A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. at t = 0, a certain point is at height 0. what is the height of the point above the ground after 15 seconds?

Answers

Answer 1

45 rpm=2π rad*45/60=1.5π rad/sec
radius=1.5 ft
axle at 2 ft and up and down from there:
thus
y=2-1.5cos(1.5πt)
to make y=0 at 0
at 15 sec
y=2-1.5cos(15*1.5π)
y=2-0
y=2 ft

Related Questions

Which transformation of Figure A results in Figure A'?

a reflection across the y-axis

a reflection across the x-axis

a clockwise rotation of 90° about the origin

a translation 12 units right and 2 units down.

Answers

the answer is D a translation 12 units right and 2 units down.

Answer:

A translation 12 units right and 2 units down.

Step-by-step explanation:

Given : Figure A and figure A'.

To find : Which transformation of Figure A results in Figure A'.

Solution : We have given that

Parent Triangle A with coordinates ( -6 ,-3) ; ( -4 ,-5) ; ( -8 , - 4)

Transformed triangle with coordinates ( 6 ,-5) ; ( 8 ,-7) ; ( 4 , - 6)

We can see from the coordinates

( -6 +12 ,-3-2) = ( 6 ,-5)

( -4+ 12 ,-5 -2) = ( 8 ,-7)

( -8 + 12 , - 4 -2) = ( 4 , - 6).

Therefore, A translation 12 units right and 2 units down.

Find the missing term of the geometric sequence. 45 ___ 1620

Answers

A geometric sequence has a common ratio. Let that ratio be r. Then you get the sequence:
[tex]45,45r,45r^{2}[/tex]
You know that the third term is 1620, so just solve for r:
[tex]45r^{2}=1620 \\ r^{2}=36 \\ r=\pm6[/tex]
So the common ratio is either 6 or -6. That means there are two possible missing terms:
[tex]45r \\ =45(\pm6) \\ =\pm270[/tex]

The missing term in the geometric sequence 45, ___, 1620 is 270.

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given the geometric sequence: 45, ___, 1620, we need to find the missing term.

Let's denote the missing term as a2 and the common ratio as r. The terms of the geometric sequence are determined by the formula:

an = a1 * rn-1

For our sequence:

The first term, a1, is 45.The third term, a3, is 1620.

We express the third term in terms of the first term and common ratio:

1620 = 45 * r2

Solving for r2:

r2 = 1620 / 45
r2 = 36
r = 6

Since the common ratio, r, is 6, we can find the missing second term, a2:

a2 = a1 * r
a2 = 45 * 6 = 270

Thus, the complete sequence is 45, 270, 1620.

At a local baseball game there are 3 hot dog vendors. collectively the vendors sold 1,700 hot dogs. if vendor a sold 456, vendor b sold 607, and vendor c sold 637, what percentage of the total did each vendor sell? (round to the nearest percent.) a) 26 percent, 40 percent, 44 percent b) 45 percent, 37 percent, 18 percent c) 27 percent, 36 percent, 37 percent d) 30 percent, 35 percent, 35 percent

Answers

The answer is C.

Vendor A= 456/1700, which is .268 or 27%
Vendor B= 607/1700, which is .357 or 36%
Vendor C= 637/1700, which is .374 or 37%

For a total of 100%

the correct answer is c) 27%, 36%, AND 37% divide how many hot dogs the vendor sold by 1700 and then round to find the percentage

The length of a rectangle is increasing at a rate of 6 cm/s and the width is increasing at a rate of 4 cm/s. when the length is 16 cm and the width is 12 cm, how fast is the area of the rectangle increasing?

Answers

The area is 192 and the speed it’s increasing at is 24 cm^2/s

Mark made a business trip of 250250 miles. he averaged 50mph50⁢mph for the first part of the trip and 60mph60⁢mph for the second part. if the trip took 4.54.5 hours, how long did he travel at each rate?

Answers

i think he traveled for 2.5 hrs at 56 mi/hr

Bart can paint one house in 3 hours. ann can paint one house in 5 hours. how long would it take bart & ann to paint one house if they worked together?

Answers

It will take them 4 hours

Is quadrilateral JKLM the result of a dilation of quadrilateral ABCD by a scale factor of 2? Why or why not? Yes, because sides JK and ML are twice as long as sides AB and DC. Yes, because both figures are parallelograms, so corresponding sides are parallel. No, because sides JK and ML are not twice as long as sides AB and DC. No, because sides JM and KL have different slopes from sides AD and BC.

Answers

Answer:

(d) No, because sides JM and KL have different slopes from sides AD and BC

Step-by-step explanation:

You want to know if quadrilateral JKLM is a dilation of ABCD by a factor of 2, and why or why not.

Dilation

Dilation multiplies the distance of each point on the figure from the center of dilation by the scale factor. Dilation by a scale factor of 2 will move JKLM twice as far from the origin as ABCD. This preserves slopes and angles, but changes lengths by the scale factor.

In the given figure, ABCD is 2 units wide and 2 units high. If JKLM is a dilation by a factor of 2, it will be 4 units wide and 4 units high.

JKLM is 5 units high, so is not a dilation. JK and ML are twice as long as AB and DC, so choice C is not an appropriate explanation.

Sides JM and KL have different slopes from sides AD and BC, choice D.

Additional comment

The slopes of JM and KL are 5/2. The slopes of AD and BC are 2/1, a different value.

Answer: D

Step-by-step explanation:

Simon invested $1,550 at 6.5% simple interest. He earned $302.25 in interest after t years. What is the value of t?

Answers

Here's the equation:
0.065t(1550) = 302.25
100.75t = 302.25
t = 3
3 years

Answer:

Marco deposited $500 in a savings account earning 4% simple interest over 5 years.

What was the total amount of interest earned at the end of 5 years?

$40

$50

$100

$200

Step-by-step explanation:

What happened to the cat who swallowed a ball of yarn?

Answers

the cat who swallowd the yarn died

Depending on the size of the ball of yarn. I the ball of yarn was small he'll live but if it was bigger than he would have died from it being stuck in it's throat or possibly could have lived if rushed to the hospital immediately. But in this case she had Mittens.

This is a "water tank" calculus problem that I've been working on and I would really appreciate it if someone could look at my work and tell me if I did it properly! Thank you.

Answers

Part A

Everything looks good but line 4. You need to put all of the "2h" in parenthesis so the teacher will know you are squaring all of 2h. As you have it right now, you are saying "only square the h, not the 2". Be careful as silly mistakes like this will often cost you points.

============================================================

Part B

It looks like you have the right answer. Though you'll need to use parenthesis to ensure that all of "75t/(2pi)" is under the cube root. I'm assuming you made a typo or forgot to put the parenthesis.

dh/dt = (25)/(2pi*h^2)
2pi*h^2*dh = 25*dt
int[ 2pi*h^2*dh ] = int[ 25*dt ] ... applying integral to both sides
(2/3)pi*h^3 = 25t + C
2pi*h^3 = 3(25t + C)
h^3 = (3(25t + C))/(2pi)
h^3 = (75t + 3C)/(2pi)
h^3 = (75t + C)/(2pi)
h = [ (75t + C)/(2pi) ]^(1/3)

Plug in the initial conditions. If the volume is V = 0 then the height is h = 0 at time t = 0
0 = [ (75(0) + C)/(2pi) ]^(1/3)
0 = [ (0 + C)/(2pi) ]^(1/3)
0 = [ (C)/(2pi) ]^(1/3)
0^3 = (C)/(2pi)
0 = C/(2pi)
C/(2pi) = 0
C = 0*2pi
C = 0

Therefore the h(t) function is...
h(t) = [ (75t + C)/(2pi) ]^(1/3)
h(t) = [ (75t + 0)/(2pi) ]^(1/3)
h(t) = [ (75t)/(2pi) ]^(1/3)

Answer:
h(t) = [ (75t)/(2pi) ]^(1/3)

============================================================

Part C

Your answer is correct.
Below is an alternative way to find the same answer

--------------------------------------

Plug in the given height; solve for t
h(t) = [ (75t)/(2pi) ]^(1/3)
8 = [ (75t)/(2pi) ]^(1/3)
8^3 = (75t)/(2pi)
512 = (75t)/(2pi)
(75t)/(2pi) = 512
75t = 512*2pi
75t = 1024pi
t = 1024pi/75
At this time value, the height of the water is 8 feet

Set up the radius r(t) function
r = 2*h
r = 2*h(t)
r = 2*[ (75t)/(2pi) ]^(1/3) .... using the answer from part B

Differentiate that r(t) function with respect to t
r = 2*[ (75t)/(2pi) ]^(1/3)
dr/dt = 2*(1/3)*[ (75t)/(2pi) ]^(1/3-1)*d/dt[(75t)/(2pi)]
dr/dt = (2/3)*[ (75t)/(2pi) ]^(-2/3)*(75/(2pi))
dr/dt = (2/3)*(75/(2pi))*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)

Plug in t = 1024pi/75 found earlier above
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75(1024pi/75))/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (1024pi)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*(1/64)
dr/dt = 25/(64pi)
getting the same answer as before

----------------------------

Thinking back as I finish up, your method is definitely shorter and more efficient. So I prefer your method, which is effectively this:
r = 2h, dr/dh = 2
dh/dt = (25)/(2pi*h^2) ... from part A
dr/dt = dr/dh*dh/dt ... chain rule
dr/dt = 2*((25)/(2pi*h^2))
dr/dt = ((25)/(pi*h^2))
dr/dt = ((25)/(pi*8^2)) ... plugging in h = 8
dr/dt = (25)/(64pi)
which is what you stated in your screenshot (though I added on the line dr/dt = dr/dh*dh/dt to show the chain rule in action)

The total price of an article is $7.02, including tax. If the tax rate is 8%, what is the retail price of the article?

Answers

1.08x = 7.02

x = 7.02 / 1.08

x = $6.50

6.50

Hope this helps.

Lynh manages a small company with 12 employees. He offers profit sharing where 5% of profits at end of year is distributed evenly to the employees. Each employee earned $2,300 in profit sharing in 2013. What was the total profit?

Answers

We need to find the total profit of Lynh Mangoes. It is given that the 5 % of profit to be distributed equally between 12 employees.

Profit received by each employee = $ 2,300

Total profit received by 12 employees = $ 2,300 × Profit received by each employee

Total profit received by 12 employees = $ 27,600

It is given that 5 % to be distributed.

Thus, 5 % of total profit = $ 27,600

Total profit = $ 27,600 ÷ 5 %

Total profit = $ 552,000

What is the value of x?

Answers

the outside angles of a polygon equal 360 degrees

total of the 3 known angles: 140 + 34 + 56 = 230
so x = 360 - 230
x = 130 degrees

Name three properties that a square and a rhombus share.

Answers

They are quadrilateral.
Their all sides are equal.
Diagonals bisect at 90° ( right angle )

At the local grocer, the prices for apples are the following: 9 ounces for $1.89 or 1 pound for $2.49. How much will you save per pound, by buying the least expensive? Round to the nearest cent.

A.) $0.87
B.) $0.10
C.) $0.60
D.) $0.21

Answers

Answer: Option 'A' is correct.

Explanation:

Cost of 9 ounces of apples = $1.89

Cost of 1 ounce of apple is given by

[tex]\frac{1.89}{9}=\$0.21[/tex]

Now, if he bought 1 pound of apple,

Cost of 1 pound of apple = $2.49

Cost of 16 ounces = $2.49

(∵ 1 pound = 16 ounces)

Cost of 1 ounce of apple is given by

[tex]\frac{2.49}{16}=\$0.156[/tex]

So, Second option is the least expensive if he bought 1 pound of apple for $2.49

Then, he will save which is given by

[tex]0.21-0.156=0.054\times 16=$0.87\ per pound[/tex]

Hence, option 'A' is correct.

Final answer:

You will save $0.87 per pound by purchasing apples at the price per pound rate ($2.49) compared to the 9-ounce rate ($1.89 for 9 ounces), with the savings calculated by converting the 9-ounce price to a per pound rate and comparing it to the given per pound price.

Explanation:

To determine how much you will save per pound by buying the least expensive option for apples, first convert the price for 9 ounces into the equivalent price per pound. Since there are 16 ounces in a pound, you need to calculate the price per ounce and then multiply by 16 for the pound equivalence. The price per ounce for the first option is $1.89/9 ounces = $0.21 per ounce. Hence, the price per pound would be $0.21 per ounce × 16 ounces/pound = $3.36 per pound.

Now compare the price per pound of both options. The specified price per pound is $2.49, and the calculated price per pound for the 9-ounce option is $3.36. The savings per pound when buying the least expensive option ($2.49 per pound) would be $3.36 - $2.49 = $0.87 per pound, rounded to the nearest cent.

Therefore, the correct answer is (A) $0.87.

What is the surface area of the right cone Below
WILL MARK BRAINIEST !!

Answers

The formula to find the surface area of a cone is pi*r squared + pi*r*length. In this case, it would be pi*3 squared which is 9pi. You then add that to pi*3*15 which is 45pi. The answer is 54pi. Hope this helped!

Answer:

Option C

Step-by-step explanation:

Given in the picture is a right circular cone with base radius = 3 units and length = 15 units.

We have to find the surface area of the cone.

The total surface area of the cone is the sum of base area + lateral surface area

Base area = area of a circle = [tex]\pi r^2[/tex]

Lateral area of cone = [tex]\pi rl[/tex] where l = length of the cone.

Hence total surface area

= [tex]\pi r (r+l)\\=\pi (3)(3+15)\\=54\pi[/tex] square units

Option C is the answer.

A child is standing at point c and flying a kite located at point a, 25 ft above the ground. as the child lets out more string, the kite rises to a point b, directly above point
a. if the angle of elevation changes from 50º to 65º, how much higher to the nearest foot, is the kite than it was initially?

Answers

Final answer:

To calculate the height increase of the kite, we can use trigonometry and the formula tan(angle) = h / distance. By plugging in the values, we find that the kite is approximately 25 * tan(65º) ft higher than it was initially.

Explanation:

To find how much higher the kite is than it was initially, we need to determine the difference in height between points a and b. Since point b is directly above point a, the difference in height can be calculated using trigonometry.

We can use the tangent of the angle of elevation to find the height increase. The tangent of an angle is equal to the opposite side divided by the adjacent side.

In this case, the opposite side is the height increase (h) and the adjacent side is the distance between points a and c. We can use the formula tan(angle) = h / distance to solve for h.

Given that the angle changes from 50º to 65º, we can calculate the height increase as follows:

tan(65º) = h / distance

Solving for h:

h = tan(65º) * distance

Plugging in the values:

h = tan(65º) * distance

h ≈ tan(65º) * 25 ft

Rounding to the nearest foot, the kite is approximately 25 * tan(65º) ft higher than it was initially.

A restaurant manager recorded the number of people in different age groups who attended her food festival: Histogram with title Food Festival Participants, horizontal axis labeled Age Group (yr) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50. Which of the following frequency tables represents the data in the histogram accurately? Age Group (year) Number of People 0–19 20 20–39 60 40–59 40 60–79 50 Age Group (year) Number of People 0–19 20 20–39 60 40–59 50 60–79 40 Age Group (year) Number of People 0–19 20 20–39 40 40–59 60 60–79 50 Age Group (year) Number of People 0–19 60 20–39 20 40–59 40 60–79 50

Answers

The third choice is the correct answer because the information provided to you about the histogram shows the height of the first bar going to 20, the second bar going to 40, the third bar going to 60, and the fourth bar going to 50. The third frequency table organized this same information in the same way.

Answer:

There are 3 times as many participants in the 40-59 age group than the 0-19 age group.

Step-by-step explanation:

Because when we take 20 and times it by three we get 60 and the 40-59 age group is 60 so there you go. Hope This Helps:) Brain-list would be greatly appreciated.

5 out of 8 bags of m&ms had exactly 32 pieces in them. How many bags out of 40 should have exactly 32 pieces

Answers

Probabilities; so 5/8 =32
So 8*?= 40
8*5=40
Then 5*5=25 that means 25 bangs is the answer

un joyero vende 13 anillos de oro y 18 de plata por 9405 euros. sabiendo que el anillo de oro cuesta el triple que el de plata ¿cual es el precio de cada anillo?

Answers

To solve this problem you must apply the proccedure shown below:

1. You have that:

- He sales 13 gold rings and 18 silver rings in 9405 euros.
- The cost of the silver ring is three times the cost of the gold ring.

2. Keeping the information above on mind, you have the following system of equations:

x: the gold ring.
y: the silver ring.

x+y=9405
x=3y

3. Then, you have:

(3y)+y=9405
y=9405/4
y=2351.23 euros

x=3y
x=3(2351.23)
x=7053.75 euros

The answer is:
- Gold ring=7053.75 euros
- Silver ring=2351.23 euros

Have you found a positive o negative correlation between the independent and dependent variables

Answers

your answer will be positive o. now please give me 5 stars

find the surface area of each figure. Round your answer to the nearest tenth, if necessary

Answers

Let A be the surface area, b the base, h the height, s the hypotenuse and l the length.

b=8
h=4.3
s=7
l=5

A= b²+bl+bs+bh

A= 8²+8*5+8*7+8*4.3

A= 194.4 m³

Will give brainliest! How many distinct triangles can be made? I think I have to first find the measure of length b and then compare measure a with b and h to find the answer. Please help me out on how to find measure length b

Answers

check the picture below.

this is a case of the ambiguous case with an SSA, AC and CB are the sides and the angle is at A.

the ambiguous case has two triangles, the case when B is acute, CB sticks out, and the case when B is obtuse, CB sticks inside, it just so happen that those two angles for B are "supplementary" angles.

if you check the sin⁻¹ of that, we'll get the acute version of B, that's because of the constraints on the range of the inverse sine function, and we get ∡B ≈ 36.86989765°.

and of course, the other angle for B will be 180 - 36.86989765.

The line graphed below passes through the points (-2, 0) and (0, -3). Use the slope formula to calculate the slope between the given points. Verify the slope by counting the rise over the run on the graph.

Answers

The slope = (-3 - 0) / (0- -2) = -3 / 2

Answer:

The answer is -4/5

Step-by-step explanation:

It just is. The test said so.

Trains on the line reached an average speed of 125 miles per hour. Approximately, what is this speed in kilometers per hour?

Answers

125 miles per hour is equal to 201.168 kilometers per hour.

Please help me with this

Answers

y=3(x²+10x)+71
Now we need to complete square for (x²+10)
It should look like this
a²+2ab+b²=(a+b)²

y=3(x²+2*5x+5²)-3*5²+71
y=3(x+5)²-75+71
y=3(x+5)²-4
Vertex has coordinates x=-5, y=-4.
Vertex in this case is the extreme value (-5,-4)

You spend 60 on clothes and buy 3 dvd movies. your friend spends nothing on clothes and buys 8 dvd movies. you both spend the same amount of money. how much does each dvd movie cost?

Answers

Each dvd cost $7.50 how? Your friends buy 8 dvd's and in total is 60, you want to divide 60 from 8 and find that it's 7.50 and then multiply 8 to 7.50 and it should be 60. Hope this helps!!

Each DVD movie costs $12. This is calculated by setting up and solving an equation where the total spending on clothes and 3 DVDs equals the spending on 8 DVDs, as both parties spent the same amount.

To find out how much each DVD movie costs, we need to set up an equation based on the given information. You spent $60 on clothes and bought 3 DVD movies, while your friend spent $0 on clothes and bought 8 DVD movies. It is given that both of you spent the same amount of money. Let's denote the cost of each DVD movie as x.

The total amount you spent is the cost of the clothes plus the cost of the 3 DVD movies, which can be expressed as $60 + 3x. Your friend spent the cost of the 8 DVD movies, which is 8x. Since both amounts are equal, we have:

60 + 3x = 8x

Solving this equation for x:

Subtract 3x from both sides: 60 = 5xDivide both sides by 5: x = $12

Therefore, the price of each DVD movie is $12.

Find d: ??? Ft. Plz help idk this question

Answers

check the picture below.

What phrase can you use to represent m-4? M less then 4/ 4 less then m/ m plus 4 or 4 less m

Answers

Final answer:

The phrase 'm less 4' or '4 less than m' can be used to represent the expression 'm-4'. The other phrases mentioned do not accurately represent the mathematical expression 'm-4'.

Explanation:

The phrase that you can use to represent the expression m-4 is 'm less 4' or '4 less than m'. The phrase suggests that we are subtracting 4 from variable m. The phrase 'm plus 4' would be used to represent m+4 and does not apply here. So, in expressing the concept of subtraction in a phrase, we often say things like '4 less than m' which clearly conveys that 4 is being subtracted from m.

Learn more about Mathematical Phrasing here:

https://brainly.com/question/33441052

#SPJ11

If the area is 72 and the perimeter is 34, what are it's dimensions

Answers

xy = 72
2x + 2y = 34 (Im assuming uts a rectangle or square)

2 (72/y) + 2y = 34
144 + 2y^2 = 34y
2y^2 - 34y + 144 = 0
y = 9 or 8

So the length is 9 and width = 8

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