Answer:For the first one, it should be f(a)=37.8(1-cos(a))+.7. My dearest apologies because I do not know why. I just used context from the previous questions. I hope that helps..!
Step-by-step explanation:
The height of the given Ferris wheel can be described with the aid of a
sinusoidal function.
The height above the ground in terms of the angle turned, a, is
presented as follows;
[tex]\underline{f(a) = 37 \cdot sin \left (a - \dfrac{\pi}{2} \right) + 0.6}[/tex]The height above the ground in terms of the distance traveled, s, is
presented as follows;
[tex]\underline{g(s) = 37 \cdot sin \left (\dfrac{37}{s} - \dfrac{\pi}{2} \right) + 0.6}[/tex]Reason:
The general form of an equation of a Ferris wheel is presented as follows;
f(a) = A·sin(a + C) + D
Where, the amplitude, A = The radius = 37 ft.
D = The midline = Height above the ground + The amplitude
D = A + 0.6 = 37 + 0.6 = 37.6
The 6 O'clock is the lower most position, therefore, at the start, where, 'B·t + C' = 0, we have;
f(a) = A·sin(0 + C) + D
Therefore
f(a) = 37·sin(0 + C) + 37.6 = 0.6
f(a) = 37·sin(C) = 0.6 - 37.6 = -37
[tex]sin(C) = \dfrac{-37}{37} = -1[/tex]
C = sin⁻¹(-1) = [tex]-\dfrac{\pi}{2}[/tex]
The equation of Ferris wheel is presented as follows;
Which gives the equation of the height above the ground (in feet) in terms
of the number of radians, a, you have swept out from the 6 O'clock
position is given as follows; Ferris ;
[tex]\underline{f(a) = 37 \cdot sin \left (a - \dfrac{\pi}{2} \right) + 0.6}[/tex]Part 2
s = a·r = a·A
Therefore;
[tex]a = \dfrac{r}{s} = \dfrac{A}{s} = \dfrac{37}{s}[/tex]
Plugging the value of s into the above equation gives the function that
determines the height above the ground (in feet) in terms of the number of
feet traveled g(s) as follows;
[tex]\underline{g(s) = 37 \cdot sin \left (\dfrac{37}{s} - \dfrac{\pi}{2} \right) + 0.6}[/tex]Learn more here:
https://brainly.com/question/23844627
State the solutions for the quadratic equation graphed below.
6x - 8y = 12 and 5x + 8y = -1 Solve using elimination
Answer:
Step-by-step explanation:
6x-8y=12
5x+8y=-1
add them
11x=11
x=1
y=-3/4
Answer:
(1,-3/4)
Step-by-step explanation:
Luckily, y is already opposites, so it should be easier:
6x-8y=12
5x+8y=-1
Combine; This should end up with y eliminated -
11x = 11
x = 1
Now we can plug 1 in for x in one of the equations to find y. I'm going to use the second one.
5(1) +8y = -1
5+8y=-1
8y=-6
y=-6/8 (you can simplify)
The point at which the lines intersect is (1,-3/4)
c=3
c2 + 5
..............
Answer:
3x2+5=11
Step-by-step explanation:
The area of the triangle below is 33.62 square feet. What is the length of the base?
Answer:
4.1
Step-by-step explanation:
Tate rents some table 362 for some chairs $3 for each party get spends $500 enter an equation to find the number of chairs,c, that Tata rents and how many chairs
Answer:Tate rents some table 362 for some chairs $3 for each party get spends $500 enter an equation to find the number of chairs,c, that Tata rents and how many chairs
Step-by-step explanation:
What is 600 minus 258?
Answer:
342
Step-by-step explanation:
Answer:
342
Step-by-step explanation:
600 - 258 = 342
Note:
Please mark as Brainliest! <3
(6x-3)(4x-1) standard form
Answer:
6x+3
Step-by-step explanation:
24x-6x-12x+3
6x+3
The table shows the number of volleyballs that fit into a given number of containers. Each container holds the same number of balls. Enter the missing value from the table.
Answer: 7
Step-by-step explanation:
It's a 1 : 3 ratio so the answer should be 7
the area of this triangle ?
Answer:
8 cm
Step-by-step explanation:
Use pythagorean theorem to find the height (a and b are equal):
[tex]a^2+b^2=16\sqrt{2}^2\\a^2+a^2=16\sqrt{2}^2\\2a^2=16\sqrt{2}^2\\2a^2=16(2)\\a^2=16\\a=\sqrt{16}\\a=4[/tex]
Area is half of the base times height. Base and height are equal for this triangle.
[tex]\frac{1}{2}(4)(4)\\\frac{1}{2}(16)\\8[/tex]
To prepare for school you need 3 notebooks for $1.09 each, 2 boxes of pencils for $2.68 each and a pack of markers for $0.89. How much will this cost?
ASAP ill give brainliest
Answer:
$9.52
Step-by-step explanation:
1.09 x 3 = 3.27
2.68 x 2 = 5.36
3.27+5.36+.89=9.52
John is a computer salesman. He makes 8% commission on all sales. If John’s sales for the week are $24,300, how much did he earn in commission?
He made $1 944 in commission
Please help and quick
4 and 2 because she is the acrooss line
Equation R: y = -2x + 10
Equation S: y = 3x - 20
What is the solution ( , )
Step-by-step explanation:
3x -20= -2x +10
or,5x=30
or,X=30/5
or,X=6
Y= -2×6 + 10
= -2
therefore solution is (6, -2)
Find the total cost, to the nearest cent, for a meal at a restaurant that cost $19.74 with
an additional sales tax of 7.5%
Which expressions are equivalent to 4/5×15: 5x3, 4x 5/15, 4x3, 3x 15/5, 4x 15/5.
Answer:
these are the equivalwnt expressions 4/5×15=4×5/15; 5×3=3×15/5
The expression equivalent to 4/5 × 15 is 4×3
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given here the expression 4/5×15 thus simplifying it we get
4/5×15= 4×3
= 12
Hence, The expression equivalent to 4/5 × 15 is 4×3
Learn more about the BODMAS rule here:
https://brainly.com/question/29795897
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A sum of money is divided among Khairul, Michael and Ethan in the ratio
6:4: 5. After Khairul gives $30 to Michael and $15 to Ethan, the ratio
becomes 7:6:7. Find the amount of money Khairul had initially.
Answer:
$360
Step-by-step explanation:
The intial ratio of the sum shared between Khairul, Michael and Ethan is 6 : 4 : 5.
This would be 6x : 4x : 5x
Khairul gives $30 to Michael and $15.
The ratio is. Now;
(6x - 45) : (4x + 30) : (5x + 15)
We are told this is equal to the ratio 7:6:7
Thus;
((6x - 45) + (4x + 30))/(5x + 15) = (7 + 6)/7
(10x - 15)/(5x + 15) = 13/7
Factorize the left hand side;
5(2x - 3)/5(x + 3) = 13/7
5 will cancel out to get;
(2x - 3)/(x + 3) = 13/7
Cross multiply to get;
7(2x - 3) = 13(x + 3)
14x - 21 = 13x + 39
14x - 13x = 39 + 21
x = 60
Amount Khairul had initially was denoted as 6x.
Thus,6x = 5 × 60 = $360
Henry has 96 marbles. he is packing containers with 8 marbles in each container. how many containers, c, does Henry need to pack all the marbles?
the distance between two cities on a map is 3.5 centimeters. The map uses a scale in which 1 centimeter reprecents 20 kilometers. what is the actual distance between these two cities in kilometers?
Answer:
70 kilometers
Step-by-step explanation:
Set up a proportion where x is the actual distance
[tex]\frac{1}{20}[/tex] = [tex]\frac{3.5}{x}[/tex]
Cross multiply:
x = (20)(3.5)
x = 70
So, the actual distance is 70 km
Number of
Popsicles
Total Cost of
Popsicles
2
6
4
12
6
18
8
24
What is the Constant Rate of Change?
Answer:
The constant rate of change is 3
Step-by-step explanation:
Given
x y
2 6
4 12
6 18
8 24
Required
Determine the constant rate of change
Represent the constant rate of change with k.
k is calculated using:
[tex]k = \frac{y}{x}[/tex]
When y = 24; x = 8
So, we have:
[tex]k = \frac{24}{8}[/tex]
[tex]k = 3[/tex]
Hello, happy Friday, I am just here with some geometry questions.
Please only answer this if you know the answer. If you have a comment, please add it to the comment box. Only answer the question if you can explain your answer and why you think it is accurate. Thanks, good luck!
Please explain how you got it.
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
By the Triangle Proportionality Theorem:
[tex]\displaystyle \frac{x}{12}=\frac{x+1}{15}[/tex]
By cross-multiplication:
[tex]\displaystyle 12(x+1)=15(x)[/tex]
Distribute:
[tex]12x+12=15x[/tex]
Subtract 12x from both sides:
[tex]12=3x[/tex]
Hence:
[tex]x=4[/tex]
Answer:
4
Step-by-step explanation:
The first thing you should notice is that the triangles (the smaller one and the larger one) are similar due to angle-angle similarity (the top angle equals itself, and because the bases are parallel lines cut by a transversal, the base angle of the bigger triangle is equal to the corresponding base of the smaller triangle.
Similar triangles' corresponding sides have equal ratios to one another. That means we can set up an equation: side of smaller triangle ÷ corresponding side of larger triangle = other side of smaller triangle ÷ corresponding side of larger triangle. We plug the values given to us and can change this equation to:[tex]\frac{x}{x + 12} = \frac{x + 1}{x + 16}[/tex] **
We now multiply both sides of the above equation by [tex](x + 12)(x + 16)[/tex] to get: [tex]x(x + 16) = (x + 1)(x + 12)[/tex]
[tex]x^{2} + 16x = x^{2} + 13x + 12[/tex]
[tex]3x = 12[/tex]
[tex]x = 4[/tex]
That means our answer, for the value of x, is 4
** Make sure you don't say [tex]\frac{x}{12} = \frac{x + 1}{15}[/tex], because those aren't the sides of the larger square.
complete the equation 5/4= ×1/4
Answer:
X = 5
Step-by-step explanation:
50 points!! I will mark brainliest to the correct answer :) please don’t put random answers... they will be reported. Thanks!
Step-by-step explanation:
Answer for the first question.
since the triangles are congruent so angles and sides are also congruent I.e. sides and angles are equal then,
3x - 3 = 12
3x = 12 + 3
3x = 15
x = 5
55° = 7x + y
55° = 7 * 5 + y
35° + y = 55°
y = 55° - 35°
y = 20°
Answer for the second question,
x + 70° = 2x - 2° {Exterior angle of a triangle is equal to the sum of two opposite interior angles }
2x - x = 70° + 2°
x = 72°
Now
<WXY = 2x - 2°
= 2 * 72° - 2
= 142 °
Hope it will help :)❤✔
is this table proportional?
explain
Answer:
yes because the hours to distance is moving at a constant rate and if you were to graph it, it would also go through the origin
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
This table is not proportional because the outputs do not get their answer using the same equation. The first to inputs and outputs ([tex]\frac{1}{2}[/tex] and [tex]\frac{1}{4}[/tex]; 1 and [tex]\frac{1}{2}[/tex]) are proportional. You multiply the input (distance) by [tex]\frac{1}{2}[/tex] to get the output (hours). The final option of input and output ([tex]2\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex]) is not proportional.
Hope it helps!
how do you simplify 4 ^2 × 4^5
Answer:
4^7
Step-by-step explanation:
4^2 + 4^5
=> 4^ 2+5
=> 4^7
Answer:
Step-by-step explanation:
1) Kayla is using mental math to find the given sum. Which equivalent
expression could she use?
A)
85 + 20
B) 90 - 13
C)
100 + 13
D) 105 - 2
of 24 maths teachers ,15 of them are left handed . what percentage of the teachers are right handed
Answer:
38%
Step-by-step explanation:
Percentage is 37.5% but you round up
:)
What day of the week was September 16, 1921?
3 points
Captionless Image
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Answer:
Friday
Step-by-step explanation:
The ratio of math teachers to choir teachers is 3:2 respectively. There are 12 math teachers. How many math and choir teachers are there all together?
Answer:
Hi liddywiddy, sorry you had to wait so long
There are 20 teachers in all
Step-by-step explanation:
the ratio 3:2 is now 12:x
12 / 3 = 4
so the multiplier is 4
now:
4x2 = 8
Next we add them: 12+ 8 = 20
Answer:
20 teachers in all
Step-by-step explanation:
12 / 3 = 4,
4 * 2 = 8,
so 12 + 8 = 20
Which statement is true? Select all that apply?
A) 2/7 x 3/8 < 3/8 because 2/7 < 1
B) 2/7 x 3/8 > 3/8 because 2/7 > 1
C) 2/7 x 3/8 > 2/7 because 3/8 > 1
D) 2/7 x 3/8 < 2/7 because 3/8 < 1
The Continental Drift Hypothesis asserts that
our continents have been for millions of
years.
a Decreasing
b Rising
C Moving
d Growing