Answer:
The answer is below
Step-by-step explanation:
The car is moving in a circular track with a radius of 1.9 miles. The distance covered by the car if the track is revolved once = 2π * radius of the track.
a) Since the car has swept out an angle of 212 degrees, the distance covered by the race car = [tex]\frac{212}{360}*2\pi(1.9)=7.03 \ miles[/tex]
b) If the car traveled 4.9 miles, the angle swept out (θ) is:
[tex]4.9= \frac{\theta}{360} * 2\pi r\\\\\theta=\frac{4.9}{2\pi (1.9)}*360 \\\\\theta=147.76^o=147.76^o*\frac{\pi}{180} \\\\\theta=2.58\ rad[/tex]
c) h = distance covered, t = time in hourss.
Hence:
h = 85.5t
The race-car's motion round the track is a repeating motion that can be
described by a sinusoidal function.
The correct responses are;
Distance travelled when the car swept an angle of 212° ≈ 7.03 milesIf the car has travelled 4.9 miles, the angle swept out, θ ≈ 2.58 radiansThe function is; [tex]\underline{h(t) = 1.9\cdot sin(45\cdot t)}[/tex].Reasons:
Known parameters are;
Radius of the track, r = 1.9 miles
Point the car starts = 3 O'clock
Speed of the car = 85.5 mph
Required:
Distance swept out when the car traveled an angle of 212°.
Solution;
Distance of one complete turn = 2·π·r
Angle of one complete turn = 360°
Therefore, at 212°, we have;
[tex]\dfrac{212^{\circ}}{360^{\circ}} \times 2 \times 1.9 \times \pi \approx 7.03[/tex]
Distance travelled when the car swept an angle of 212° ≈ 7.03 milesRequired:
The measure of the angle swept out by the car if the car has travelled 4.9 miles.
Solution;
Let, θ represent the angle, we have;
[tex]\dfrac{\theta}{2 \cdot \pi} \times 2 \times 1.9 \times \pi \approx 4.9 \ miles[/tex]
We get;
[tex]{\theta} = \dfrac{4.9 \ miles}{2 \times 1.9 \ miles \times \pi } \times 2\cdot \pi \approx 2.58 \ radians[/tex]
If the car has travelled 4.9 miles, the angle swept out, θ ≈ 2.58 radiansRequired:
The function, h, that gives the distance of the above the horizontal
diameter of the track (in miles) in terms of the number of hours since the
race-car started driving, t.
Solution;
The function that gives the car height can be presented as follows;
The angular velocity, ω = [tex]\dfrac{v}{r}[/tex]
Therefore;
[tex]\omega = \dfrac{85.5 \ mph}{1.9 \ miles} = 45 \ rad/hour[/tex]
The general form of the sinusoidal function is h = A·sin[k·(θ - b)] + c
Therefore, we get;
h = 1.9·sin[k·(θ - b)] + c
The period, T = 2·π/ω = 2·π/k
Therefore, given that ω·t = θ, we get;
h = 1.9·sin[ω·t - b] + c = 1.9·sin[45·t - b] + c
The vertical sift, c, and the horizontal shift, b, can both be taken as zero,
given that the sin(0) = 0, therefore;
h = 1.9·sin[0] + c = c = 0, such that the at the start, t = 0, the car is at a
distance of h = 0 above the horizontal line.
The function, h, that gives the distance of the car above the
horizontal track, in terms of the number of hours since the car started
driving, t, is therefore;
[tex]\underline{h(t) = 1.9\cdot sin(45\cdot t)}[/tex].Learn more here:
https://brainly.com/question/16014064
which statement is true about the graphed lines
write 8z + z - 5 - 9z +2 in simplest form
find square root of 82369 by division method step by step
Answer:
I think this ans may help you
is this graph a function
Answer: yes because it if u plug in x values u get y values
7/8 x 1/3
please help me :)
Answer: 7/24
Step-by-step explanation:
Answer:
7/24 or about 0.29
Step-by-step explanation:
when multiplying fractions you first have to remember that:
a/b * c/d = a*c / b*d
If you remember that then its not hard to calculate:
7/8 * 1/3 = 7*1 / 8*3 = 7/24
Hope i could help :D
Dont be afraid to ask questions :)
What is 12x12x14 equal to?
Answer:
The answer is 2016.
Step-by-step explanation:
12 times 12 = 144.
144 times 14 = 2016.
I hope this helps you. Have a nice day.
Answer:
2016
Step-by-step explanation:
Hope thos helpfull to tou
José is making frult-filled tart shells for a party. He has 80 raspberries and 48 blueberrles. The tarts will each
have the same number of berrles. Raspberrles and blueberrles will not be in the same tart If he puts the
greatest possible number of fruits in each tart, how many tarts can he make?
When the greatest possible number of berrles Is In each tart, there are
tarts In total.
Answer:8
Step-by-step explanation:the GCF for 80 and 48 is 16 so divide 80 by 16 and you will get 5 and 48 by 16 and you’ll get 3 and when you and 5 and 3 you’ll get 8 as your answer.
Factor completely.
- 3x² + 14x- 8
Answer =
= - 3x² + 14x - 8
= - 3x² + 12x + 2x - 8
= - 3x(x - 4) + 2(x - 4)
= (x - 4)(-3x + 2)
Which graph is a parabola?
THE ANSWER IS SHOWN IN THE PICTURE
Answer:
3rd one :D
Step-by-step explanation:
° • .°• ✯
★ * ° °·
. • ° ★ • ☄
▁▂▃▄▅▆▇▇▆▅▄▃▁▂
Pomóżcie potrzebne jak najszybciej się da proszę
Answer:
can you please write it in english
The human heart beats an average of 4,320 times an hour. At this rate, about how many times will a person's heart beat in one full day?
103,680
[tex]4320 \times 24[/tex]
To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained.
132 students ate breakfast.
183 students ate lunch.
273 students ate dinner.
69 students ate breakfast and lunch.
113 students ate breakfast and dinner.
95 students ate lunch and dinner.
55 students ate all three meals.
How many students ate
(a) At least one meal in the cafeteria?
students
(b) Exactly one meal in the cafeteria?
students
(c) Only dinner in the cafeteria?
students
(d) Exactly two meals in the cafeteria?
students
Answer:
920 Students
Step-by-step explanation:
Add all of the meals together
Please dont judge me if i get this wrong this is why i joined brainly i don´t know nothing
d.
a.
b.
12
8
Which triangles are similar?
8
3
25
(25
25
25
6
6
16
Ос
od
Оа
O
b
Answer:
C and d
Step-by-step explanation:
C and d are similar triangles. I think that’s what you mean. I just did the test
is the product of 3/6×5/4 equal to the product of 3/4×5×6? explain how you know
Answer:
yes
Step-by-step explanation:
I think you mean
"Is the product of 3/6 × 5/4 equal to the product of 3/4 × 5/6?"
If we can turn 3/6 * 5/4 into 3/4 * 5/6 using only legal math steps, then the answer is yes.
3/6 * 5/4 =
Breakup each fraction into a product of fractions.
= 3/1 * 1/6 * 5/1 * 1/4
Use the associative and commutative properties of multiplication to change the order and grouping of the multiplication.
= (3/1 * 1/4) * (5/1 * 1/6)
Do each product in parentheses.
= 3/4 * 5/6
This shows that 3/6 * 5/4 = 3/4 * 5/6
Answer: yes
find ratio of 120 :80
120 : 80
= 12 : 8
= 6 : 4
= 3 : 2
This is the answer
Answer:
120/10=12
80/10=8
12/4=3
8/4=2
Nothing can further decide, then we have
3:2
please help !!!!!
What is the slope of the line shown in the graph?
A. -3/2
B. -1/2
C. 3/2
Answer:
-3/2
Step-by-step explanation:
Answer:
The slope of the line shown is -3/2.
Step-by-step explanation:
You can find this by using the rise/run method between the two points.
Between the two points, the line falls 3 units down (this is the rise part) and goes 2 units to the right (this is the run part). Since the line falls 3 units down between the two points, this number would be -3, and since it runs to the right by two units, the slope can be identified as -3/2.
Factor Completely;;;;;
Answer:
2x²-24x+54
2(x²-12x+27)
2(x²-9x-3x+27)
2(x(x-9)-3(x-9))
2(x-9)(x-3)
solve for a, 1/3 + a = 5/4
Answer:
[tex]a = \frac{11}{12}[/tex]
Step-by-step explanation:
[tex]a = \frac{5}{4} - \frac{1}{3}[/tex]
[tex]a = \frac{11}{12}[/tex]
Answer:
[tex] \frac{1}{3} + a = \frac{5}{4} [/tex]
[tex]a = \frac{5}{4} - \frac{1}{3} [/tex]
[tex]a = \frac{15 - 4}{12} [/tex]
[tex]a = \frac{11}{12} [/tex]
I used a tutor for this and the answer I was given is 17.5. Which is incorrect. I am trying to understand how to solve.
Answer:
A right angle is 90 degree
Step-by-step explanation:
73 -90 degrees is 17 degrees. A right angle, shown is at 90 degrees
Find the base of a triagnle with a
height of 12 and an area of 192
square units.
Answer:
B(ase) = 32 square units.
Answer:
32
Step-by-step explanation:
Using the formula, a = h(b)/2
192 = 12b/2
good luck, i hope this helps :)
What percent of 94 is 23?
Answer:
24.5%
Step-by-step explanation:
23/94 = 0.2446
what number is 0.001 less than 1,000.1
Answer:
Its Smaller by 100, because 0.001 times 100 = 0.1
Step-by-step explanation:
Answer:
I believe the answer is 1000.099
Step-by-step explanation:
I believe all you need to do is subtract 1,000.1 - 0.001 which equals 1000.099.
Tasha has foam blocks stored in a box that measures 314 ft long by 3 ft wide by 1 ft tall.
Each foam block is a cube with 14 -ft edge length.
How many blocks can fit into the box?
156 blocks
312 blocks
624 blocks
2496 blocks
Answer:
624
Step-by-step explanation:
I hope it helps i did the test btw <3
Answer:
624
Step-by-step explanation:
I also did that same exact test. K12 right? That is what I go to. Anyway that answer is correct. Your welcome!
4/5 - 2/3 =
Find equivalent fractions and rewrite the problem and solve
Answer:
1001/1500
Step-by-step explanation:
The easiest method for doing this is to just average the two numbers.
e.g. to find a number x between the two numbers ab and cd
x=12[ab+cd]
=12[adbd+bcbd]
=ad+bc2bd
In this case…
x=(2×5)+(3×4)2×2×5=10+1230=2230=1115
You can easily see where that came from.
23=1015 and 45=1215
and the ‘common denominator’ means you just have to pick a value between 10 and 12 . i.e. 11
But you can also say…
23=100150 and 45=120150
and choose any of 101150,102150,...,119150
or
23=10001500 and 45=12001500
and choose any of 10011500,10021500,...,11991500
Answer:4/5 and 2/3 each have a common bottom of 15 so 4/5 is
12/15 and 2/3 will be 10/15
Step-by-step explanation:So than 12/15 forget the bottom don't subtract the bottom just look at it like [12-10] then you got 2 then you go back to the bottom and put it together so your answer is [2/15]
In the past year, Raina watched 6 movies that she thought were very good. She watched 15 movies over the whole year. Of the movies she watched, what percentage did she think were very good?
Answer:6/15 so 40%
Step-by-step explanation:
do kramagat dhanatmak purnanko ka yog 145 hai purnank gyat kijiye
Answer:
hssssskwkwkkkayak toa
ehekkekekekek
eemeeememe
Step-by-step explanation:eeekekekee dd ejndkekd3kd3kd3kd3kdb3
wkwdwugudhwkwkwkekekwkwka,akkKKkKSNBEVEVVRTTVKALALALAL
Answer:
72, 73
Step-by-step explanation:
माना दो क्रमागत धनात्मक पूर्णाक x और (x + 1) हैं |
इसलिए...
प्रश्नानुसार,
x + (x + 1) = 145
2x + 1 = 145
2x = 145 - 1
2x = 144
x = 144/2
x = 72
x + 1 = 72 + 1 = 73
Which pair of numbers is opposite?
Select all that apply.
|-6| and -6
|-6| and 6
6 and 1/6
6 and -6
0 and 6
Answer:
Step-by-step explanation:
A,b,d,e
Use the graph f(x)=x^3 to graph h(x)=1/2(x-3)^2-2
A robot's height is 120 centimeters. How tall is the robot in millimeters? Record your answer and fill in the bubbles on your answer document, Be sure to use the correct place value.
Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose that you study a simple random sample of 80 professional basketball games and find that 52 of them are won by the home team. Assuming that there is no home court advantage and that the home team therefore wins 50% of its games in the long run, determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games
Answer:
0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
The home team therefore wins 50% of its games
This means that [tex]p = 0.5[/tex]
Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games
Sample of 80 means that [tex]n = 80[/tex] and, by the Central Limit Theorem:
[tex]\mu = p = 0.65[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5*0.5}{80}} = 0.0559[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 0.65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.65 - 0.5}{0.0559}[/tex]
[tex]Z = 2.68[/tex]
[tex]Z = 2.68[/tex] has a pvalue of 0.9963
1 - 0.9963 = 0.0037
0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games
