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
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solve using quadratic formula
3n^2-2n-5=0
=5/3 =−1
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
Logan is a great babysitter. He makes $9 an hour. Jeanette is an even better babysitter. She makes $16 an hour. Jeanette works 18 hours each week. How many
hours does Logan need to work in order to earn as much money as Jeanette earns in a week?
Answer:
18hx16money=288 dollars
Step-by-step explanation:
to ez and np
Answer:
32 hours a week
Step-by-step explanation:
First you have to find out how much Jeanette makes. You can do this by multiplying 16 x 18 since she makes $16 18 times a week. This gives you $288 that she makes each week.
Now to find how much Logan would have to work you take 288 and divide it by 9. You do this because you need to see how many times 9 goes into 288 to give you the amount of hours. When you divide you get 32.
How much force is required to accelerate a 4 kg mass at 6 m/s2
Answer:
is it 24 N?
as we know ....
force=mass * acceleration
force=4kg*6m/s2
hence force is 24N
The required Force = 24 N
What is Force?The push or pull on an object with mass causes it to change its velocity.
Given that a body of 4 kg mass is accelerated at 6 m/s²
Force = ma
where m = mass and a = acceleration
F = 6*4 = 24 N
Hence, the Force required = 24 N
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#SPJ2
(9x+3)5 i really need help with this pleaseeee
Answer:
1/15
Step-by-step explanation:
Thats my guess I think its that though.
Answer: 3
Step-by-step explanation:
PEMDAS
1.Amulya is x years now. Write expressions for her age 5 years ago?
Take Sarita’s Age to be y years
a) What will be her age 5 years from now?
b) What was her age 3 years now?
c) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
d)Grandmother is 2 years younger than grandfather. What is his grandmother ’s age?
e) Sarita’s father’s is age is 5 years more than 3 times Sarita’s age. What is her father’s age?
Answer:
Step-by-step explanation:
1) a = x - 5
a) z = y + 5
b) z = y - 3
c) z = 6y
d) z = 6y - 2
e) z = 3y + 5
Snow fell from 6:30 am to 11:00 am, accumulating at a constant rate. At 8:00 am, the snow was 8 inches deep. By 11:00 am, it was 20 inches deep. How much snow fell each hour? (Part one)
The answer to the first box would be 4
Answer:
4 for the first box
Step-by-step explanation:
Round any answers to the nearest tenth if necessary.
ad
Technology required. Find the
missing measurements.
nd
35
А.
21
B
BC is 40
I
units,
degrees, and
60
degrees.
Are the ratios 6:1 and 19:3 equivalent?
Answer: no<3
Step-by-step explanation:
leave a thanks if helped plz
Body surface area is calculated a) in m2 from weight and height. b) from height. c) from weight. d) in meters from weight and height.
Answer:
Body surface area is calculated a) in m2 from weight and height.
Step-by-step explanation:
Basically the surface has to be in m2, because you have two dimensions when you multiply: e.g. when you have a lawn 10m x 10m, then you multiply 10 times 10, and meters times meters, so
[tex]10m * 10m = 100m^2[/tex]
5/12+2/3=37 I need help
Answer:
13/12=37
Step-by-step explanation:
What is 4% of 4% of 40,000? Show the working please.
Answer:
64
Step-by-step explanation:
4% of 40,000= 1,600
4% of 1600= 64
Answer:
64
Step-by-step explanation:
4% = 4/100=0.04
[tex](\frac{4}{100} )(\frac{4}{100} )(40000)=(0.04)(0.04)(40000)=64[/tex]
Hope this helps
13. A stack of lumber contains the following: three 1" x 6" X 8' pieces of yellow pine. six 2" x 10" x 12' pieces of redwood. six 1" x 8" 10' pieces of fir. How many total board feet of lumber are in this stack? *
180 board ft
162 board ft
192 board ft
172 board ft
Answer:
Step-by-step explanation:
A board foot is 1 inch thick by 1 ft by 1 ft
(3) 1 x 6 8' are already 1 inch thick ½ ft wide and 8 ft long
3 x 1 x (6/12) x 8 = 12 board ft.
(6) 2" x 10" x 12' are 2 thick x 10/12 ft wide by 12 ft long
6 x 2 x (10/12) x 12 = 120 board ft.
(6) 1" x 8" x 10'
6 x 1 x (8/12) x 10 = 40 board ft
12 + 120 + 40 = 172 board ft
e/kaid_274404147475337871026587/assig!
Khan Academy
Percent word problems
Of the 50 U.S. states, 4 have names that start with the letter W.
What percentage of U.S. states have names that start with the letter W?
0
Stuck? Review related articles/videos or use a hint.
Answer:
Step-by-step explanation:
4/50 = 0.08
0.08(100) = 8%
when a company produces 5,000 units, variable costs are $35 per unit and total cost in $200,000. What is the total cost when the company produces 8,000 units? (both 8000 and 5000 units produced are within the relevant range.)
If x = 5-2√6, find the value of:
(i) x + 1/x
(ii) x² + 1/x²
Please solve ASAP
Answer:
x+(1/x) = 10 and x²+ (1/x²) = 98Step-by-step explanation:
Given that :
x = 5-2√6
1/x = 1/(5-2√6)
The denominator = 5-2√6
The Rationalising factor of 5-2√6 = 5+2√6
On Rationalising the denominator then
⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]
⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]
⇛ 1/x = (5+2√6)/[5²-(2√6)²]
Since (a+b)(a-b) = a²-b²
Where ,
a = 5 and b = 2√6⇛1/x = (5+2√6)/(25-24)
⇛ 1/x = (5+2√6)/1
⇛ 1/x = 5+2√6
Now,
x +(1/x)
⇛ 5-2√6+5+2√6
⇛ 5+5
⇛ 10
Therefore, x+(1/x) = 10.
On squaring both sides then
⇛ [x+(1/x)]² = 10²
⇛ x²+2(x)(1/x)+(1/x)² =100
⇛ x²+2+(1/x)² = 100
⇛ x²+(1/x²) = 100-2
⇛ x²+(1/x²) = 98
Therefore, x²+(1/x²) = 98.
Read more:
Similar questions;
Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = 1/2 (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1.....
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regal furniture company allocates its indirect salaries of $22,500 on the basis of sales. Determine the indirect salaries allocated to Departments 1 and 2 using the following information.
Answer:
$15750 and $6750Step-by-step explanation:
Revenue share of Dept. 1:
182000/260000*100% = 70%Revenue share of Dept. 2:
100% - 70% = 30%Allocate the indirect salary with same ratio.
Dept. 1:
22500*70/100 = 15750Dept. 2:
22500 - 15750 = 6750Is ( - 1, 2) a solution of the system y > x and x + y > 0?
O No, because ( - 1, 2) is a solution to only one of these inequalities.
O Yes, because ( – 1, 2) is a solution to both inequalities.
O Yes, because ( - 1, 2) is the point of intersection of the two boundary lines of this system.
No, because ( – 1, 2) is not a solution to either inequality.
Answer:
Yes, because (-1,2) is a solution to both inequalities
Step-by-step explanation:
2>-1 so the first inequality is correct
-1+2>0 so the second inequality is correct
What determines whether a relationship
is proportional or not?
Answer:
When two ratios exhibit the same connection, they are said to be proportionate. Two ratios may be tested for proportionality by writing them as fractions and then reducing them to the smallest possible number. In this case, your ratios are proportionate since the reduced fractions are the same.
Step-by-step explanation:
Hope it helps:)
if 9/24 equals 3/x , then x is ____
[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]
5. Use the point-slope formula to determine the equation of a line that passes through the points (1, 2) and (-2, 1).
Answer:
In point-slope form the equation is:
[tex]y - 2 = \binom{1}{3} \times (x - 1)[/tex]
Solve for B -(12 x 2) x (-6) = -12 x (2 x b)
A. -6
B. 6
C. -12
D. 12
Answer:
Option A
Step-by-step explanation:
-(12 x 2) x (-6) = -12 x (2 x b)
=> -24 x -6 = -12 x 2b
=> 144 = -24b
=> b = -6
Hoped this helped.
Mort and George are 18 miles apart on a path when they start moving toward each other. Mort runs at a constant speed of 7 miles per hour, and George walks at a constant speed of 5 miles per hour. How long does it take until Mort and George meet?
Answer:
1 1/2 hours
Step-by-step explanation:
In one hour, the distance between them is reduced by 7+5 = 12 miles. At that rate, the 18 mile distance between them will be reduced to zero in ...
time = distance/speed
time = (18 mi)/(12 mi/h) = 3/2 h
It will take 1 1/2 hours until Mort and George meet.
3. If Superman can fly .25 miles in 8 seconds, how far could he fly in...
(a) 40 seconds?
Answer:
1.25 miles
Step-by-step explanation:
0.25 miles = 8 seconds
x miles = 40 seconds
0.25/8 = x/40
0.25 * 40 = 8x
10 = 8x
x = 1.25
-Chetan K
Pls i need an answer now
Answer:
Step-by-step explanation:
1. 5, 3.5, [tex]\sqrt{9\\}[/tex], [tex]-\frac{12}{5}[/tex], -7
2. 10, π ,3.1415, 0, -10
3. 1[tex]\frac{1}{2}[/tex], 1.44, 1.4(3), 1.(43), [tex]\frac{7}{5}[/tex]
Can someone please help me
Answer:
Answer for question 16 $24.64
Answer:
$3.36
17. 31%
18 $ 24.50
Step-by-step explanation:
28 x 0.12 = $3.36
17. 484 - 333.96 = 150.04
What percentage is 150.04 of 484
X/100 = 150.04/484 (% / 100 = is/of)
= 31%
8. 35 x 0.30 = 10.50
$35 - $10.50 = $24.50
help me due today it is mathematics
Answer:
Miranda is correct because the value 7 makes the equation equal
I am not sure what goes in the blanks, those are my best guesses.
Step-by-step explanation:
34 = 27 + p
7 = p
Hopefully this helps!
Brainliest please?
Question 5 of 10
Which of the following rational functions is graphed below?
10 H
10
10
O A. F(x) =
FIX) *-*
X5
X1
B. Fx) = 6-14-5
(x - 1)(x-5)
c. F(X) = 1
D. F(X) = x+5
-
x + 1
We want to find the equation for the graphed rational function. Notice that the options are not given, so I will try to find the function only from the graph.
The function is:
[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]
How to analyze the graph of a rational function?The first thing that we can see in the graph is that we have vertical asymptotes at x = 1.
The one in the positive side (of the x range) goes to negative infinity, while the other goes to positive infinity, then the equation will be something like:
[tex]f(x) = \frac{something}{x - 1}[/tex]
Such that the asymptotes are caused when the denominator is equal to zero.
We can see that we also have a horizontal asymptote at y = 1.
This means that, as x tends to infinity, our function will tend to 1, so we have something like:
[tex]f(x) = \frac{(x + b)}{x - 1}[/tex]
The horizontal asymptote is equal to the ratio of the leading coefficients when both polynomials have the same degree, like here, so we can take the two leading coefficients equal to 1, such that:
y = 1/1 = 1
To find the value of b, we evaluate the function in 0:
[tex]f(0) = \frac{b}{-1} = -b[/tex]
And if you look at the graph, you can see that at x = 0 we have:
f(0) = 5
then b = -5
So the function is:
[tex]f(x) = \frac{(x - 5)}{x - 1}[/tex]
If you want to learn more about rational functions, you can read:
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Repost
A group of tourists are on a three-day hiking trip. They hike ⅛ of the trail on the first day. On the second day, they hike 4/7 of the remaining distance. On the third day, they hike 1/3 of the remaining distance, plus the final 8 km. How many kilometers long is the trail?
Answer:
you told me to resolve this problem
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
you add the thing then multipy it then do math!
Han rides his bike for 50 miles over 4 hours.How long will it take him to ride 75 miles?
Answer:
6 hours.
Step-by-step explanation:
This is directly proportional, meaning if you multiply one side by a number, you multiply the other side by the same number. For the ratio 50:4, you would have to multiply 1.5 to 50 to get 75 miles, so you would also have to multiply 4 by 1.5. This would get you 6 hours.
In February Lana got a puppy that weighed 13 kilograms. By October the puppy weighed 16.9 kilogram. What was the puppy’s weight increase?.
Answer:
3.9
Step-by-step explanation:
16.9 take away 13 and you get 3.9 kilograms