Algebraic expression for each work phrase and then simplify The sum of four and x minus two
A race-car is driving counter-clockwise on a circular track with a radius of 1.9 miles. The car starts at the 3 o'clock position and travels at a constant speed of 85.5 miles per hour.
What distance (in miles) has the race-car traveled if the car has swept out an angle of 212 degrees?
_____miles
What is the measure of the angle swept out by the car (in radians) if the car has traveled 4.9 miles?
_____radians
Define a function, h, that gives the race-car's distance above the horizontal diameter of the track (in miles) in terms of the number of hours since the race-car started driving, t.
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:
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What is the length of side BC 2x+7, 4x-7 4x
Answer:
64.6x
Step-by-step explanation:
5. Scott planted 20% of a garden with roses. What is the area of
the section of the garden that is planted with roses?
A. Add the following integers.
11.7 + 9 =
12. - 9+ (- 10 ) =
13. (- 14 ) + 5 =
14.9+(-14) =
15.-5+ (-8)=
Answer:
11. 16
12. -19
13. -9
14. -5
15. -13
Step-by-step explanation:
A pastry bag full of frosting forms a cone with the dimensions shown. Find the volume of frosting in the pastry bag.
Answer:
kajhfsdbbcbb,bnmcxbvljhhjw eutiugvawgygewfcufbuicmauigpuygpvghsfBgeilvlhkdb;bwgvPWIHITVNUAHUEIGEOYUGE8GPUWIEHOIgorucrugc t rueagurwWUGHCRWGCugpgpuyGPGCPGUGGUyguUYFUYGUOYUOYGOUYGOFUGIcefgyxsnjdfryugvouscbaknqpiuvhrwklemfnvvvvvvvr4uhui4jqkwserupwehdnjqhbgiwebduudirbgdqfwaiqjnweisdkrfmtguiwdnnnnnnnnnnnnnnerijjjjjjj
Step-by-step explanation:
3) An air conditioner has a marked price of $350. It is placed on sale at 12% off. What are the
discount and the sale price?
Show work please !
Answer:
12/100 = x/350
4200 = 100x
4200/100 = 100x/100
42 = x
350 - 42 = 308
the sale price is $308
the discount is $42
. Lightning Lucy’s burnable CDs are on sale this
month for 10% off regular prices. If a pack of 10
blank CDs normally costs $15, how much do you
save per CD?
Original unit cost of CDs = $_________ per CD
10% of original cost = $_________
Original cost minus the 10% discount = $_______
Discounted unit cost of CDs = $_______ per CD
Subtract the two unit costs to find
how much saved per CD = $_________
Answer:
Original Cost = $1.50 per CD
Discount = $1.50
Discounted Cost = $13.50
Discounted Cost = $1.35 per CD
You Saved = $0.15 per CD
Step-by-step explanation:
$15/10CDs = $1.50
$15x10% = $1.50
$15-$1.50 = $13.50
$13.50/10CDs = $1.35
$1.50-$1.35 = $0.15
help me pls i need help
Answer:
B
Step-by-step explanation:
:-)
Answer:
B
Step-by-step explanation:
This problem is to compare the value of the two numbers. Obviously, 0.21>0.012
What is true about (0, 5)
Answer:
0/5 equals zero as anything divided by zero gives zero. However 5/0 is an undetermined form which gives infinity.
Step-by-step explanation:
Complete the following statement. The conditional probability of B given A can be found by _______. a. adding P(A) and P(B).b. assuming that event B has occurred, and then calculating the probability that event A will occur c. multiplying P(A) times P(B).d. assuming that event A has occurred, and then calculating the probability that event B will occur.
Answer: Assuming that event A has occurred
Step-by-step explanation:
The conditional probability of B given A can be found by assuming that event A has occurred, and then calculating the probability that event B will occur.
So, the correct answer is d.
The conditional probability of B given A, denoted as P(B|A), represents the probability of event B occurring given that event A has already occurred.
It is calculated by assuming that event A has occurred and then determining the probability of event B occurring under that assumption.
Mathematically, the conditional probability is calculated as:
P(B|A) = P(A and B) / P(A)
Where P(A and B) represents the probability of both events A and B occurring together, and P(A) represents the probability of event A occurring.
Therefore, option d. assumes that event A has occurred and then calculates the probability that event B will occur, which aligns with the definition of conditional probability.
Learn more about conditional probability click;
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Write a polynomial in standard form with the zeros –4, 0, 1, and 4.
Answer:
uhhm
Step-by-step explanation:
....
The required polynomial in standard form with zeros –4, 0, 1, and 4 is x⁴- x³ - 16x²+16x
Polynomial functions are functions that have a leading variable of 3 and above.
Given the zeros of a polynomial as -4, 0, 1, and 4, their corresponding factors will be:
(x+4)), x-0, x-1 and x - 4
To get the polynomial function required, we will take the product of the factors as shown:
= x(x-1)(x+4)(x-4)
= (x²-x)(x²-4²) (Note that (x+4)(x-4) is from different of two square)
f(x)= x⁴-16x²-x³+16x
Rearranging
f(x) = x⁴- x³ - 16x²+16x
Hence the function x⁴- x³ - 16x²+16x gives the required polynomial in standard form.
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The diagram shows as scale drawing of a playground
The scale of the drawing is 1:500
Answer:
45
Step-by-step explanation:
3+1.5+3+1.5=9
9*500=4500
4500/100=45
Lillian wants to give 1/3 of a pizza to each of six girls at her party
Answer:
[tex]Fraction = \frac{1}{18}[/tex]
Step-by-step explanation:
Given
[tex]Pizza = \frac{1}{3}[/tex]
[tex]Girls = 6[/tex]
Required [Missing Information]
Determine the fraction each girl gets
To do this, we simply divide the pizza by the number of girls i.e.
[tex]Fraction = \frac{Pizza}{Girls}[/tex]
[tex]Fraction = \frac{1}{3} / 6[/tex]
Change / to *
[tex]Fraction = \frac{1}{3} *\frac{1}{6}[/tex]
[tex]Fraction = \frac{1}{18}[/tex]
Hence, each girl gets 1/18
M(6,5) is the mid-point of the straight line joining A(2 , 3) to the
point B. Find the coordinates of B.
Given :
M(6,5) is the mid-point of the straight line joining A(2 , 3) to the
point B.
To Find :
The coordinates of B.
Solution :
Let, coordinates of point B is ( h , k ) .
It is given that M is the mid - point of the straight line joining points A and B.
Coordinates of M is given by :
[tex]M = (\dfrac{2+h}{2},\dfrac{3+k}{2})\\\\(6,5 ) = (\dfrac{2+h}{2},\dfrac{3+k}{2})\\\\\dfrac{2+h}{2} = 6 \ , \ \dfrac{3+k}{2} = 5\\\\h = 10 \ ,\ k = 7[/tex]
Therefore, coordinates of point B is ( 10 , 7 ).
For what value of x do the expressions 2x +3 and 3x -6 have the same value?
Answer:
9
Step-by-step explanation:
2x+3=3x-6
3+6=3x-2x
9=x
Answer:
x= 9
Step-by-step explanation:
hello :
2x +3 = 3x -6
2x-3x=-6-3
-x= -9
so : x= 9
I need help solving 4th grade math
Answer:
Whats the math?
Step-by-step explanation:
sir/miss please add something to answer or this can be reported so remake this add something then we will answer
What is the area of the square?
Step-by-step explanation:
it has 4 sides, all of whick are equal. Answer is 4*4, 16.
WIll GIVE BRAINLYEST TO WHOEVER ANSWERS BOTH QUESTIONS FIRST CORRECTLY
Answer:
1. 8.4 in 2. 33.6
Step-by-step explanation:
I need help please...
Answer:
16^2+32cd+16d^2
Step-by-step explanation:
(4c×4d)(4c+4d)
16c^2+32cd+16d^2 use the foil method
Diana spent $5 on lunch. She purchased a sandwich and a drink. The drink cost $2. The
equation s + 2 = 5 can be used to find the cost s of the sandwich. Which model shows the
equation?
I NEED HELP ASAP I WILL MARK YOU BRAINLIEST
Which pair of angles are Complementary Angles?
45 degrees and 95 degrees
or
38 degrees and 42 degrees
or
30 degrees and 51 degrees
or
63 degrees and 27 degrees
Answer:
63 degrees and 27 degrees
Step-by-step explanation:
Complementary angles are when two angles add to 90 degrees.
So, we can check if these pairs add up to 90 degrees.
45 + 95 = 140
38 + 42 = 80
30 + 51 = 81
63 + 27 = 90
The only pair of angles that are complementary is 63 degrees and 27 degrees.
For the following integral, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition.
∫(x+5)/x^3+7x+5 dx
Answer:
hello your question is incomplete attached below is the complete question
answer :
for I1 = [tex]\frac{1}{x^2} + \frac{4}{x^3}[/tex] The integral converges
for I2 = [tex]\frac{2x + 6}{2(x^2 + 6x + 4 )}[/tex] The integral diverges
for I3 = [tex]\frac{1}{x^2}[/tex] The integral converges
for I4 = 1 The integral diverges
Step-by-step explanation:
The similar integrands and the prediction ( conclusion )
for I1 = [tex]\frac{1}{x^2} + \frac{4}{x^3}[/tex] The integral converges
for I2 = [tex]\frac{2x + 6}{2(x^2 + 6x + 4 )}[/tex] The integral diverges
for I3 = [tex]\frac{1}{x^2}[/tex] The integral converges
for I4 = 1 The integral diverges
attached below is a detailed solution
help Jake is a bully. He likes to pick on little kids, but they don’t have a way to defend themselves. They complain to teachers about Jake and tells on him.
Answer:
cool
Step-by-step explanation:
Answer:
tells i think
Step-by-step explanation:
it would be tattling not telling..righttttt?????
the sum of a number and its inverse equals 3 29/52, write the mathematical expression
Answer:
Step-by-step explanation:
The sum of a number and its inverse is 3 29/52. Find the number?
x+1/x=329/52
x+1/x-329/52=0
solve the fraction
(
using the quadratic formular
Answer:
Step-by-step explanation:
the yellow is the glow in the dark kind
find the remainder when x³-2x²+4x-3 is devided by x-2
Answer:
x²+4
Step-by-step explanation:
Which investment would make you the most interest? Explain.
A: $450 at 7% for 10 years
B: $1,300 at 5% for 6 years
Please help I’m really stuck on this
Answer:
120
Step-by-step explanation:
Above 44 years ----> 45 to 84.
44 - 64 range 70 are there
65 to 84 range 50 are there
Totally 70 + 50 = 120
120 residents
The area of the four walls of a room is 156 m2. The breadth and height of the room are 8 m and 6 m
respectively. Find the length of the room.
(I SUCK AT MATHS)
If 15 metres of rope costs £22.50, how much would 12 metres cost?
Answer:
$18
Step-by-step explanation:
22.50×15=1.50
1.50×12=18