The final distance is 31 km.
Time, t = Distance, d/Velocity, v
Let's assume the ambulance drives a distance of x along the road, which leaves us 50-x on the road, after which it has reached the road.
It forms a triangle, after which we can use Pythagoras Theorem.
Using it, we get distance down the hill, d1, and we can calculate distance on the road remaining till the hospital, d2.
t = d1/v1 + d2/v2
= [tex]\frac{\sqrt{x^{2} + 30^{2} } }{30} + \frac{50 - x}{120}[/tex]
We need to minimise t. Therefore, we have to differentiate.
On differentiating and equating it to 0, we get the value of x as [tex]\sqrt{60} = 7.75[/tex]
How far down the road should the vehicle aim to reach the road to reach the hospital at the minimum time?
[tex]= \sqrt{900 + 7.75^{2} } = 31 km[/tex]
Thus, the final distance is 31 km.
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Which of the following represents the series? (2 points)
–12 + (–5) + 2 + 9 + 16
sum from k equals 0 to 4 of negative 19 plus 7 times k
sum from k equals 1 to 5 of negative 19 minus 7 times k
sum from k equals 0 to 4 of negative 12 plus 7 times k
sum from k equals 1 to 5 of negative 12 minus 7 times k
The option that represents the arithmetic series is;
Option C: sum from k equals 0 to 4 of negative 12 plus 7 times k
What is the formula for the arithmetic sequence?
An arithmetic series is defined as an arithmetic sequence, whereby each term of the series is gotten from the previous term by the addition or subtraction of a common term.
The series is given as;
-12 + (-5) + 2 + 9 + 16
By careful observation, we see that each term in the series is gotten from the previous term by the addition of 7.
The series here is therefore an example of arithmetic sequence.
The equation of the series when the first term is -12 can therefore be written as; -12 + 7·k
Where;
-12 is the first term
7 is the common difference
n is the number of terms
k = n - 1
When k = 0, we have;
-12 + 7·k
= -12 + 7 × 0
= -12
When k = 1, we have;
-12 + 7·k
= -12 + 7 × 1
= -5
When k = 2, we have;
-12 + 7·k
= -12 + 7 × 2
= 2
When k = 3, we have;
-12 + 7·k
= -12 + 7 × 3
= 9
When k = 4, we have;
-12 + 7·k
= -12 + 7 × 4
= 16
Therefore, we conclude that using values of k that range from k = 0 to k = 4, the expression that represents the series is therefore the option C
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14) The sum of the digits of a two digit number is 12. The number obtained by reversing the digits is 18 less than the original number. What is the original number? Solve by using a system of equations. Write the 2 equations in the space provided. Show all work, including the method of your choice, used to solve.
Equation 1:
Equation 2:
The original number is 57.
The two equations are x+y = 12 and (10y+x)−(10x+y) = 18.
Let the digit at the tens place be x and the digit at the unit place be y.
x+y = 12 .........(1)
Required Number = (10x+y).
Number obtained on reversing the digits = (10y+x).
According to the condition, we get
(10y+x)−(10x+y) = 18
→ 9y−9x = 18
→ y−x = 2 ..........(2)
Adding (1) and (2), we get
2y = 14
y =7
x = 12 - 7
x = 5
Hence, the required number is 57.
The equations used to solve this is x+y = 12 and (10y+x)−(10x+y) = 18.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The volume of the cone is approximately 134 ft cube.
The cone would fit in 4 times in the red beach ball.
How to find the volume of a sphere and cone?The diameter of the red beach ball is 8 inches, then the cone has the same radius and a height of 8 inches .
Therefore, to know the number of times the beach ball will fit into the cone, we have to find the volume of each solid shape.
Therefore,
volume of the beach ball(sphere) = 4πr³
where
r = radiusr = 8 /2 = 4 inches
volume of the beach ball(sphere) = 4 × π × 4³
volume of the beach ball(sphere) = 256π ft³
Therefore,
volume of the cone = 1 / 3 πr²h
where
r = radiush = heightvolume of the cone = 1 / 3 × π × 4² × 8
volume of the cone = 128π / 3
volume of the cone = 42.7π
volume of the cone = 134.078
volume of the cone ≈ 134 ft³
Therefore,
volume of beach ball / volume of cone = 256π / 42.7π = 5.99531615925
Therefore, the cone will fit 4 times into the red beach ball.
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Financial analysts forecast Safeco Corp.’s (SAF) growth rate for the future to be 12 percent. Safeco’s recent dividend was $1.60.
What is the value of Safeco stock when the required return is 14 percent? (Round your answer to 2 decimal places.)
The value of Safeco stock given the required return growth rate and the dividend of the stock is $89.60.
What is the value of Safeco stock?The value of the stock can be determined using the constant growth dividend model. According to the model, the value of the stock is a function of the growth rate, dividend and the required return of the stock.
Value of the stock = [dividend x (1 + g)] / (r - g)
where
r = required return
g = growth rate
Value of the stock = [1.60 x (1.12) / (0.14 - 0.12)
Value of the stock = 1.792 / 0.02
Value of the stock = $89.60
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Simplify the expression to a polynomial in standard form:
(x + 3)(2x" + 3x + 7)
Answer:
2x³ + 9x² + 16x + 21-------------------------------------
Given expression:
(x + 3)(2x² + 3x + 7)Distribute and simplify:
(x + 3)(2x² + 3x + 7) = Givenx(2x²) + x(3x) + 7x + 3(2x²) + 3(3x) + 21 = Distribute2x³ + 3x² + 7x + 6x² + 9x + 21 = Collect like terms2x³ + 9x² + 16x + 21 AnswerPLEASE ANSWER! I WILL GIVE BRAINEST!
A student is building a squirrel feeder for a family member. The figure is a model of the feeder.
(A rectangular prism with dimensions 2 and three fourths inches by 16 and one half inches by 4 inches.)
How much feed can the container hold?
the formula for the area of a triangle is A=1/2bh. find the area of a triangle with a base (b) of 8 feet and a height (h) of 11 feet. the area of the triangle is_ spuare feet.
Answer: 44ft^2
Step-by-step explanation:
plug it into the equation, h=11, b=8
so A=1/2(11)(8) = 44ft^2
use exponential fitting to find a closed formula for the sequence: 4, 5, 7, 11, 19, 35, 67, ...
The exponential form of the given sequence is - [tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex] where x is a set of whole numbers and n is a set of natural numbers.
The given sequence is - 4, 5, 7, 11, 19, 35, 67, ...
the first term - [tex]t_1[/tex] is 4
Hence, we can write the sequence as follows-
4 + [tex]2^0[/tex] = 5
5+[tex](2)^1[/tex]=7
7+[tex](2)^2[/tex]=11
11+[tex](2)^3[/tex]=19
and so on.
Here, we are adding the previous term with the exponential form of 2.
thus, we can conclude that -
[tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex]
where, x is a set of whole numbers, and n is a set of natural numbers.
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Player First
Round Final
Round
Golfer 11 72 72
Golfer 12 72 70
Golfer 13 70 73
Golfer 14 70 77
Golfer 15 68 70
Golfer 16 68 66
Golfer 17 71 70
Golfer 18 70 68
Golfer 19 69 68
Golfer 20 67 71
Suppose you would like to determine if the mean score for the first round of a golf tournament event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?
(a) Use α = 0.10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. State the null and alternative hypotheses. (Use μd = mean score first round − mean score fourth round.
Calculate the value of the test statistic. (Round your answer to three decimal places.)
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
(b) What is the point estimate of the difference between the two population means? (Use mean score first round − mean score fourth round.)
The point estimate of the difference between the two population means is -1.05.
Here, we are given the data representing the scores of the golf players in the 1st and final rounds.
a. The significance level is: α = 0.10
we can construct the following hypothesis test-
Null hypothesis H₀ ⇒ μd = 0
This implies that there is no difference between the population mean of the first round and final round.
Alternative hypothesis: Ha ⇒ μd ≠ 0
This implies that there is a difference between the population mean of the 1st round and final round.
Now, the test statistic will be-
[tex]t = (d-mean_{d})\sqrt{n}/ s_{d\\}[/tex]
we can use excel to calculate the test statistic.
This will give us: 0.10 < P < 0.20
b. the main margin of error is 90% confidence level. This means that there is no significant difference, hence - 1.05.
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Your question was incomplete. Check for the missing figure below.
solve the system of equations x = 17 - 4 y = x - 2
Answer:
To solve the given system of equations, we can start by substituting the value of x in the second equation into the first equation. Since the second equation tells us that x = y - 2, we can substitute y - 2 for x in the first equation to get:
x = 17 - 4y
y - 2 = 17 - 4y
Then, we can combine like terms on the right-hand side to get:
x = 17 - 4y
-3y = 15
Finally, we can divide both sides by -3 to solve for y, and then substitute this value back into one of the original equations to solve for x:
x = 17 - 4y
y = -5
x = 17 - 4(-5) = 17 + 20 = 37
Therefore, the solution to the system of equations is x = 37 and y = -5.
Determine whether the graph represents a function. Explain.
Answer:
No.
Step-by-step explanation:
A function have only one output (y) for each x. This is not true with this graph. For example: the point (6,1) and ( 6,5) are both on the graph. The input 6 has more than 1 output. It has the output of 1 and 5. Since it has more than one output, it is not a function.
Donnelle has already saved $350.00
Donnelle can save $45 per week from her
part-time job. How many weeks will it take her to
save at least $2150 to pay cash for a used car?
a satellite traveling in a circular orbit 1,000 miles above the earth passes directly over a tracking station at noon. assume that the satellite takes 2 hours to make an orbit and that the radius of the earth is 4,000 miles. find the distance between the satellite and tracking station at 12:03 p.m. draw a picture (using the idea of orbits like above), then solve.
The distance between the satellite and the tracking station is 1220 miles
To find the distance between the satellite and the tracking station we need to apply cosine law:
[tex]c^{2} =a^{2} +b^{2} -2ab cos(\beta )----------(1)[/tex]
where:
c=length of side c
a=length of side a
b=length of side b
β=angle opposite c
we need to find the angle of β
computing the angle β gives
[tex]\beta =\frac{3min}{120min} *360[/tex]
β=9°
Now substitute the β value ,a=4000,b=5000,in cosine law, and we get
[tex]x^{2} =4000^{2} +5000^{2} -2(4000)(5000)cos 9[/tex]
[tex]=(16+15-39.51)*10^{6 }\\=1.49*10^{6}[/tex]
x=1.22x10^3
x=1220 miles distance from the satellite to the tracking station.
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State the null and alternative hypotheses you would use to test the following situation.An annual report showed that Florida topped the nation with 24% of its motorist uninsured. After implementing several new programs during the last two years, the state reevaluated its percentage of uninsured motorists. Determine the null and alternative hypotheses for a test to determine whether the proportion of uninsured motorists has decreased over the last two years.H_{0} / p = 0.24H_{1} / p > 0.24H_{0} / p = 0.24H_{1} :p ne0.24H_{0} / p > 0.24 H_{1} / p < 0.24H_{0} / p = 0.24 H_{1} / p < 0.24
Answer: Im sorry I cant help im just doing this for points
Step-by-step explanation:
The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].
How to write this in maths notationIn mathematical notation, the null hypothesis can be written as:
H_0: p = 0.24
where p is the proportion of uninsured motorists in Florida.
The alternative hypothesis can be written as:
H_1: p < 0.24
This means that we are testing the hypothesis that the proportion of uninsured motorists has decreased to a level that is less than 24%.
The null hypothesis is the default assumption, and we will only reject it if we have enough evidence to support the alternative hypothesis. In this case, we would need to collect data that suggests that the proportion of uninsured motorists has decreased to a level that is significantly less than 24%.
The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].
The other options are incorrect because they either do not specify the direction of the hypothesis test (i.e., whether we are testing whether the proportion of uninsured motorists has increased or decreased) or they are not supported by the given information.
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the table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. which statements about the function described by the table are true? check all that apply. the independent variable is the number of people. the initial value (initial fee) for the picnic is $40. the rate of change is $8.67 per person. as the number of people increases, the total cost of the picnic increases. if 4 people attended the picnic, the total cost would be $46.
The correct statements are:
a) The independent variable is the number of people.
b) The initial value (initial fee) for the picnic is $40.
d) As the number of people increases, the total cost of the picnic increases.
A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:
m = (y - y')/x - x'
Now let's analyze the table:
The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:
(6, 52) and (9, 58).
Then the slope is:
a = (58 - 52)/9 -6 = 2
Then the line is something like:
y = 2*x + b
To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.
We will get:
52 = 2*6 + b
52 = 12 + b
52 - 12 = b = 40
Then the linear equation is:
y = 2*x + 40
Now let's see which statements are correct.
a) The independent variable is the number of people.
True, the "x" represents the number of people.
b) The initial value (initial fee) for the picnic is $40.
True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.
c)The rate of change is $8.67 per person.
False, the rate of change is equal to the slope, in this case is $2 per person.
d) As the number of people increases, the total cost of the picnic increases.
True.
e) If 4 people attended the picnic, the total cost would be $46.
To see if this is true or not, we just need to evaluate the function that we got in x = 4.
y = 2*4 + 40 = 48
So we can see that this is false.
Therefore, the correct statements are A, B, D
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for all negative semidefinite matrix, the first principal determinant has to be either 0 or negative. A. True B.False
A is negative semidefinite if and only if all the kth order principal minors of A are ≤ 0 if k is odd and ≥ 0 if k is even. The given statement is true.
What is a negative semidefinite matrix?
A Hermitian matrix with all of its eigenvalues being nonpositive is known as a negative semidefinite matrix. Using the Wolfram Language's NegativeSemidefiniteMatrixQ[m], a matrix may be checked to see if it is negative semidefinite.
The direction of space is inverted when the determinant is negative. If you give your fingers dimensions before transformation and they remain true after, it indicates that the orientation of space has not changed and the determinant is positive.
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The weight of meteorite A is 8times the weight of meteorite B. If the sum of their weights is 189 tons, find the weight of each.
The weight of meteorite A and B are 21 and 168 tons respectively.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, The weight of meteorite A is 8 times the weight of meteorite B. And the sum of their weights is 189 tons,
To find their weights we need to establish an equation, relating their weights,
Let weight of meteoroid B be x, then weight of meteoroid A will be 8x,
Establishing the equation,
8x+x = 189
9x = 189
x = 21
8x = 21x8 = 168
Hence, The weight of meteorite A and B are 21 and 168 tons respectively.
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g give a derivation to show that the following argument is valid in tfl. be sure to submit your answer by clicking the submit button.
g give a derivation to show that the following argument is valid in tfl. be p ∨ q) → r, p → s, ¬s → ¬r
1. (p ∨ q) → r Premise
2. p → s Premise
3. ¬s → ¬r Premise
4. p Assumption
5. s Modus Ponens (2, 4)
6. ¬r Modus Ponens (3, 5)
7. ¬(p ∨ q) Assumption
8. ¬p Simplification (7)
9. ¬q Simplification (7)
10. r Addition (1, 9)
11. Contradiction (6, 10)
12. ¬¬(p ∨ q) Double Negation (7-11)
13. (p ∨ q) Simplify(12)
14. r Modus Ponens (1, 13)
15. p → r Hypothetical Syllogism (4-14)
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A group of 2342 students were surveyed about the courses they were taking at their college with the
following results:
1031 students said they were taking Dance.
1058 students said they were taking Science.
1059 students said they were taking English.
449 students said they were taking Science and Dance.
459 students said they were taking Science and English.
456 students said they were taking Dance and English.
218 students said they were taking all three courses.
Fill in the following Venn Diagram with the cardinality of each region then answer the questions
below.
Science
IV.
11.
VII.
V.
English
VI.
How many students took Science, Dance, or English?
How many students took Dance and English, but not Science?
How many students took Science or didn't take Dance?
How many students took none of the courses?
Dance
III.
How many students took Science or English, but not Dance?
VIII.
The missing features of the Venn diagram include the following:
I=472, II=449 ,IV=459 ,V=218 , VI=456,
What is a Venn diagram?A Venn diagram is a circular illustration of how variables are interrelated to each other.
To solve for I;
Total number of students taking dance = 1031
Total number of students taking science and dance= 449
Total number of students taking all three courses= 218
Total number of students taking science and English = 459
Therefore, the number of students taking only science;
I =( II-V)+ (IV-V)
I= (449-218)+(459-218)
I = 231+241
I= 472
The number of students that took Science, Dance, or English =V= 218
The number of students took Dance and English, but not Science = VI = 456
The number of students took Science or didn't take Dance = IV = 459
The number of students took none of the courses = VIII = U
The number of students took Science or English, but not Dance = 459 students.
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write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8
A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.
Define polynomial function.In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Given,
As stated, the polynomial's leading coefficient is equal to 1.
The function's zeroes are also listed as -2, 3, and 6.
For root 3: ( x - 3)
for root 6: (x - 6)
As a result, the polynomial function is
f = 1(x+2)(x-3)(x-6) (x-6)
f = (x+2)(x² - 6x - 3x + 18)
f = (x+2)(x² - 9x + 18)
f = x³ - 9x² + 18x + 2x² - 18x + 36
f = x³ - 7x² + 36
A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.
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Write the standard form of the equation of the line that passes through the points (-3,-2) and (-1,0).
A) x + y = 0
C) x + y = 2
B) x - y = 0
D) x - y = -1
In standard form the equation of the line passing through the points,
(-3, -2) and (-1, 0). is
x - y = -1
How to determine the equation of the line passing through the given pointsInformation given in the question include
points, (-3, -2) and (-1, 0).
Standard form of linear equations is of the form Ax + By = C
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m calculating using the points (-3, -2) and (-1, 0).
m = (0 - (-2)) / (-1 - (-3))
m = (2) / (2)
m = 1
if the line passes through point X(-1, 0)
y - 0 = 1(x - (-1))
y = x + 1
x - y = -1
the intercept C = 1
The equation of the line is x - y = -1
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Part 1: Choose the equation represented by the model given below.
The linear equation that representing the given model is 6x-3 = 15.
In the given question, we have to choose the equation represented by the model given below.
As we know that;
A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.
The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.
To write the equation that represented by the given model, we count the variable that are of the same type. Then we write them after counting.
As we can see that in the model have 6 triangles of x, 3 circles of -1 and 15 circles of 1. So the linear equation that representing the given model is 6x-3 = 15.
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The steps your friend took to divide two mixed numbers are shown below.
4 2/3 / 2 1/4=14/3x9/4=21/2= 10½
Part A:
What should your friend change in order to divide the two mixed numbers correctly?
A) Find a common denominator of 3 and 4
B) Multiply by the reciprocal of 14/3
C) Multiply by the reciprocal of 9/4
D) Rename 4 2/3 as 3 5/3
Part B:
What should your friend do to check that their answer is correct using the inverse
operation?
The friend should change the multiplication of 9/4 to multiplication by the reciprocal of 9/4.
Option C is the correct answer.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
4(2/3) and 2(1/4)
Divide 4(2/3) by 2(1/4)
4(2/3) ÷ 2(1/4)
= 14/3 ÷ 9/4
Multiply the reciprocal of 9/4.
= 14/3 x 4/9
= 56/27
= 2(2/27)
Thus,
The value of the division of the fraction is 2(2/27).
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Use the diagram to solve for x.
5. El lado canadiense de las Cataratas del Niagara tiene un caudal de 600,000 litros por segundo. ¿Cuántos
galones de agua fluyen por las cataratas en 1 minuto?
Answer:
9,510,223.49 galones!
Step-by-step explanation:
Primero, tienes que saber la cauntidad de los litros en un galon.
Hay 3.7854 litres en un galon
ahora, hacemos un ratio
1 galon = 3.7854 litres
? galones = 600,000 litres
Para encontrar la respuesta, divide 600,000 por 3.7854 para obtener la cauntidad de los galones
600,000 ÷ 3.7854 = 158,503.725 galones
158,503. 725 litres fluyen por segundo.
Hay 60 segundos en un minuto asi que, tenemos que multiplica nuestra respuesta por 60 para calcular nuestra respuesta final.
158,503. 725 × 60 = 9,510,223.49 galones!
1) 2x+7x=
2) 8b-5b=
3) 5m+2m-4m=
4) a+a+a+a+a=
5) 2x+3x+6x-4x=
6) 2a+2b+a+3b=
7) 2x+7x-4=
8) 2m-2b-m+4b=
9) 10a+2b+2c+3a-b+4c=
10) 5+2 b-4+7 b=
11) 9 p+3 q-2 p-3 q=
12) a+2 b+a-b-10=
Answer: 1: 9x
Step-by-step explanation:
2: 3b
3: 3m
4: 5a
5: 7x
6: 3a+5b
7: 9x-4
8: m-6b
9: 13a+3b+6c
10: 1+9b
11: 7p
12: 2a+1b-10
Please help!!!!!!!!!!
Answer:
[tex]6^{\frac{1}{12}}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} } =\frac{6^{\frac{1}{3} } }{6^\frac{1}{4} }[/tex]
[tex]= 6^{\frac{1}{3}[/tex] ÷ [tex]6^{\frac{1}{4}}[/tex]
= [tex]6^{\frac{1}{3}-\frac{1}{4}}[/tex]
=[tex]6^{\frac{4}{12}-\frac{3}{12}}[/tex]
[tex]= 6^\frac{1}{12}[/tex]
Solve the equation.12d-14=-2
Show Hint
Hint: Be sure to use inverse operations.
Solve the equation. 10 s -9=32
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Hint: Be sure to use inverse operations.
Solve the equation. {c}/{-10}-5=9
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Hint: Be sure to use inverse operations.
Answer: The answer is -2.34
Step-by-step explanation: Get Good
7 of 107 of 10 Questions
Question 1
Write the inverse variation equation for xand yif yvaries inversely with x,and y=34when x=8.
The inverse variation equation is
Question 2
Find ywhen x=12and find xwhen y=30.
If an answer is not an integer, enter it as a fraction.
When x=12, y=
Question 3
When y=30, x=
1. The equation of the inverse variation is, y = 272/x.
2. When x = 12, y = 68/3
When y = 30, x = 136/15.
What is an Inverse Variation?An inverse variation is defined by the equation, y = k/x, where k is the constant of proportionality between the relationship of y and x.
1. Given that y varies inversely with x, substitute y = 34 and x = 8 into y = k/x, and find the value of the constant of proportionality, k:
34 = k/8
34 × 8 = k
k = 272
To write the equation, substitute k = 272 into y = k/x:
y = 272/x
2. When x = 12, we have:
y = 272/12
Simplify
y = 68/3
When y = 30, we have:
30 = 272/x
30x = 272
30x/30 = 272/30
x = 136/15
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Derek boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed. Let h represent John's height above the center of the Ferris wheel (in feet) and let t represent the number of mintues since the ride started. a. Suppose the radius of the Ferris wheel is 20 feet and the Ferris wheel rotates at 1 radian per minute. Plot the relationship between h and t for this scenario. 20- 1o -10 -20 ear All Draw: b. Now, suppose the radius of the Ferris wheel is 20 feet and the Ferris wheel rotates at 2 radians per minute. Plot the relationship between h and t for this scenario. 30 20- 10 10 20 ear All Draw c. Now, suppose the radius of the Ferris wheel is 25 feet and the Ferris wheel rotates at 2 radians per minute. Plot the relationship between h and t for this scenario. 30 20 10 20 r All Draw:
The result for all expressions are
a) r(t) = 6.5t radians
b) C(t) = 20cos(6.5*t) feet
c) H(t) = 36 - C(t)
The situation is depicted in the picture attached considering the center of the wheel as the center of the coordinates system.
Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply:
6.5 radians __________ 1 minute
r(t) radians ____________ t minutes
and obviously, r(t) = 6.5t radians
The height C(t) above the center after t minutes is given by
C(t) = 20cos(r(t)) ===> C(t) = 20cos(6.5*t) feet
When C(t) < 0 means that derek wheel is below the center of the wheel.
Since the center of the Ferris wheel is 36 feet above the ground, the height H(t) above the ground after t minutes is given by
H(t) = 36 - C(t)
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