The sales of homes in a new development have been increasing. In January, 8 homes were sold, in February, 12 homes were sold. In March, 16 homes were sold. This pattern continued for the remainder of the year.
What is the explicit rule that can be used to find the number of homes sold in the nth month of the year?
an=4n−4
an=−4n−4
an=4n+4
an=−4n+4
Answers
a1 = 8
For the second month we have:
a2 = 12
For the third month we have:
a3 = 16
Let's assume that n is the number of months.
The rule that meets the number of homes sold is:
an = 4n + 4
We observe for example that for the third month: (n = 3)
a3 = 4 (3) +4
a3 = 12 + 4
a3 = 16 (result that we already knew according to the statement).
Answer:
an = 4n + 4
Answer:
Answer:
an = 4n + 4
Step-by-step explanation:
Related Questions
An angle is 14° more than the measure of its complement. find the number of degrees in each angle. the angles measure
Answers
let the complementary angle be x.
x+x+14˚=90˚
2x=76˚
x=38˚.
x+14=52˚.
Therefore, the angles are 38˚ and 52˚.
Triangle ABC has vertices at (2,2), (4,3), and (6,1).
Using triangle ABC as the pre-image and origin as the center of dilation, what are the coordinates of a dilation of these vertices that uses a scale factor of 0.5?
A. (10,10)(20,15)(30,5)
B. (-1,-1)(-2,-15)(-3,-0.5)
C. (1,1)(1.5,2)(0.5,3)
D. (1,1)(2,1.5)(3,0.5)
Answers
This point is only found on the list of Selection D.
Answer:
The correct answer is D.
Step-by-step explanation:
Recall that when we make a dilation with center at the origin, the only needed operation is to multiply the coordinates of each point by the factor of dilation. In this particular case the dilation factor is 0.5 so we must do the following operations:
0.5*(2,2) = (0.5*2,0.5*2) = (1,1)0.5*(4,3) = (0.5*4,0.5*3) = (2,1.5)0.5*(6,1) = (0.5*6, 0.5*1) = (3,0.5)So, the vertices of the triangle after the dilation are those who appear in D.
How to rewrite the function 2x^2-7x+5 by completing the square
Answers
(x-1)(2x-5)
To rewrite[tex]\(2x^2 - 7x + 5\) by completing the square, first factor out the coefficient of \(x^2\), then add and subtract \(\frac{49}{16}\) inside the parentheses, rewrite as a perfect square trinomial, and simplify. The result is \(2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\).[/tex]
To rewrite the quadratic function[tex]\(2x^2 - 7x + 5\)[/tex]by completing the square, follow these steps:
1. Factor out the coefficient of[tex]\(x^2\):\[2x^2 - 7x + 5 = 2(x^2 - \frac{7}{2}x) + 5\][/tex]
2. Take half of the coefficient of [tex]\(x\)[/tex]and square it:
[tex]\[\left(\frac{-7}{2} \div 2\right)^2 = \left(\frac{-7}{4}\right)^2 = \frac{49}{16}\][/tex]
3. Add and subtract this value inside the parentheses:
[tex]\[2\left(x^2 - \frac{7}{2}x + \frac{49}{16} - \frac{49}{16}\right) + 5\][/tex]
4. Rewrite the expression inside the parentheses as a perfect square trinomial:
[tex]\[2\left[\left(x - \frac{7}{4}\right)^2 - \frac{49}{16}\right] + 5\][/tex]
5. Distribute and simplify:
[tex]\[2\left(x - \frac{7}{4}\right)^2 - 2 \times \frac{49}{16} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + 5\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{49}{8} + \frac{40}{8}\]\[= 2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}\]So, the quadratic function \(2x^2 - 7x + 5\) rewritten by completing the square is \(\boxed{2\left(x - \frac{7}{4}\right)^2 - \frac{9}{8}}\).[/tex]
This figure is made up of a triangle and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round only your final answer to the nearest tenth.
Enter your answer as a decimal
Answers
Given is a composite figure where we have a semicircle and a triangle.
To find the area of the semicircle, we need diameter of the circle which is the distance between two given points (2,4) and (2,-3). So the diameter is 4-(-3) = 7 and radius would be 3.5 units.
Area of circle = π·r² = 3.14 × (3.5)² = 38.465 squared units.
So, area of semicircle = 38.465 ÷ 2 = 19.2325 squared units.
To find the area of the triangle, we need base and height of the triangle. The base is same as diameter = 7 and the height would be distance between given point (5,0) and (2,0), so height is 5-2 = 3.
Area of triangle [tex] =\frac{1}{2} bh = \frac{1}{2} (7)(3) = 10.5 [/tex] 1/2 * 7 * 3 = 10.5 squared units.
Total area = Area of triangle + Area of semicircle = 10.5 + 19.2325 = 29.7325 squared units.
So, final answer is 29.7325 squared units.
One base angle of an isosceles triangle measures 33 degrees. What is the number of degrees in the vertex angle?
Answers
what is area of a parallelogram that has a base of 12 3/4 in. and a height 2 1/2in.?
Answers
Area = b * h
b =12 3/4 in
h = 2 1/2 in
Area = 12.75 * 2.5 = 31.875 or 31 7/8 square inches.
Maxine picked 7 1/4 pounds of blueberries and kodi picked 3 3/4 pounds of blueberries thy want to package into 1 1/2 to sell at their family what is the greatest number of 1 1/2 bags of blueberries they can make?
Answers
11/1.5= 7 plus .5 pounds left
So the greatest number they can make is 7
Blueberry bushes are planted in a field in the year 2009. The blueberry bushes start to grow and cover the field in such a way that the area covered by the bushes doubles every year. If they continue to grow in this way, the field will be entirely covered with blueberry bushes by the year 2016.
When will the field be covered 25% of the way
Answers
They are planted in 2009, and the field will be covered by 2016. 2016-2009= 7. They will be growing for 7 years.
If it's covered 1.5625% in the first year,
Then 3.125% second year,
6.25% 3rd year,
12.5% 4th year,
25% 5th year,
50% 6th year,
100% 7th year.
So the 5th year? Maybe... I don't know. Please tell me if it's wrong!
PLEASE HELP
6.02B
Respond to the following prompt in a word processing document.
Describe, in detail, when to use the law of cosines, the law of sines, and the law of sines with the ambiguous case. Provide general guidelines, in your own words, for each law that can be applied to any triangle situation with which you are presented. To aid in your explanation, you may refer to specific problems from the text.
Your response must include:
A discussion of
The law of cosines
The law of sines
The ambiguous case (law of sines)
General guidelines in your own words that can be applied to any triangle.
Answers
Law of cosines :
The law of cosines establishes:
[tex] c ^ 2 = a ^ 2 + b ^ 2 - 2*a*b*cosC.
[/tex]
general guidelines:
The law of cosines is used to find the missing parts of an oblique triangle (not rectangle) when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.
Law of the sines:
In ΔABC is an oblique triangle with sides a, b, and c, then:
[tex] \frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC} [/tex]
The law of the sines is the relation between the sides and angles of triangles not rectangles (obliques). It simply states that the ratio of the length of one side of a triangle to the sine of the angle opposite to that side is equal for all sides and angles in a given triangle.
General guidelines:
To use the law of the sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an opposite angle of one of them (SSA).
The ambiguous case :
If two sides and an angle opposite one of them is given, three possibilities may occur.
(1) The triangle does not exist.
(2) Two different triangles exist.
(3) Exactly a triangle exists.
If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we can not use the law of the sines because we can not establish any proportion where sufficient information is known. In these two cases we must use the law of cosines
The Law of Sines, Law of Cosines, and the Ambiguous Case are used to solve triangles depending on the given information. The Law of Sines is used when you have angles and sides but no right angle, the Law of Cosines is used when you have at least one side and angles, and the Ambiguous Case is used when you have one angle and two sides with two possible triangles. General guidelines are provided for each law.
Explanation:The Law of Sines:
The law of sines is used to solve triangles when you have information about the measures of angles and sides, but do not have a right angle. It relates the ratios of the lengths of the sides of a triangle to the sines of its angles.
The Law of Cosines:
The law of cosines is used to solve triangles when you have information about the measures of angles and sides, and at least one side is known. It relates the lengths of the sides of a triangle to the cosine of one of its angles.
The Ambiguous Case:
The ambiguous case, also known as the law of sines with the ambiguous case, is used to solve triangles when you have information about the measures of angles and sides, and want to find all possible solutions. It occurs when you have one angle and two sides given, but there are two possible triangles that can be formed.
General Guidelines:
Use the law of sines when you have the measure of an angle and the length of its opposite side, or two pairs of an angle and its opposite side.Use the law of cosines when you have the length of one side and the measures of the other two sides or when you have two sides and the included angle.Use the law of sines with the ambiguous case when you have the measure of an angle and the length of its opposite side, and there are two possible triangles that can be formed.
What is the slope of a line that is perpendicular to the line y=1
Answers
Here, we have to use our intuition. A horizontal line has slope 0, and the negative reciprocal of zero is undefined (division by zero). But, thinking visually, you by able to tell that the perpendicular line will be vertical, that is, the line x = a, where a is any number.
The slope of such a line is generally considered undefined or, depending on whom you ask, equal to infinity.
Perform the indicated operation. (r 4 - r 2 + 4) ÷ (r 2 - r + 2)
Answers
r² + r - 2 R -4r+8 just got this wrong on quiz so i know this is the right answer now
The simplified expression of (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (r⁴ - r² + 4) ÷ (r² - r + 2)
r power four minus r square plus four divided by r square minus r plus two.
The expression can not be simplified further as the denominator (r^2 - r + 2) cannot be factored into linear factors
The expression is a rational function and can only be simplified by partial fraction decomposition which involves writing it as a sum of simpler fractional terms.
r (r³ -r+ 4/r) ÷ r(r - 1 + 2/r)
r³ -r+ 4/r ÷ r - 1 + 2/r
Hence, the simplified expression of (r⁴ - r² + 4) ÷ (r² - r + 2) is r³ -r+ 4/r ÷ r - 1 + 2/r
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*Will give medal!* Which is the direct linear variation equation for the relationship?
y varies directly with x and y = 10 when x = 2.
A. y = x – 8
B. y = x + 8
C. y = 5x
D. y = 2x + 6
Answers
Varies directly means to multiply and add a constant.
Y varies directly with X means y=kx.
Since y=10 when x=2
10=k2 so k=5
y=5x
For a school play the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row after setting up all the chairs they were five chairs short how many tears did the class setup
Answers
= (20*25) - 5
= 500 - 5
= 495
They set up 495 chairs.
Hope this helps! :)
David drops a ball from a bridge at an initial height of 100 meters.
(a) What is the height of the ball to the nearest tenth of a meter exactly 3 seconds after he releases the ball?
(b) How many seconds after the ball is released will it hit the ground?
Answers
(b) About 4.518 seconds.
_____
A graphing calculator can be helpful for these.
[tex]y = y_{o} + v_{o}t - \frac{1*g*t^{2} }{2} [/tex] -- (A)
Where g = 9.8 m/s/s
[tex]v_{o}[/tex] = 0
[tex]y_{o}[/tex] = 100
a)
Time=t=3s.
Plug-in the values in (A)
y = 100 -(1/2*9.8*3*3)
y = 100-44.1 = 55.9m
Height of the ball exactly after 3 seconds = 55.9m.
b)
At ground, y=0; Plug-in values in (A):
A=> 0 = 100 - (1/2* 9.8 * [tex]t_{2}[/text])
Therefore t = + 4.52 s and - 4.52 seconds.
As t cannot be negative, therefore:
Time when ball hits the ground = 4.52s
-i
Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? k – 2 = 1/9(t – 18) k – 18 = 1/9(t – 2) k – 2 = 9(t – 18) k – 18 = 9(t – 2)
Answers
Answer:
the answer is C
Step-by-step explanation:
using her first part 2 kilometers in 18 minutes
total kilometers - 2
and total time - 18
so you would get:
k – 2 = (t – 18)
Factor the expression.
24−18y
Enter your answers in the boxes to complete the factored expression.
____(___ − 3y)
Answers
Answer:
6(4 - 3y)
Step-by-step explanation:
Factor the expression 24−18y
The first thing to check is the common factor to be able to factorize the expression. Take for instance where we have
xa - xb = x ( a - b)
The common factor is x which is outside the bracket
24−18y
The greatest common factor between 24 and 18 is 6.
Therefore,
24−18y = 6(4 - 3y)
24−18y = 6(4) - 6(3y)
A mortgage broker charges $4000 plus 1.8% of the mortgage amount. What is the mortgage broker fee for a $309,000 mortgage?
Answers
The answer is 9,562. Thank you very much.
The mortgage broker fee for a $309,000 mortgage is calculated by multiplying the mortgage amount by 1.8% and then adding a fixed charge of $4000, resulting in a total fee of $9,562.
Explanation:The mortgage broker fee for a $309,000 mortgage can be calculated by taking 1.8% of the mortgage amount and adding the fixed charge of $4000. To find 1.8% of $309,000, we multiply 0.018 by 309,000.
0.018 \( \times \) $309,000 = $5,562.
Then we add the fixed charge:
$5,562 + $4,000 = $9,562.
So, the mortgage broker fee for a $309,000 mortgage is $9,562.
Tourists were on a hiking trip for three days. On the first day, they hiked 1/8 of the trail. On the second day they hiked 4/7 of the remaining trail. On the third day they hiked 1/3 of the remaining trail and the last 8 km. How many km is the whole trail?
Answers
1st day:
(1/8)x = 0.125x traveled.
Remaining amount = (1 - 0.125)x = 0.875x
2nd day:
(4/7) of 0.875x = 0.5x traveled.
Remaining amount = (1 - 0.5)x = 0.5x
3rd day:
(1/3) of 0.5x = 0.1667x traveled + 8 km
The total fractional parts traveled is
0.125x + 0.5x + 0.1667x = 0.7917x
The remaining fractional shares is (1 - 0.7917)x = 0.2083x.
This is equal to the 8 km traveled, therefore
0.2083x = 8
x = 8/0.2083 = 38.406 km
Answer: 38.4 km (nearest tenth)
The total distance of the trail is 100/7 km, which simplifies to approximately 14.29 km.
To find the total distance of the trail, let's break down the information provided step by step.
First day: They hiked 1/8 of the trail.
Second day: They hiked 4/7 of the remaining trail after the first day. So, on the second day, they covered (1 - 1/8) × (4/7) of the total trail.
Third day: They hiked 1/3 of the remaining trail after the second day, plus the last 8 km.
Now, we can set up an equation to solve for the total distance:
1/8 + (1 - 1/8)× (4/7) + (1 - 1/8 - (1 - 1/8)× (4/7)) × (1/3) + 8 = Total Distance.
Let's calculate each part:
First day: 1/8 of the total trail.
Second day: (1 - 1/8)× (4/7) = 28/56 - 7/56 = 21/56 of the total trail.
Third day: (1 - 1/8 - 21/56)× (1/3) = (56/56 - 7/56 - 21/56) × (1/3) = 28/56× (1/3) = 28/168 = 1/6 of the total trail.
Now, let's add all these parts together:
1/8 + 21/56 + 1/6 + 8 = Total Distance.
To simplify, let's find a common denominator:
1/8 + 3/8 + 14/56 + 8/8 = Total Distance.
Now, add the fractions:
16/56 + 14/56 + 14/56 + 56/56 = Total Distance.
Combine:
100/56 = Total Distance.
Now, simplify:
Total Distance = 100/56×8/8 = 800/56 km.
Divide both numerator and denominator by the greatest common divisor, which is 8:
Total Distance = 100/7 km.
So, the whole trail is approximately 14.29 km.
When Marsha went shopping, she decided to buy some nuts to take home. She bought 1 3/4 lbs. of cashews, 5/8 lbs. of almonds, and 2 1/2 lbs. of peanuts. How many pounds of nuts did she buy?
Answers
x-------------> lbs. of cashews-------> 1 3/4 lbs------> (4+3)/4-----> 7/4 lbs
y-------------> lbs. of almonds-------> 5/8 lbs
z-------------> lbs. of peanuts-------> 2 1/2 lbs--------> (2*2+1)/2-----> 5/2 lbs
T-------------> total pounds of nuts
we know that
T=x+y+z
T=[(7/4)+(5/8)+(5/2)]--------> (1/8)*[14+5+20]-----> (1/8)*[39]=39/8 lbs
T=39/8=4.875 lbs----------> 4 7/8 lbs
the answer is 4 7/8 lbs
Answer: 4 7/8
Step-by-step explanation:
i just took the test
Too many nutrients is not good for bodies of water. This man-made is called what?
A. Cultural eutrophication
B. Point-source pollution
C. Eutrophication
Answers
I believe the answer is most likely Cultural eutrophication because it's the process that speeds up natural eutrophication because of human activity.
Find the x value for point C such that AC and BC form a 2:3 ratio.
A) 6
B) −0.6
C) 4
D) −2.4
Answers
The x value for point C is not one of the given options.
Explanation:To find the x value for point C such that AC and BC form a 2:3 ratio, we first need to find the coordinates of point C. The given components are Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21, we get:
C = sqrt((-2/3)² + (-4/3)² + (7/3)²) = sqrt(23/3)
Therefore, the x value for point C is not one of the options given. None of the options (A) 6, (B) -0.6, (C) 4, or (D) -2.4 are correct.
Final answer:
To find the x value for point C such that AC and BC form a 2:3 ratio, substitute the coordinates of point C into the equation and solve for C.
Explanation:
To find the x value for point C such that AC and BC form a 2:3 ratio, we can use the coordinates of points A, B, and C. We have Cx = -2/3, Cy = -4/3, and C₂ = 7/3. Substituting these values into Equation 2.21 gives:
C = √((-2/3)² + (-4/3)² + (7/3)²) = √(4/9 + 16/9 + 49/9) = √(69/9).
So the x value for point C is √(69/9).
Please help asap! lots of points
Answers
y2: -5
y1: -9
x2: 10
x1: 9
Fill in the numbers for the equation and solve. -5 - (-9) is 4. 10 - 9 is 1. 4/1 is just simply 4. There. The slope is 4, but we're not done. We'll use one of the points as x and y. Point-slope form is in the form of y - y1 = m(x - x1). y1 is -9. Because that is a negative number, we will be adding, so that part is y + 9, which eliminates answer choices A and B. x1 is 9. The other part will be 4(x - 9). That eliminates answer choice C. That leaves D, with the problem in point-slope form being y + 9 = 4(x - 9). When you subtract 4x from both sides, subtract 9 to isolate the y, multiply -10 and 4 together to get -40, and subtract 5 from -40 to get -45, the equation becomes -4x + y = -45. You use the values of the second point to find the value on the x-side. There. The answer is D.
Answer:
The answer is D.
Hope I helped :)
Have a blessed day <3
~Michael~
PLEASE HELP, 40 points, absurd answers will be reported, good answers will get brainliest
8.03b
(PART 1)
Find at least three examples of conic sections in the real world (marketing, architecture, nature, etc.). Make sure your collage demonstrates at least two of the conic categories you have learned. You may use circles, ellipses, parabolas, or hyperbolas. Arrange your images on paper or in a document.
(PART 2)
Respond to each of the following prompts in a word processing document.
Write a brief description about one of the conics from your collage.
Write the equation that represents your conic in its standard form. To do this either find the measurements of your conic example to create the equation or guess the measurements of the conic.
Your assignment must include:
Your conics collage.
A description about one conic from your collage.
The standard form equation of one of the conics.
An explanation of how the equation for the conic was found.
Answers
Part 2) The Golden Gate Bridge is a suspension Bridge spanning the Golden Gate, a short strait in San Francisco. It is one of the wonders of the Modern World and it was opened in 1937. It cost around 500 million dollars in today's currency and it is one of the longest suspension bridges in the world and from land to land the distance is 1280 m. The height of the suspensions is 230 m.
Part 3) We can think of a parabola of the form y=ax^2 where we need to substitute the values to find a.
The formula for the volume of a cone is v=1/3pir^2h. Find the radius, to the nearest hundredth, of a cone with a height of 3 in. and a volume of 12in.^3.Show your steps to finding the radius to receive credit.
Answers
The radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.
What is radius?Radius is the line that connects any point of the circumference of a circle to the center of that circle.
Given:
V = 1/3(πr²h)............... Equation 1Where:
V = Volume of the coner = radius of the coneh = height of the coneMake r the subject of the equation
r = √(3V/πh)................ Equation 2From the question,
Given:
V = 12 in³h = 3 inSubstitute these values into equation 2
r = √[(3×12)/(3.14×3)]r = √(12/3.14)r = √(3.82)r = 1.95 in.Hence, the radius of the cone with a height of 3 in and a volume of 12 in is 1.95 in.
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Final answer:
The radius to the nearest hundredth is 1.38
Explanation:
To find the radius of a cone with a given height and volume, use the formula [tex]V = 1/3 * \pi * r^2 * h[/tex], where V is the volume, r is the radius, and h is the height.
In this case, the volume is given as 12 in^3 and the height is given as 3 in.
Substituting these values into the formula:
[tex]12 = 1/3 * \pi * r^2 * 3[/tex]
Multiply both sides of the equation by 3:
[tex]36 = \pi * r^2 * 3[/tex]
Divide both sides of the equation by 3π:
[tex]12/\pi = r^2[/tex]
Take the square root of both sides of the equation:
[tex]r = \sqrt{(12/\pi )[/tex]
Approximating it to nearest hundredth -
r ≈ 1.38
What is the solution of the system? Use the elimination method. {4x+3y=62x+2y=5 The only solution is (−32, 4) .
The only solution is (0, 2) .
There are an infinite number of solutions.
There is no solution.
Answers
The cross products property states that the product of the ___ equals the products of the ___
Answers
For example:
3/6 = 4/8
Cross multiplying we get
3*8 = 6*4
24 = 24
The "means" are the middle values 6 and 4. The extremes are the outer edge values 3 and 8
Find the height of the top of the goal post, rounded to the nearest tenth of a foot
Answers
Due to insufficient and irrelevant information, the height of the goal post can't be determined.
Explanation:Unfortunately, the provided information does not allow us to ascertain the height of the goal post. The information presented primarily consists of measurements and heights of trees and people. Without any relevant information specific to the height of the goal post on which the question is based, it's not possible to provide a thorough answer. If further details were provided, such as the angle of the viewer's line of sight toward the top of the post and their distance from the post, then we could use trigonometric principles to resolve the answer.
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a. True
b. False: the fixed manipulator causes a number to be displayed in scientific notation.
Answers
WILL GIVE A BRAINLEST
Which piecewise relation defines a function?
Answers
The 3rd Image defines a piecewise function because for it to be a function, every input must match to exactly one and only one output. In Images 1, 2, and 4, there are certain inputs that have two outputs or stated otherwise, have two y-values for the same x-value. Only the 3rd Image matches 1 x-value to every 1 y-value. So, that's your answer.
Answer: C! The 3rd graph
Step-by-step explanation: Why does your equations have f(x)= and g(x)= ? Mine is only y= for every graph shown. All same numbers though.
Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
Answers
The complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:
h(t) = 25 · sin((π / 3) t) + 4
To model Amare's height above the ground, use the equation of a sinusoidal function.
In this case, since the Ferris wheel has a diameter of 50 meters, the amplitude of the function is half of the diameter, which is 25 meters. The Ferris wheel completes three revolutions in six minutes, so the period of the function is 6 minutes.
The equation for the height function is given by:
h(t) = A · sin((2π / T) t + φ) + h0
Where:
A is the amplitude (25 meters)
T is the period (6 minutes)
φ is the phase shift (0 radians, since Amare enters at the low point)
h0 is the vertical shift (4 meters, since the Ferris wheel sits four meters above the ground)
Substitute the given values into the equation
h(t) = 25 · sin((2π / 6) t + 0) + 4
Simplifying further:
h(t) = 25 · sin((π / 3) t) + 4
Therefore, the complete function that models Amare's height above the ground, h(t), as a function of time, t, in minutes is:
h(t) = 25 · sin((π / 3) t) + 4
Complete question
Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
h(t)=--- ·sin---- πt+---- π )+ ----