The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times cosine theta plus radical 3.
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length.
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function?
Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal?
Answers
The given function for the difference in length is presented as follows;
[tex]f( \theta) = 2 \cdot cos( \theta) + \sqrt{3} [/tex]
When the pogo stick will be equal to its non compressed length, the difference is zero, therefore;
[tex]f( \theta) = 2 \cdot cos( \theta) + \sqrt{3} = 0[/tex]
[tex] 2 \cdot cos( \theta) = - \sqrt{3} [/tex]
[tex]\theta= arccos \left( \frac{ - \sqrt{3} }{2} \right) [/tex]
Which gives;
[tex] \theta = \frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{6} [/tex]
[tex] \theta = -\frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{6} [/tex]
Part B; If the angle was doubled, we have;
[tex]f( \theta) = 2 \cdot cos(2 \cdot \theta) + \sqrt{3} = 0[/tex]
Therefore;
[tex] 2 \cdot cos(2 \cdot \theta) = - \sqrt{3} [/tex]
Which gives;
[tex] \theta = \frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{12} [/tex]
[tex] \theta = -\frac{12 \cdot \pi \cdot n1 + 5\cdot \pi}{12} [/tex]
Between 0 and 2•π, we have;
[tex] \theta = \frac{5\cdot \pi}{12} [/tex]
[tex] \theta = \frac{ 17\cdot \pi}{12} [/tex]
Part C;
The toddler's pogo stick is presented as follows;
[tex]g( \theta) = 1- son^2( \theta) + \sqrt{3} [/tex]
Integrating the original function between 0 and theta gives;
[tex]2 \cdot sin( \theta) + \sqrt{3}\cdot \theta [/tex]
The original length =
Therefore, when the lengths are equal, we have;
[tex]1- son^2( \theta) + \sqrt{3} = 2 \cdot sin( \theta) + \sqrt{3}\cdot \theta [/tex]
Related Questions
The upper-left coordinates on a rectangle are (- 8, 8) and the upper-right coordinates are (- 3, 8) The rectangle has an area of 15 square units
Answers
Answer:
See attachment for diagram
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-8,8)[/tex]
[tex](x_2,y_2) = (-3,8)[/tex]
[tex]Area = 15[/tex]
Required
Draw the rectangle on a coordinate plane --- (missing from the question)
First, we calculate the distance between the given pairs.
[tex]D = \sqrt{(x_1 - x_2)^2 + (y_1-y_2)^2}[/tex]
[tex]D = \sqrt{(-8-(-3))^2 + (8-8)^2}[/tex]
[tex]D = \sqrt{25}[/tex]
[tex]D = 5[/tex]
So, the distance between the given pairs is 5 units... Let this be the length of the rectangle.
Using:
[tex]Area = Length * Width[/tex]
[tex]15 = 5 * Width[/tex]
[tex]Width = \frac{15}{5}[/tex]
[tex]Width = 3[/tex]
The width is 3 units.
This implies that the opposite sides of the rectangle are either 3 units down or 3 units up the given pairs.
Assume they are 3 units up.
[tex](x_1,y_1) = (-8,8)[/tex] and [tex](x_2,y_2) = (-3,8)[/tex]
[tex](x_3,y_3) = (x_1,y_3 + 3) = (-8,8+3) = (-8,11)[/tex]
[tex](x_4,y_4) = (x_2,y_2 + 3) = (-3,8+3) = (-3,11)[/tex]
What is an
equation of the line that passes through the points (0, -2)
and (6, 6)?
Answers
Answer:
8/6x+2................
Answer: y=(4/3)x-2
Step-by-step explanation:
(y-y1)/(x-x1)=(y2-y1)/(x2-x1)
x1=0, x2=6
y1=-2, y2=6
(y-(-2))/(x-0)=(6-(-2))/(6-0)
(y+2)/(x)=(6+2)/6
(y+2)/(x)=8/6=4/3
Cross multiply
3(y+2)=4x
y+2=(4/3)x
y=(4/3)x-2
Sara bought 12 feet of fabric to make curtains. She needs to cut it into 1/4 foot sections. How many sections of fabric will she have.
Answers
Answer: 48 sections
Step-by-step explanation:
Sara bought 12 feet of fabric. From that 12 feet, she needs to cut out sections that are 1/4 in length.
The number of sections she will have if she does so is:
= Total length of fabric / Length of sections
= 12 ÷ 1/4
= 12 * 4/1
= 48 sections
*EXTRA PTS* find the value
Answers
16) -7
17) 9
18) 5
19) 4
20) 10
21) -9
How?
X+139=132 by the alternate interior angle rule so solve and get -7
-1+14x=12x+17 by the alternate exterior angle rule so solve and get 9
21x+5= 23x-5 by the corresponding angles rule solve and get 5
20x+5+24x-1= 180 because when an angle is one a parallel line the sun of angle to the right or left of it is 180 solve and get 4
6x= 5x+10 by the corresponding angles rule solve and get 10
X+109+x+89= 180 because x+89 is equal to the angle that is too the right of x+109 by the alternate interior angle rule making the sum equal to 108. Solve and you get -9
That was a lot of math
Hope it helps :D
The price have changed from $120 to $75. By how many
percent did it change?
Plz show how you did it
Answers
Answer:
35.7%
Step-by-step explanation:
The change is 45 dollars. (120-75)
The percent of change is the dollars divided by the original price.
45/120=0.357
Or 35.7%
Answer:
35.7
Step-by-step explanation:
Which points define the solution set of this linear-quadratic system of equations?
A. Point A & B
B. Point D & F
C. Point C & E
D. Point B & D
Answers
Answer:
point D y F ese el la respuesta
Vitai ir 8 reizes vairak konfekšu neka Annai, bet Uldim ir par 10 konfektēm vairak neka Annai. Cik konfektes ir katram no bērniem, ja kopa viņiem ir 60 konfektes? Lai atrisinatu, sastadi vienadojumu!
Answers
Atbilde:
Anna = 14
Vita = 14 + 8 = 22
Uldis = 14 + 10 = 24
Soli pa solim:
Latvietis
Anna = x
Vita = x + 8
Uldis = x + 10
Kopā = 60
x + x + 8 + x + 10 = 60
3x + 18 = 60
3x = 60 - 18
3x = 42
x = 42/3
x = 14
Anna = 14
Vita = 14 + 8 = 22
Uldis = 14 + 10 = 24
Angus has a big test coming up. Should he stay up and study or go to bed early the night before the test? Defend your recommendation.
Answers
Answer:
he should study
Step-by-step explanation:
Help.Find the length of y
Answers
work out the value of x
Answers
x + 3x + 90° = 360°
4x = 360° - 90°
4x = 270°
4x/4 = 270°/4
x = 67.5°
Hope it helps! Make me brainliest if it’s correct.
It takes Diego of an hour to complete a lap on a circular bike track. The track is mile long. What is Diego's bike speed? 8 hours per mile 1/8 mile per hour 8 miles per hour 1/8 hours per mile
PLEASE HELP, I DON'T UNDERSTAND THE WORDING
Answers
Answer:
C. 8 miles per hour
Step-by-step explanation:
It takes Diego [tex]\frac{1}{8}[/tex] of an hour to complete the lap = [tex]\frac{1}{8}[/tex] x 1 hour = [tex]\frac{1}{8}[/tex] hour
Distance of the track = 1 mile long
The speed of an object expresses the ratio of distance moved to time taken to cover the distance.
i.e speed = [tex]\frac{distance}{time taken}[/tex]
= [tex]\frac{1}{\frac{1}{8} }[/tex]
= 8
Speed = 8 mile per hour
Therefore, Diego's bike has a speed of 8 miles per hour.
If the blue radius below is perpendicular to the chord , which is 14 units long, what is the length of the segment ?
Answers
Answer:
The answer is 7 bc 7 is half of 14
Step-by-step explanation:
find the equation of the straight line passing through the point (0,2) which is perpendicular to the line y = 1/4x + 5
Answers
Answer:
The slope will be y= -1/4x+2
Step-by-step explanation:
Hope this Helped
The baker at weis supermarket will cut 5 indeticial loaves of bread into pices that are 1/3 . After he cuts the 5 loaves how many pices will the baker have
Answers
Answer:
15 pieces
Step-by-step explanation:
we see if we get 3 pieces from one bread then 5 will be 15
hope it helps you
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On a map, the distance between Louisville, Kentucky, and Nashville, Tennessee, is 1 3/4 inches. The scale of the map is 1 in:100 mi. What is the actual distance between the two cities?
Answers
Answer:
Step-by-step explanation:
The distance between 2 cities is 175 miles
What is scale on graph?
A scale is a set of numbers that help to measure or quantify objects. A scale on the graph shows the way the numbers or pictures are used in data.
Given data ,
The distance between Louisville and Nashville = 1 3/4 inches
Scale of the map = 1 in : 100 miles
Now , 1 inch = 100 miles on the map
And , 1 3/4 = 7 / 4 inches
So , 7 / 4 inches = ( 7 / 4 ) x 100 miles
= 1.75 x 100 miles
= 175 miles
Hence , the distance between 2 cities is 175 miles
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Sam surveyed his classmates to find out if they played a sport after school or practiced in the
school band
- 14 of his classmates played a sport
- of those 14 who played, 5 participated in the school band
- 8 students played in the school band, and out of those 8, 3 did not play sports
- there were 10 students who did not play a sport nor participate in the school band
Create a two way table to represent the data and answer the following questions
Answers
Answer:Sam surveyed his classmates to find out if they played a sport after school or practiced in the
school band
- 14 of his classmates played a sport
- of those 14 who played, 5 participated in the school band
- 8 students played in the school band, and out of those 8, 3 did not play sports
- there were 10 students who did not play a sport nor participate in the school band
Create a two way table to represent the data and answer the following questions
Step-by-step explanation:
Here is a two-way table that represents the given data:
Look at the pic
To create this table, we first divided the students into two categories: those who play a sport and those who do not. Then, we further divided each category into those who play in the school band and those who do not.
From the table, we can answer the following questions:
How many students did Sam survey in total?
To find the total number of students surveyed, we can add up the values in the table:
14 + 5 + 3 + 9 + 10 = 41
Therefore, Sam surveyed a total of 41 students.
How many students played a sport but did not participate in the school band?
From the table, we can see that 14 students played a sport, and 5 of those also participated in the school band. Therefore, the number of students who played a sport but did not participate in the school band is:
14 - 5 = 9
So, 9 students played a sport but did not participate in the school band.
How many students did not play a sport but participated in the school band?
From the table, we can see that 8 students played in the school band, and 3 of those did not play a sport. Therefore, the number of students who did not play a sport but participated in the school band is:
8 - 3 = 5
So, 5 students did not play a sport but participated in the school band.
Hope this helps <3
Please give me Brainliest :)
1. Does each relation represent a function? Circle Yes or No. a. (2, 2), (2, 6), (3, 5), (1,8) Yes No b. (1, 2), (2, 3), (3, 4), (4, 5) Yes No c. (1, 4), (2, 6), (3, 6), (4, 8) Yes No d. (4, 3), (4, 4), (4, 5), (4, 6) Yes No
Answers
B. Yes
C. Yes
D. No
Please help me id you want BRIANLEIST!!! :)) ty!!!
Answers
Answer:
5/3
Step-by-step explanation:
4 × x = (6×3+2)/3
---> 4x = 20/3
----> x = 20/12
----> x=5/3
Hope it helps
Answer:
5/3
Step-by-step explanation:
what factored pair has a product of -24 and a sum of 2?
Answers
42 out of 100
how do u do this question?
Answers
Help me please answer thanks
Answers
Colleen's movie collection contains 8 movies, including 4 romance movies. What is the probability that a randomly selected movie will be a romance movie?
Answers
Answer: 1/2
Step-by-step explanation:
There are 8 movies in total.
4 of those movies are romance movies.
The probability of picking a romance movie is the proportion of romance movies to the total number of movies.
= Number of romance movies / Number of total movies
= 4 / 8
= 1 / 2
Answer:
1/2
Step-by-step explanation:
An online furniture store sells chairs and tables. Each day, the store can ship at most 25 pieces of furniture. Write an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint.
Answers
9514 1404 393
Answer:
t + c ≤ 25
Step-by-step explanation:
"At most 25" means "less than or equal to 25." The total number of pieces of furniture is the sum of the numbers of tables and of chairs: t + c.
The shipping constraint can be written as ...
t + c ≤ 25
Jace invested $380 in an account paying an interest rate of 6.2% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 15 years?
Answers
Answer: 960
Step-by-step explanation:
Which of the following is the equation for the graph shown?
Answers
Answer:
y
+
0
=
0
⋅
(
x
+
5
)
Step-by-step explanation:
question: find the value of t
Answers
Answer:
t = 5
Step-by-step explanation:
since those 2 angles make up 180 degrees turn it into an equation
20t + 5 + 15t = 180
combine like terms 20t + 15t = 35t
the equation is now 35t + 5 = 180
subtract 5 from both sides, 5 - 5=0, 180 - 5 = 175
35t = 175
now divide each side by 35, 35t/35 = t, 175/35= 5
t = 5
hope this helps :)
Answer:
5
Step-by-step explanation:
Line (which has the the equation)= 180
So,
15t + 20t + 5 = 180
35t + 5 = 180
35t = 180 - 5
35t = 175
t = 175/35
t = 5
Solve for G
6G = -72
(show your work)
Answers
Answer:
-12
Step-by-step explanation:
6G = -72
G = -72 / 6
G = -12
A woman is standing 12 feet from a sculpture. The angle of elevation from her eyes to the top of the sculpture is 35º. If the woman's eyes are 5 feet 6 inches off the ground, how tall is the sculpture? Round answer to the nearest thousandth of a foot.
Answers
Answer:
13.903 feet
Step-by-step explanation:
Let the height from the woman's eyes to the top of the sculpture be represented by x.
So that,
Tan 35 = [tex]\frac{x}{12}[/tex]
x = Tan 35 x 12
= 0.70021 x 12
= 8.4025
x = 8.403 feet
The height of the sculpture = The woman's eye level to the ground + x
= 5 feet 6 inches + 8.403 feet
= 5.50 feet + 8.403 feet
= 13.903 feet
Thus, the sculpture has a height of 13.903 feet.
A bottle contains 500 ml of orange juice. Write an expression for EACH of the following.
The amount of juice left in the bottle after pouring out
(i) p ml.
(ii) q glasses each containing r ml
Answers
Answer:
1. 500-p
2. qr=500
(i) Amount of juice left in the bottle after pouring out [tex]p\,ml\boldsymbol{=(500-p)\,ml}[/tex]
Amount of juice left in the bottle after pouring out [tex]q[/tex] glasses each containing [tex]r[/tex] [tex]ml[/tex] [tex]\boldsymbol{=(500-qr)\,\,ml}[/tex]
An algebraic expression refers to a combination of symbols, numbers, variables, and arithmetic operations.
Volume of bottle of orange juice [tex]\boldsymbol{\boldsymbol{=500\,ml}}[/tex]
(i) Amount of juice left in the bottle after pouring out [tex]p\,ml\boldsymbol{=(500-p)\,ml}[/tex]
(ii) Amount of juice contained in [tex]q[/tex] glasses [tex]=(qr)\,ml[/tex]
So,
Amount of juice left in the bottle after pouring out [tex]qr\,\,ml[/tex] of juice [tex]\boldsymbol{=(500-qr)\,\,ml}[/tex]
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Evaluating 1/4 check all that apply the base is 1/4 the expanded form is 1/4 1/4 1/4 the expanded form is 1x1x1x1/4 1/4 2 = 1/4 1/4 3 = 1/64
Answers
Answer:
[tex](\frac{1}{4})^3 = \frac{1}{64}[/tex]
Step-by-step explanation:
Given
[tex](\frac{1}{4})^3[/tex]
Required: Evaluate
The options are not clear. So, I'll answer without considering the options:
[tex](\frac{1}{4})^3[/tex]
Apply law of indices:
[tex](\frac{1}{4})^3 = (\frac{1}{4}) * (\frac{1}{4}) * (\frac{1}{4})[/tex]
Remove brackets
[tex](\frac{1}{4})^3 = \frac{1}{4} * \frac{1}{4} * \frac{1}{4}[/tex]
Combine
[tex](\frac{1}{4})^3 = \frac{1*1*1}{4*4*4}[/tex]
[tex](\frac{1}{4})^3 = \frac{1}{64}[/tex]
Answer988
Step-by-step explanation: