation on the given interval is:

y = 11

We want to find the maximum of the linear function:

y = 2x + 1

On the interval [3, 5]

Notice that we have a line with a positive slope, thus, this is an increasing line.

Then the maximum is just what we get when we evaluate the function on the maximum value of the interval:

y = 2*5 + 1

y = 10 + 1

y = 11

The maximum value is 11.

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A two-variable function's graph can be thought of as a surface in three dimensions.

The points (x, y, f(x, y)) where x and y are in the domain make up the graph of z=f(x, y). You can fine-tune the shape of the surface by drawing the curve k=f(x, y) in the plane z=k for different values of k. For instance, we're trying to comprehend the graph of z=f(x, y)=x2+y2. Keep in mind that k=f(x, y) is a circle for k>0 and since 0=x2+y2 implies that x=y=0.

Additionally, it is symmetric in relation to the z axis. We have a parabola for x=k or y=k. As a result, the graph represents the revolution of the parabola z=x2 over the z axis (see Thomas, math).

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The slices that each person gets from the 16 slices of pizza will be 2 slices.

It should be noted that 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.

In this case, Mitchell and his friends go out to eat at Perfect Slice Pizzeria and order to large pizzas that has 16 slices.

The slices that each person gets from the 16 slices of pizza will be:

= 16 / 8.

= 2 slices.

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Complete question

Mitchell and his friends go out to eat at Perfect Slice Pizzeria.They order to large pizzas to share.Each large pizzas has 16 slices.Mitchell and friends split it between the 8 of them. How many slices will each person get?

Solve each equation in steps:

Answer:

Step-by-step explanation:

1) 2(3b + 6) = 78, value of b?

→ 2(3b + 6) = 78

→ 6b + 12 = 78

→ 6b = 78 - 12

→ 6b = 66

→ b = 66/6

→ [ b = 11 ]

Hence, the value of b is 11.

2) -2(6c - 3) = -72, value of c?

→ -2(6c - 3) = -72

→ -12c + 6 = -72

→ -12c = -72 - 6

→ -12c = -78

→ c = (-78)/(-12)

→ c = 78/12

→ [ c = 6.5 ]

Hence, the value of c is 6.5.

The standard form of the line is Ax + By + C = 0 or we can say y = mx + c.

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The value of x is 39 and the values of angle m1 and m2 is 63 and 117. We can solve the question using linear pair.

What is linear pair?

When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear pair. A linear pair's angles add up to 180° in every case. These angles are additionally referred to as. Angles with a shared vertex are those that are adjacent.

Therefore, the linear angles also have a common vertex in this instance.

Additionally, a common arm that symbolizes both angles will be present.

A ladder against a wall that creates linear angles at the ground is an example of a linear pair in real life. One who is straight is represented by linearity.

Using linear pair, we have equation

m1 +m2 = 180

x+24 +3x = 180

4x = 156

x = 39

Then the values of m1 =x +24 = 64

m2 = 3x = 117

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Answer: (3, 4)

Step-by-step explanation:  Hello! To do this, you have to substitute one of the equations into the other.  You know that in the first equation, y = -x + 7.  Substitute -x+7 for y in the second equation.  You now have -x + 7 = x + 1.  Add x to both sides of the equation.  -x + 7 + x = x + x + 1.   You now have 7 = 2x + 1.  Subtract 1 from both sides of the equation.  You now have 6 = 2x.  Divide both sides of the equation by 2.  You now have 3 = x.  The x-coordinate of where both linear equations intersect is 3.  (3, y).

You now have to solve for the y-coordinate.  To do this, look at your given equations.  Subtract 2 from both sides of the second equation.  You now have y - 1 = x.  Substitute y-1 for x in the first equation.  You now have y = -(y - 1) + 7.  Simplify to get y = -y + 1 + 7.  Add y to both sides of the equation.  y + y = -y + y + 1 + 7.  You now have 2y = 1 + 7.  Add 1 + 7 to get 2y = 8.  Divide both sides by 2 to get y = 4.  You now know that the x-coordinate where both linear equations intersect is 3, and you know that the y-coordinate where both linear equations intersect is 4.  Your answer is in the format of (x, y), which is (3, 4).

Answer:

75x = 300

x = 4

So he has

4 quarters

3x = 3*4 = 12 dimes

4x = 4*4 = 16 nickels

Step-by-step explanation:

Answer: The answer would be y = −4x − 5

Step-by-step explanation: I hope this helps!

He need a fence that is 54 feet long.

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

Consider the length to be 40 feet, which is how long one side of the yard is known to be. The yard's size is 280 square feet, as you are already aware. Knowing the yard's width is necessary in order to calculate the perimeter:

A = LW

W= 280/40 = 7 feet

The two 7-foot sides and one 40-foot side are fenced in by him . He,

therefore, He needs a fence that is 54 feet long.

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Answer:

See attached

Step-by-step explanation:

You can write 1 as 1.00 then line up the decimals with0.30 and subtract.  The answer will be .7 or 0.7.  They mean the same thing.

Yes, 36 is a perfect square because 36 = 2² × 3², all numbers are in the power of two. This means that the square root of 36 is a positive integer. Therefore, 36 is a perfect square.

Perfect squares are special numbers in mathematics that have a pair of integer factors that are equal to each other. A number N is called a perfect square if it is equas to product of number, x with itself. Formula for perfect square,

N = x²

this implies that if N is equals to second power of a whole number then N is called perfect squares. We have, N = 36 and we have to check that it is perfect square or not. For this, firstly determine the prime factors of 36, that is 36 = 2× 2× 3 × 3 . Now, 36 = 2² × 3² = 6² ( since, 2 and 3 are prime numbers, a²×b² = (ab)² ). Therefore, 36 is equals to square of whole number 6. So, 36 is perfect square.

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Complete question:

Why is 36 a perfect square? or Is 36 a perfect squares?

For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.

The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.

Given a right triangle with base = 8 and an angle = 24°

Using angle sum property of triangle

24 + 90 + angle L = 180

L = 66°

Using Sohcahtoa

Tangent: tan(θ) = Opposite / Adjacent

tan(24°) = LK/8

0.445 = LK/8

LH = 8 × 0.445

LK = 3.56

LM = [tex]\sqrt{MK^2 + LK^2}[/tex]

LM = [tex]\sqrt{8^2 + 3.56^2}[/tex]

LM = 8.75

Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.

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So,  Y = -3 is not a horizontal line but a vertical line.

A horizontal line is a line that runs along the x-axis and has a constant y-value. In the equation of a line, y = mx + b, a horizontal line has a slope of zero (m = 0) and a y-intercept of the constant value (b = constant).

The equation Y = -3 is not a horizontal line. This is an equation of a vertical line, which is a line that runs along the y-axis and has a constant x-value. In this case, the constant x value is -3.

A vertical line has no slope since it does not change in the x direction. The x-value is constant, which means the slope is undefined.

In a graph, a horizontal line can be represented by a straight line that is parallel to the x-axis, while a vertical line is represented by a straight line that is parallel to the y-axis.

To summarize, Y = -3 is not a horizontal line but a vertical line, which means that all the points on this line have the same x-coordinate (-3) and can take any value for y.

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Answer:

n=8

Step-by-step explanation:

40=5n

40=5x8

Answer:n=8 I hope this helps mark brainlist if correct

Step-by-step explanation:

40=5n

Swap the sides of the equation

5n=40

Divide both sides of the equation by 8

n=8

Answer:

Elena's calculator is not broken.

Step-by-step explanation:

0.06 x 0.5

You can also do this by ignoring the decimals and multiplying normally.

6 x 5 = 30

Then you you count the decimal places and start at the end of your product and move the number of decimal places to the left.

0.030 or 0.03

You will save as much as $1000 each year if you start recycling with the company.

If your current order of 150 boxes of paper per year costs $50 per box, and in exchange of starting recycling with the company, the recycling company will donate 20 boxes of new paper each year to your business, then you will save as much as $1000 each year.

Determine how much you will save by multiplying the amount of boxes of paper the recycling company will give to your business with the cost of each box of paper.

20 boxes of new paper x $50 per box = $1000

Therefore, the amount you will save if you start recycling with the company will be as much as $1000 each year .

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Answer:

Step-by-step explanation:

You haven’t given the points mentioned. (-4 6) is a point on the line. slope-intercept equation of the line: y=7x+34 (0,34) is a point on the line.

The range formula determines the difference between the highest and the lowest values in a given set of numbers.

The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.

The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:

R = Highest Value (H) - Lowest Value (L)

Range Formula

R = H - L

In this context,

R is the range

H is the highest value

L is the lowest value

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Answer:

Step-by-step explanation:

The range formula determines the difference between the highest and the lowest values in a given set of numbers. The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.

The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:

R = Highest Value (H) - Lowest Value (L)

Range Formula

R = H - L

In this context,

R is the range

H is the highest value

L is the lowest value

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