Emily is on a Ferris wheel and her height is modeled by the equation
27
y = 30.48 cos2pi/4.25 (x - 2) + 34.27 where x = the number of minutes since the
ride began and y = the height in feet of Emily.
a) What is the radius of the Ferris wheel?
b) How long does it take Emily to make one rotation?
The radius is______
feet and it takes Emily_____
minutes for one rotation.
Answers
The given function for the height of the Ferris wheel is a sinusoidal equation.
a) The radius is 30.48 feet and it takes Emily 4.25 minutes for one rotationReasons:
The function that gives the height of the Ferris wheel is presented as follows;
[tex]\displaystyle y = 30.48 \cdot cos \frac{2\cdot \pi }{4.25} \cdot \left(x - 2 \right) + 34.27[/tex]
Where;
x = The number of minutes since the ride began
y = The height in feet of Emily
a) Required:
The radius of the Ferris wheel
Solution:
Comparing the given equation with the general equation of a Ferris wheel, we have;
[tex]\displaystyle f(t) = \mathbf{A \cdot trig\left(B \cdot \left(t + C\right) \right) + D}[/tex]
The amplitude of the Ferris wheel = A = 30.48
The amplitude, A = The largest distance from the center = The radius, r
A = r
Therefore;
The radius of the Ferris wheel, r = A = 30.48 feet
b) The time it takes the Emily to make one rotation is given by the period, T, of the motion of the Ferris wheel as follows;
[tex]\displaystyle T = \mathbf{\frac{2 \cdot \pi}{B}}[/tex]
By comparison, we have;
[tex]\displaystyle B = \frac{2 \cdot \pi}{4.25}[/tex]
Therefore;
[tex]\displaystyle The \ period, \, T = \frac{2 \cdot \pi}{\left(\frac{2 \cdot \pi}{4.25} \right)} = 4.25[/tex]
The time it takes Emily to make one rotation, T = 4.25 minutes
Learn more here:
https://brainly.com/question/21165143
Related Questions
The slope of a line is -1/2 What is the slope of a line that is perpendicular to it?
Answers
A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 feet deep at its deepest point. If the pool is being filled at a rate of 0.8ft3/min, how fast is the water level rising when the depth at the deepest point is 5 ft
Answers
Using implicit differentiation, it is found that the water level is rising a rate of 0.001 ft/sec.
The volume of a pool of length l, width w and height h is given by:
[tex]V = lwh[/tex]
Applying implicit differentiation, the rate of change of the volume is given by:
[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]
Neither the width nor the length changes, hence [tex]\frac{dl}{dt} = \frac{dw}{dt} = 0[/tex], and:
[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]
We are given that:
[tex]\frac{dV}{dt} = 0.3, l = 20, w = 40[/tex], hence:
[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]
[tex]0.8 = 20(40)\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{0.8}{800}[/tex]
[tex]\frac{dh}{dt} = 0.001 [/tex]
Water level is rising at rate of 0.001 ft/sec.
A similar problem is given at https://brainly.com/question/9543179
Due to the heightened demand for Clorox wipes, the company has marked up their prices by 20%. If they used to only cost $3.75, how much do they cost now?
A theme park ticket usually costs $154. Due to lower attendance rates, they have marked down their ticket costs by 18%. How much is the ticket cost now?
Answers
Answer:
hey there!
Step-by-step explanation:
FIRST QUESTION
3.75
10%= 0.375
20%= 0.75
3.75 + 75 = 4.50
$4.50
SECOND QUESTION
18/100 = X/154
X/154 = 18/100
X*154/154 = 18*154/100
X = 2772/100
X = 27.72
154- 27.72 = 126.28
$126.28
pleas help on the second ASAP it was due yesterday.. i dont even understand how to do any of it and i will give brainliest <3
Answers
Answer:
[tex]3x^{4}[/tex]
Step-by-step explanation:
I suggest looking lessons on it online if you don't understand... It's hard to do your work especially if you don't understand it. Or if your online, go to past lessons or something.
Answer:
The answer is 3x^4
Step-by-step explanation:
Will be giving brainliest! Have a good day and you’ll get through it !
Answers
Answer:
ok you to !!!!!!!!! good night!!
Step-by-step explanation:
What is the length of side YZ to the nearest tenth please show your work!
Answers
Length of side YZ to the nearest tenth is 16 ft
To solve this question we would use the sine rule. The sine rule states that
A/sin a = B/sin b
if we take our angle a to be XZY, and b to be ZXY.
Going by angles in a triangle, ZXY = 180 - 90 - 35 = 55. This means that our angle b is 55º
applying the sine rule, we have
11/sin 35 = B/sin 55
11/0.5736 = B/0.8192, if we cross multiply, we have
B = (11 * 0.8192)/0.5736
B = 9.0112/0.5736
B = 15.7 ft
learn more about sine rule here https://brainly.com/question/9599008
Answer:
15.7
Step-by-step explanation:
Drag each relation to the correct location on the table. Classify the relations according to whether or not they are functions.
Answers
they are all functions
There are 564 men and women working in a factory.
There are twice as many women as men.
How many men are working in the factory?
Answers
Answer:
564x2=1128 men
Step-by-step explanation:
Answer:
there are1139 women are working in the factory
Can someone answer this correctly for my sister please
Answers
Answer:
12) A ( 9, 11, 13, 15)
13) A ( o , a)
14) A (b ∈ ( a, b, c, d, e, f))
15) C ( -364)
16) D (-1°C)
17) B (Negative)
18) C (26 feet)
19) B (7)
Step-by-step explanation:
12) All of these are odd numbers greater than 7
13) These are the only vowels in "MONDAY"
14) Point B cannot belong in a set that already has B
15) -9876 + 9512 = -364
16) 4 - 5 = -1
17) ex: -2 + (-2) = -4
18) -20 + 12 - 18 = -26
19) 3(5) + 4(-2) = 15 - 8 = 7
-Chetan K
the sum of three consecutive odd integers is 17 less than four times the smallest integer. find the largest integer.
PLSSS helPPP :')
Answers
Answer:
Find three consecutive integers where their sum is 17 less than four times the smallest integer. So consider any integer -- let's call it n.
7 answers
·
1 vote:
Let the smallest of those numbers be [math]n[/math], then the other numbers w
Step-by-step explanation:
Pls answer, will award brainliest
Answers
1.00065528... Is the correct answer.
what is the area of a rectangle if 1 base is 14 in, the 2nd base is 3.5 in and the height is 8 in?
Answers
Check the picture below.
notice, we have three pair of sides, let's add them all up to get the area
[tex]\stackrel{\textit{left and right}}{2(8\cdot 14)}+\stackrel{\textit{front and back}}{2(3.5\cdot 8)}+\stackrel{\textit{top and bottom}}{2(3.5\cdot 14)}\implies 378~in^2[/tex]
In circle O, what is mArc A E?
Answers
Answer:
Step-by-step explanation:
By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …
By using the theorem of secants intersecting externally, Measure of angle formed by two secants, from a point outside the circle is half the difference of the measures of the intercepted arcs. m∠C =. 36° =. 72° = °. …
What is -105/-77 simplified?
Answers
Answer:
[tex]\frac{-15}{-11}[/tex]
Step-by-step explanation:
To simplify more known as reduced we have to find the fraction as and equivalent fraction
DefinitionEquivalent Fraction - are the fractions that have different numerators and denominators but are equal to the same value.
Look for the GCFTo find the we must list out the of and
[tex]77:1, 7, 11 ,77\\\\1, 3, 5, 7, 15, 21, 35 , 105[/tex]
Our [tex]GCF[/tex] is [tex]7[/tex]
Our fraction[tex]\frac{-105}{-77}[/tex]ReduceDefinition of reduce - reduction refers to the rewriting of an expression into a simpler form
Divide the numerator and denominator by [tex]7[/tex]
Our fraction is [tex]\frac{-15}{-11}[/tex]6 + 2f = 8
f =
what the awnser i need help
Answers
Answer
f= 1
step by step explanation
If a ½ gallon of paint covers ⅙ of a wall, continuing at this rate how much paint is needed for the entire wall?
Answers
Answer:Full wall is 6 times 1/6 (6*1/6=1), so 6 times half a gallon, or 3 gallons.
Step-by-step explanation:
25Y^2/5y-4 + 16/4-5y
Answers
Answer:
5Y2y-5y
Step-by-step explanation:
5
Y
2
y
−
5
y
what is the value of x?
(3x-1)º
Answers
(3x-1)))))]))))))))])))))))))))))])))))))))))))))))))))))
tap the word that "they" refers to
a. birds
b. frogs
c. feets
Answers
Step-by-step explanation:
we would a small text, or give us a picture so we can read it, then we can answer this question, without it, I'd have to guess
what is (12x2)-(45/5)
Answers
Answer:
[tex](12 \times 2) - \left(\dfrac{45}5 \right) =24 -9 = 15[/tex]
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
(12 × 2) - (45 / 5) ← evaluate parenthesis
= 24 - 9
= 15
Find the distance between points A(−1, 5) and B(0, 4) to the nearest tenth.
Answers
Answer:
1.4
Step-by-step explanation:
Use the distance formula
d= √(x2-x1)² +(y2-y1)² , where x1, x2, y1, y2 are the coordinates of the points
A(x1 = −1, y1 = 5) and B(x2 = 0, y2 = 4)
d= √(0 - -1 )² +(4 - 5)²
d= √(1)² +(-1)²
d= √2
d= 1.414213562, round to the nearest tenth
d≈ 1.4
if 9/24 equals 3/x , then x is ____
Answers
[tex]\\ \sf\longmapsto \dfrac{9}{24}=\dfrac{3}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3}{8}=\dfrac{3}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=24[/tex]
[tex]\\ \sf\longmapsto x=24/3[/tex]
[tex]\\ \sf\longmapsto x=8[/tex]
Is (1,5) a solution to this system of equations?
y=
–
3x+7
y=3x+2
Answers
Answer:
no, there is no solution
Step-by-step explanation:
put it in desmos, but the slopes are the same, so they are parallel and never touch. So, no solution.
Select the correct answer from each drop-down menu.
The graph of g(x) is shown.
The graph of h(x) = g(x + 5) has
and
.
Answers
The function h(x) has a horizontal asymptote at y=5 and the vertical asymptote is x=-2.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Given that, h(x)=g(x+5.
Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.
Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.
Here, the horizontal asymptote is 3, and the vertical asymptote is -2
The graph of h(x) = g(x+5) had a horizontal asymptote at y=5 and the same vertical asymptote as function g(x).
Therefore, the function h(x) has a horizontal asymptote at y=5 and the vertical asymptote is x=-2.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ2
Evaluate each expression.
12
N
3
(2511)
-
DONE
Answers
Answer:
1/5Step-by-step explanation:
[tex](25^{-3/2})^{1/3} = 25^{-3/2*1/3} = 25^{-1/2}=5^{-1/2*2}=5^{-1}=1/5[/tex]Let's evaluate the expression,
→ (25^-3/2)^1/3
→ 25^-3/2×1/3
→ 25^-3/6
→ 5^-1/2×2
→ 5^-1 {or} 1/5
Hence, the answer is 1/5.
A corporation recently sold zero-coupon $400 bonds maturing in 4 years with an annual yield of 12%. Find the price. [Hint: The price is the present value of $400 4 years from now at the stated interest rate.] (Round your answer to the nearest cent.)
Answers
Answer:
Step-by-step explanation:
400*1.12^-4= 254.2072314
Calculate percentage to the nearest 0.1%.
The markup on desserts in a restaurant is 70% of the menu price. The restaurant is adding key lime pie to its dessert list.
The cost to the restaurant works out to $1.25 per slice.
Determine:
a. The menu price of a slice of pie. (Round your answer to the nearest cent.)
Price
$
b. The rate of markup on cost. (Round your answer to one decimal place.)
Rate
%
Answers
9514 1404 393
Answer:
a. $4.17
b. 233.3%
Step-by-step explanation:
a. The proportion the markup (m) is to the total (t) is ...
m : t = 7 : 10
The total is the cost (c) plus the markup, so we have ...
m : t = 7 : 10 = m : (m +c) = 7 : 7 +3
Then the ratio of total price to cost is ...
t : c = 10 : 3
The menu price of the pie slice will be ...
$1.25 × 7/3 ≈ $4.17
__
b. The ratio of markup to cost is ...
m : c = 7 : 3 ≈ 2.333 = 233.3%
What is the area of the figure below?
16 square units
14 square units
10 square units
12 square units
Answers
How do you get this answer?
start by counting the boxes there’s a total of six in the first rectangle and 6 on the other so 6+6= 12!!!
Just count the boxes and that’s it:)
Clip 102
2
2
Standard Questions
Question Progress
Two families go to a zoo.
The Smith family of two adults and three children pay £66.
The Jones family of three adults and five children pay £105.
Work out the cost of an adult ticket and the cost of a child ticket.
In your working, let 'a'stand for an adult ticket and 'C'stand for a child ticket.
Answers
Answer:
Let's solve your system by elimination.
2a + 3c =66 ; 3a + 5c = 105
Multiply the first equation by 5,and multiply the second equation by -3.
5 (2a + 3c = 66)
−3 (3a + 5c = 105)
Becomes:
10a + 15c = 330
−9a − 15c = −315
Add these equations to eliminate c:
a = 15
Now that we've found a let's plug it back in to solve for c.
Write down an original equation:
2a + 3c = 66
Substitute 15 for a in 2a + 3c = 66:
(2)(15) + 3c = 66
3c + 30 = 66 (Simplify both sides of the equation)
3c + 30 −30 = 66 −30 (Add -30 to both sides)
3c = 36
3c3= 363 (Divide both sides by 3)
c = 12
Answer:
a = 15 and c = 12
Please answer all these question
Answers
Answer:
it's 10.00 because I used a calculator