Answer:
34.56
Step-by-step explanation:
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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Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream store for $8 per hour. Leah cannot work for more than 20 hours total per month for both jobs. Let x represent the number of hours Leah babysits and y represent the number of hours Leah works at the ice cream store. Which of the following graphs and system of inequalities shows the set of solutions for Leah earning at least $120 and working no more than 20 hours?
Answer:
its D
Step-by-step explanation:
5x+8y>120 and x+y<20 are the two inequalities shows the set of solutions for Leah earning at least $120 and working no more than 20 hours
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Let x=babysitting hours paid at $5
y=ice cream shop hours paid at $8.
Total earned >120
total hours<20
So here is what our equations will look like:
5x+8y>120
x+y<20
Convert the first equation into y>mx+b format
8y>-5x+120
y>-5/8x+15
Convert the second equation into y>mx+b
x+y<20
y<-x+20
We can also solve this mathmatically by finding the point where our equations are equal:
-5/8x+15=-x+20
Add x to both sides to get:
3/8x+15=20
subtract 15 from both sides:
3/8x=5
divide both sides by 3/8:
x=13.33
The question asks us to round to the nearest whole hour, so the minimum she can babysit is 14 hours to still make $120 a week.
Hence, 5x+8y>120 and x+y<20 are the two inequalities shows the set of solutions for Leah earning at least $120 and working no more than 20 hours
To learn more on Inequality click:
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Help!
Find the distance between A and B .
Answer:
2.6
Step-by-step explanation:
1.3-(-1.3)
1.3+1.3
2.6
The function above models the height, y, in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second
Answer:
3.94 seconds
Step-by-step explanation:
h = - 16t² + 248
If stone is dropped, then h = 0
- 16t² + 248 = 0
t² = [tex]\frac{248}{16}[/tex]
t = ± [tex]\frac{2\sqrt{62} }{4}[/tex]
t < 0 is a solution of equation, but not a solution of the task
t = [tex]\frac{2\sqrt{62} }{4}[/tex] ≈ 3.94 seconds
Answer:
≈ 3.74 seconds
Step-by-step explanation:
Oops! The numbers I had to work with were "The function y = –16t2 + 224..."
Someone help I’ll give brainlist lol
The speed of a train increases from 650 km/hr to 800 km/hr in 5 hours. What is its acceleration?
Answer:
\overline{a} = \frac{v - v_0}{t} = \frac{\Delta v}{\Delta t}
Step-by-step explanation
i do not really understand but use this formula
= average acceleration
v = final velocity
v_0 = starting velocity
t = elapsed time
Write down the next two numbers in the sequence.
81, 64, 47, 30, ___, ___
Answer:
81, 64, 47, 30, 13, -4
Answer:
The next two numbers are 13 and -4.
Step-by-step explanation:
We are subtracting 17 each time.
30 - 17 = 13
13 - 17 = -4
Please help :)Please help :)Please help :)
Answer:
the first one is correct
Step-by-step explanation:
Find the 87th term of the arithmetic sequence 12, 0, -12,
Answer:
- 1020
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = a₂ - a₁ = 0 - 12 = - 12 , thus
a₈₇ = 12 + (86 × - 12) = 12 - 1032 = - 1020
Answer:
-1008
Step-by-step explanation:
Solve for the value of x.
Answer:
x= 12
Step-by-step explanation:
The sum of both of the equasions equal up to 180. so you set up the problem like this:
(9x-4)+(6x+4)=180
15x=180
x=12
To check;
(9(12)-4)+(6(12)+4)=180
104+76=180
Find the value of f(-3).
Step-by-step explanation:
the value is -5 hope that is good
Questlon 2 of 10
The amount of time between interest payments is known as:
A. simple interest.
B. interest.
C. principal.
D. period
SUBMIT
Answer: D) Period
You could refer to this as the time period. Usually the time period is in months. So you make monthly interest payments, often with the principal mixed in somewhat.
Annie is participating in a winner-take-all World Series of Poker tournament that costs 101010 thousand dollars to enter. The prize for winning the tournament is 500500500 thousand dollars. Annie estimates that there is a 0.5 \%0.5%0, point, 5, percent chance that she will win the tournament. Find the expected value of entering the tournament for Annie.
Answer: −7.5 thousand dollars
Step-by-step explanation: Khan Academy
Using the expected value formulae, the expected value of Annie entering the tournament is -$7950
Creating a probability distribution table :
Net amount won = (500 - 100) = 400 thousand
Amount lost = 100 thousand
X ___ : - 10,000 ____ 400,000
P(X) _ : __ 0.995 _______ 0.005
Using the expected value formulae:
E(X) = Σ[X × P(X)]E(X) = (0.995 × - 10,000) + (0.005 × 400,000)
E(X) = - 9950 + 2000
E(X) = -7950
Hence, the expected value of entering the tournament is -$7950
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Joanne hit a ball straight up into the air. The height of the ball in meters, is given by the function h(t)= -5(t-3)^2+45 t seconds after the ball is hit. What is the maximum height the ball will reach
9514 1404 393
Answer:
45 meters
Step-by-step explanation:
The equation is given in vertex form:
h(t) = a(t -b)^2 +c
where (b, c) is the vertex (maximum).
The values of the parameters are ...
a = -5, b = 3, c = 45
Then the maximum height is (time, height) = (3, 45).
The maximum height of the ball is 45 meters.
witch 2 numbers are 4 units away from zero on a number line
Answer:
it depends which way youre going, but 4 and -4 work.
Step-by-step explanation:
You spend $23 to spend on 4 avocados. After buying them you had $11. How much did each avocado cost? Write an equation about this.
Answer: Each avocado cost $3
Equation: 23 - 4x = 11
Answer:
$3 per avocados
Step-by-step explanation:
23-11= 12. 12 divided by 4 = 3
A newborn baby what weighs 3⁷ kilograms. An adult blue whale weighs 81 times the newborn. How many kilograms does the adult bluewhale weigh? Write your answer as a power of 3.
Answer:
2187
Step-by-step explanation: 27 times 81 equals 2187
8x + 7y = 2
8x + 3y = 10
Answer:
what do you want from this question?
Step-by-step explanation:
How much money is collected in tolls if 55 two axle cars cross the bridge? Type your answer in a
complete sentence.
Y•55=x
Step-by-step explanation:
Please help ill mark brainliest
What is -3(5+5)>5x?
Answer:
The answer is x < -6
hope that helps
-3(5+5)>5x
-15+-15>5x
-30>5x
5x<-30
Divide both side by 5
5x÷5 < -30÷5
x<-6
Answer:
-15 is the incorrect answer the correct answer is x < --6
Step-by-step explanation: Simplify 5+55+5 to 1010.
-3\times 10>5x−3×10>5x
2 Simplify -3\times 10−3×10 to -30−30.
-30>5x−30>5x
3 Divide both sides by 55.
-\frac{30}{5}>x−
5
30
>x
4 Simplify \frac{30}{5}
5
30
to 66.
-6>x−6>x
5 Switch sides.
x<-6x<−6
Expand and simplify 3(2x + 1) +2(x + 4)
Answer:
8+11
Step-by-step explanation:
Answer:
3(2x + 1) +2(x + 4)
6x + 3 + 2x + 8
8x + 11
Step-by-step explanation:
Marcus can choose between a monthly salary of $1,500 plus a 5.5% commission of sales or $2,000 plus a 3% commission of sales. He expects about $8,000 in sales each month. Which salary option should he choose?
Answer:
The second option is betterStep-by-step explanation:
Total for the first choice:
8000*5.5/100 + 1500 = $1940Total for the second choice:
8000*3/100 + 2000 = $2240As we see the second choice is better as more salary is expected
write the equation of the line in slope intercept form
Answer:
y = x - 600
Step-by-step explanation:
y = mx + b , "m" is slope and "b" is y-intercept
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
~~~~~~~~~~~~~
y-intercept is (0, - 600) and x-intercept is (600, 0)
The slope is 1
y + 600 = x - 0
y = x - 600
In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generates a random integer between 1 and 50. Explain how you could use this number to simulate the weather in the video game
Answer: answer 80%
Step-by-step explanation:
Answer:
ew teachers really out here trying to make video games about school huh
Step-by-step explanation:
Can someone help me with this last one please
(7,-20), (1,-3)
Find the slope of the line through each pair of points
Answer:
-17/6
Step-by-step explanation:
You find the slope by using the equation: y2-y1/x2-x1.
-20-(-3)/7-1
-20+3/6
-17/6
Find the length of BD in rectangle ABCD. a2 + b2 = c2 5 23 25 31
Answer:
B
23
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
[tex]24^{2} + 7^{2}[/tex] = 625
[tex]\sqrt{625\\}[/tex] = 25
Therefore, the length of BD in rectangle ABCD is 25mm. I just did the test and it is correct. 23 is wrong.
What is the rate of inflation if an account has a nominal interest rate of 4.2% and a real interest rate of 2.8%
A. 1%
B. 1.8%
C. 2.4%
D. 1.4%
Answer:
Rate of inflation = 1.4%
Step-by-step explanation:
Given:
Nominal interest rate = 4.2%
Real interest rate = 2.8%
Find:
Rate of inflation
Computation:
Rate of inflation = Nominal interest rate - Real interest rate
Rate of inflation = 4.2% - 2.8%
Rate of inflation = 1.4%
Janna and Anthony walk home from school on Monday Wednesday and Friday their mother picks them up on Thursday and they ride the bus on Tuesday what fraction of time do they walk hom from school
Answer: 3/5
Step-by-step explanation:
Out of 5 school days, Janna and Anthony walk home on Monday, Wednesday and Friday.
This means they walk home on 3 days out of 5.
The fraction of time they walk home from school is;
= 3/5