A racecar is racing along a circular track. The car starts at the 3-o'clock position and travels CCW along the track. The car is constantly 8 feet from the center of the race track and travels at a constant speed and it takes the car 7.854 seconds to complete one full lap.
a. How many radians does the car sweep out per second? radians per second Preview
b. Write a function fthat determines the car's distance to the right of the center of the race track (in feet) in terms of the number of seconds t since the start of the race. f(t)
Answer:
a. The car sweeps out 0.799 radians per second.
b. f(t) = 8 cos (0.799t)
Step-by-step explanation:
Given that:
The radius r = 8 feet
a.
The time t it takes to complete one full lap = 7.854 seconds
Recall that:
Angular velocity ω = 2π / t
So if in 7.854 seconds, the car sweeps = 2π radian
∴
per second, the car will sweep ω = 2π/ 7.854
ω = 0.799 rad/sec
Thus, the car sweeps out 0.799 radians per second.
b.
Since, r = 8 feet.
Suppose the car travels an angle θ in time (t),
Then the general equation for the horizontal component is:
f(t) = rcos( ωt)
f(t) = 8 cos (0.799t)
The true statements are:
The car swept out [tex]0.255 \pi[/tex] radians per secondsThe function f that determines the car's distance at time t is: [tex]f(t) = 8\cos( 0.255\pi t)[/tex]The given parameters are:
Radius = 8 feetTime = 7.584 seconds(a) The radian swept per secondsTo do this, we simply calculate the angular velocity as follows:
[tex]\omega = \frac{2\pi}{T}[/tex]
Substitute 7.854 for T
[tex]\omega = \frac{2\pi}{7.854}[/tex]
Simplify
[tex]\omega = 0.255 \pi[/tex]
Hence, the car swept out [tex]0.255 \pi[/tex] radians per seconds
(b) The function at time tTo do this, we simply make use of the general equation for the horizontal component as follows:
[tex]f(t) = r\cos( \omega t)[/tex]
Substitute 8 for r
[tex]f(t) = 8\cos( \omega t)[/tex]
Substitute [tex]\omega = 0.255 \pi[/tex]
[tex]f(t) = 8\cos( 0.255\pi t)[/tex]
Hence, the function f that determines the car's distance at time t is: [tex]f(t) = 8\cos( 0.255\pi t)[/tex]
Read more about angular velocity at:
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is y=x/4 a proportional relationship
Answer:
yes
Step-by-step explanation:
The function f(x) = x/4 represents a proportional relationship.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. A straight line represents a proportional relationship. Mathematically -
y = mx + b
(y - b)/x = m [m is constant]
or
y = mx
m = y/x [m is constant]
Given is the following function -
y = x/4
We have -
f(x) = x/4
Now, we know a straight line represents a proportional relationship. The general form of equation representing the proportional relationship is -
y = mx
where - [m] is constant
y = x/4
y = (1/4)x
On comparing, we get -
m = 1/4
Hence, the function f(x) = x/4 represents a proportional relationship.
Therefore, the function f(x) = x/4 represents a proportional relationship.
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Which function could this graph represent?
A) an even-degree function with two relative extrema
B) an odd-degree with three relative extrema
C) an even-degree function with three relative extrema
D) an odd-degree with two relative extrema
Answer:
Option (A)
Step-by-step explanation:
From the graph attached,
Right and left ends of the graph are moving downwards.
Ends moving upwards or downwards (In the same side of x-axis) tells the graph to be an even function.
There are two maximum points (points having maximum y-values)represent the two relative extrema of the function.
Therefore, Option (A) will be the correct option.
Misaki cut some wood for a bookcase she is building.She needs to find how many 13 ft boards she can make from a 5 ft board.Explain how to model with fraction bars to solve the problem.
Complete question :
Misaki cut some wood for a bookcase she is building.She needs to find how many 1/3 ft boards she can make from a 5 ft board.Explain how to model with fraction bars to solve the problem
Answer:
15
Step-by-step explanation:
Total Size of board = 5 feets
Size of board to be made = 1/3 feets
Number of 1/3 feets board to be made from 5 feets board :
Total size of board / size of board to be made
5 feets ÷ 1/3 feets
5 feets * 3 / 1 feets
= 15
Hence, number of 1/3 feets board that can be made from 5 feets board = 15
plss help ASAP
What is the ratio of blue shapes to all shapes in the set below?
4.9
5.9
4.5
5.4
Answer:
5:9
Step-by-step explanation:
There are 5 blue shapes out of 9 total shapes.
What is the slope of the line that passes through the points (-4, 4)(−4,4) and (-6, 6) ?(−6,6)? Write your answer in simplest form.
Write a function g whose graph represents a reflection in the x-axis of the graph of f(x)=1/2x−3.
Use the graph below to answer the question. Quadrilateral PQRS will be rotated 90° clockwise about the origin resulting in quadrilateral P'Q'R'S'. Which statement is true
Answer: it’s D
Step-by-step explanation:
What does x an y represent
Answer:
x represents the bottom and y represents the top
Step-by-step explanation:
Answer:
grid
Step-by-step explanation:
So they x in the grid it a straight line in the middle ok. Then we have the y which is the one that's up and down in the grid. Also when the numbers are added that are ploted somewhere on the x goes first because x goes first in the alphabet.
help please i need it
dhhdkhdkjhdkdhkshdksj
Answer:
26 percent sodium
also can i have brainliest please
Select all that apply.
The figures below are not similar because
the corresponding angles are congruent
the corresponding sides are not proportional
the corresponding sides are proportional
they are not the same shape
The two given figures are not similar because they are not the same shape. Option D is correct.
Given that,
A figure of two shapes has been shown, we have to discuss why the two shapes are not similar,
In congruent geometry, the shapes that are so identical. can be superimposed to themselves.
Here,
The two shapes are not similar because one is square and the other is a rectangle, There is why both are not the same shape, because they are cyclic and regular shapes their corresponding angles are congruent.
Thus, the two given figures are not similar because they are not the same shape. Option D is correct.
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Help ASAP plz
Jacob bought 5 boxes of pencils for his drawing class. Each box contains 12 pencils. Which point on the graph shows the number of pencils he bought?
Answer:
it would be (5,60)
Step-by-step explanation:
he bought 5 boxes
each box has 12 pencils
5*12=60
An airplane flying at an altitude of 2600 m is approaching an airport run away located 56 km away (from the airplane to the run away). Calculate the airplane’s angle of decent. (Hint: the angle of decent is the same as the angle of depression.)
Given :
An airplane flying at an altitude of 2600 m is approaching an airport run away located 56 km away.
To Find :
The airplane’s angle of decent.
Solution :
Height of plane, h = 2600 m.
Horizontal distance of airplane from vertices is, d = 56 km = 56000 m.
Let, angle of depression is Ф.
So,
[tex]tan \ \phi = \dfrac{56000}{2600}\\\\tan \ \phi = 21.54\\\\\phi = 87.34^o[/tex]
Therefore, the angle of decent is 87.34°.
Hence, this is the required solution.
Which two points on the number line are opposites? A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. Point A is 1 mark to the left of negative 1. Point B is half-way between negative 1 and 0. Point C is half-way between 0 and 1. Point D is half-way between 1 and 2. points A and B points B and C points C and D points A and D
Answer:
Points B and C are opposite
Step-by-step explanation:
0 on the number line marks the center of the number line. To the right on the number line are positive integers and to the left from zero are negative integers.
Points B and C are opposite because they are each half way between 0 and 1 on the right and 0 and -1 on the left
Answer:
b and c are opposites
Step-by-step explanation:
other guy was right
3(2x – 14) = -3(-13 + x)
Answer:
9
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
AnswerX=9
Step-by-step explanation:
6x-42=39-3x
Randy bought 6 candy bars for $7.20. What is the cost per candy bar? PLS HELP FAST IT IS WORTH 45 POINTS AND MY GRADE
Answer:
$1.20 per candy bar
Step-by-step explanation:
7.2 ÷ 6 = 1.2
rob bought 15 concert tickets worth $322.50. Floor tickets cost $25 each while balcony tickets cost $17.50 each. How many tickets of each type did rob bye?
Answer:
8 floor tickets and 7 balcony tickets.
Step-by-step explanation:
f+b=15
25f+17.50b=322.50
Answer:
8 floor tickets, 7 balcony tickets
Step-by-step explanation:
F + B = 15
25F + 17.50B = 322.50
Please please help! Its due soon!! Ill mark brainliest!!
I need side b, using tangent!! Thank you!!
Answer:
tan 68 degrees = b/60
60 * tan 68 degrees = b
b = 148.5 in tenths, 149 as a whole number, and 148.51 in hundredths
Step-by-step explanation:
Hope it helps!
Answer:
tan 68 degrees = b/60
60 * tan 68 degrees = b
b = 148.5 in tenths, 149 as a whole number, and 148.51 in hundredths
. Step-by-step explanation:
Hope it helps!
Type the correct answer in the box. If necessary, use / for the fraction bar and simplify the fraction. cos(75°)cos(15°) =
Answer:
1/4
Step-by-step explanation:
If you type cos(75)cos(15) into a scientific calculator, the answer comes out as 1/4.
The value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a trigonometric expression:
= cos(75°)cos(15°)
As we know the trigonometric identity:
cos(a)cos(b) = (1/2)[cos(a + b) + cos(a - b)]
a = 75
b = 15
Plug the above values in the trigonometric identity:
cos(75)cos(15) = (1/2)[cos(75 + 15) + cos(75 - 15)]
cos(75)cos(15) = (1/2)[cos(90) + cos(60)]
The trigonometric ratio is the ratio of the pair of a right-angled triangle.
The value of cos90 = 0
cos60 = 1/2
cos(75)cos(15) = (1/2)[0 + 1/2]
cos(75)cos(15) = 1/4
Thus, the value of the trigonometric expression cos(75)cos(15) is 1/4 after applying the trigonometric identity.
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A newspaper surveyed households to determine how likely they were to subscribe to their publication. The results are shown below by annual household income.
Household Income
< $60,000 > $60,000
I would never purchase a newspaper subscription. 40 63
I might or might not purchase a newspaper subscription. 53 70
I would probably purchase a newspaper subscription. 65 32
I already purchase a newspaper subscription. 73 16
Identify the percentage of families with an income more than $60,000 who might or might not purchase a newspaper subscription. What does this number represent?
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
The sample
Household Income
< $60,000 > $60,000
I would never purchase a newspaper subscription. 40 63
I might or might not purchase a newspaper subscription. 53 70
I would probably purchase a newspaper subscription. 65 32
I already purchase a newspaper subscription. 73 16
Generally the sample size is mathematically represented as
[tex]n = 40 + 53 + 65+ 73 + 63 + 70 + 32+ 16[/tex]
=> [tex]n = 412[/tex]
Generally the number of the sample with an income greater $60,000 is mathematically represented as
[tex]N = 63 + 70 + 32 + 16[/tex]
=> [tex]N = 181[/tex]
Generally the number of families with an income more than $60,000 who might or might not purchase a newspaper subscription is
[tex]X = 70[/tex]
Generally the percentage of families with an income more than $60,000 who might or might not purchase a newspaper subscription is
[tex]P(X) = \frac{70}{181} * 100[/tex]
=> [tex]P(X) = 39\%[/tex]
I need help with this question -3/8 + 1/6
Answer:
5/24
Step-by-step explanation:
Step-by-step explanation:
[tex] - \frac{3}{8} + \frac{1}{6} [/tex]
[tex] (- \frac{3}{8} \times \frac{3}{3} ) + ( \frac{1}{6} \times \frac{4}{4} )[/tex]
[tex] - \frac{9}{24} + \frac{4}{24} [/tex]
[tex] - \frac{5}{24} [/tex]
(Geometry) Please help! 50 points
Answer:
A) similar; SSS similarity
Step-by-step explanation:
You have to find the proportion by dividing each side to the according side
35/14 = 2.5 - S/D
20/8 = 2.5 - R/E
30/12 = 2.5 - Q/F
Answer:
A B AND C
Step-by-step explanation:
The answers are
abcTwo students are taking a math test. After 5 minutes, one student is 13 done and the other is 28 done. How much ahead of the second student is the first
Given :
Two students are taking a maths test.
After 5 minutes, one student is 13 done and the other is 28 done.
To Find :
How much ahead of the second student is the first.
Solution :
Number of questions second student is ahead is :
[tex]n = 28 - 13\\\\n = 15[/tex]
Therefore, second student is ahead by first by 15 questions.
Hence, this is the required solution.
1 Admission to the local movie theater is $3 for each child and $7 for each adult. A group of 12 people pay $64 admission. How many children are in this group?
Given:
Admission to the local movie theater is $3 for each child and $7 for each adult.
A group of 12 people pay $64 admission.
To find:
The number of children in a group.
Solution:
Let the number of children be x and number of adults be y.
According to the question,
Total persons : [tex]x+y=12[/tex] ...(i)
Total cost : [tex]3x+7y=64[/tex] ...(ii)
Multiply equation (i) by 7 and subtract the result from (ii).
[tex]3x+7y-7(x+y)=64-7(12)[/tex]
[tex]3x+7y-7x-7y=64-84[/tex]
[tex]-4x=-20[/tex]
Divide both sides by -4.
[tex]x=5[/tex]
Therefore, the number of children is 5.
Work out, giving your answer in its simplest form:
5/
14
x
7/
30
Can someone please help me? I can't find the h(x) for 0. I also need help with the last question. Please I need it very soon.
9514 1404 393
Answer:
see attachments for a table and graph
Step-by-step explanation:
I find it convenient to use a graphing calculator or spreadsheet to do repetitive computations reliably.
__
Your specific question asks for h(0):
h(0) = -|0 +2| +1 = -2 +1
h(0) = -1
You may want to check your other table values.
You have $22 to spend on four raffle tickets. After buying them you had $6. How much did each raffle ticket cost?
Answer:
$4 each
Step-by-step explanation:
Answer:
each ticket cos $4
Step-by-step explanation:
because is you multiply 4 × 6 is 16
and 22-16=6
What is the Simplified Answer: (5x+11)-(2x-3)
Answer: 3x + 14
Step-by-step explanation: you have to combine the terms 11 + 3 = 14 5x - 2x = 3x
is the product of 8 negative numbers and 7 positive numbers a positive number or a negative number?
Answer:
negative
Step-by-step explanation:
Positive numbers do not change the polarity of a number in multiplication, only negative numbers.
How do you find slope? like...what's the equation? Cause nothing in my math class makes sense rn and finding the slope of things is the reason why