Answers
When the radius is 9cm, it increases at a rate of 0.06 cm per second.
How fast is the radius increasing?We assume the ballon is a perfect sphere. Remember that the volume of a sphere as a function of the radius is given by:
V = (4/3)*3.14*(R)³
When the radius is R = 9cm, the volume is:
V = (4/3)*3.14*(9cm)³ = 3,052.08 cm³
Isolating the radius as a function of the volume, we get:
R = ∛((3/4*3.14)*V)
And we know that the volume increases at a constant rate of 6cm³/s, if we assume that the initial volume is 3,052.08 cm³ then we can write the radius as a function of time as:
R(t) = ∛((3/4*3.14)*(3,052.08 cm³ + 6cm³/s*t))
Where t is the time in seconds.
Now we need to differentiate this and evaluate in t = 0.
R'(t) = (1/3)*(3/4*3.14)*(3,052.08 cm³ + 6cm³/s*t)^(-2/3)* (6cm³/s*3/4*3.14)
Evaluating in t = 0 we get:
R'(0) = (1/3)*(3/4*3.14)*(3,052.08 cm³ + 6cm³/s*0)^(-2/3)* (6cm³/s*3/4*3.14)
= (1/3)*(3/4*3.14)*(3,052.08 cm³)^(-2/3)* (6cm³/s*3/4*3.14) = 0.06 cm/s
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Related Questions
A waterskier skis over the ramp shown in the figure at a speed of 30 ft/s. How fast is she rising as she leaves the ramp?
Answers
The waterskier has a final speed of approximately 25.350 feet per second.
What is the final speed of the waterskier?
In this question we need to determine the final speed of the waterskier, that is, the final speed of the waterskier when she leaves the ramp. This can be done by means of the principle of energy conservation, where the total energy is the result of combining translational kinetic energy (K), in pounds-feet per second, related to the speed of the waterskier, and gravitational potential energy (U), in pounds-feet per second.
The equation that represents the situation is described below:
K = U + K'
0.5 · m · v² = m · g · h + 0.5 · m · v'²
0.5 · v² = g · h + 0.5 · v'²
v'² = v² - 2 · g · h
Where:
K' - Final translational kinetic energy, in pounds-feet per second.K - Initial translational kinetic energy, in pounds-feet per second.m - Mass of the waterskier, in pounds.v - Initial speed of the waterskier, in feet per second. v' - Final speed of the waterskier, in feet per second.g - Gravitational acceleration, in feet per square second. h - Final height of the waterskier, in feet.If we know that v = 30 ft / s, g = 32.174 ft / s² and h = 4 ft, then the final speed of the waterskier is:
v' = √[(30 ft / s)² - 2 · (32.174 ft / s²) · (4 ft)]
v' ≈ 25.350 ft / s
The final speed of the waterskier is approximately 25.350 feet per second.
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Joyce paid $120.00 for an item at the store that was 40 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
Answers
4 and 3 half's divided by 2 and 7
halfs minus 8
Answers
Answer:
4/3/2/7-8= -7
Step-by-step explanation:
How many units are in 10 lots
Answers
A standard lot is an amount of currency which is the same as 100,000 units of a base currency .
What are the types of lot sizes?There are three lot sizes;
The standard lotThe mini lotThe micro lotIn finance, a lot indicates a measure or increment of a commodity that can be transacted. Products are bought and sold using different lot sizes. Products such as spot forex are sold in lots of 100,000, 10,000, 1,000, or 100 units.
Competition and brokerage online has resulted in the introduction of various lot sizes and forms.
A change of $10 corresponds to a pip movement of a standard lot.
By buying $100,000 at ¥110.00 and the price increases to ¥110.50, which indicates a 50 pip movement and a gain of $500 and vice versa.
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15 more than twice Janelle's age
Use the variable j to represent Janelle's age
Answers
Use the variable j to represent Janelle's age
1. Represent "twice than Janelle's age":
-> 2j.
2. Represent "fifteen more than twice than Janelle's age":-> 15+2j.
3. Final answer.15+2j.
Can you calculate the area of this land and if so, can you help me?
Se podría calcular el area de este terreno? y si es así pueden ayudarme?
Answers
The area of the rectangular land is 208,607 square meters,
A rectangle is defined as a quadrilateral whose opposite sides are equal and parallel
How to find the area of a rectangle?
The lengths of a rectangle are denoted by L and W
where: L=length
w=width
Area of the land (A)= Area of the larger land minus Area of the smaller land carved out
A= (LW) - (lw)
A=(513x466.5)-(267x113)
A=239,312-30705
A=208.607 meters square
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What is the equation of this graph the line?
Answers
The slope-intercept form of the given line be,
y = -(9/8)x + 7
Given, a line is passing from two points (0 , 7) and (8 , -2)
we have to find the slope-intercept form of the equation of the line passing from the given points.
Using the slope-intercept form, we get
(y - y1)/(x - x1) = (y1 - y2)/(x1 - x2)
(y - 7)/(x - 0) = (7 - (-2))/(0 - 8)
(y - 7)/(x - 0) = 9/-8
-8(y - 7) = 9x
-8y + 56 = 9x
9x + 8y = 56
Slope-intercept form of the equation is,
y = -(9/8)x + 7
Hence, the slope-intercept form of the given line be, y = -(9/8)x + 7
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Which of the following is a rational expression?
1) 2
2) 6/x-20
3) 20x^2+2/9x^3+x
4) All of them are rational expressions?
Answers
Answer:
All of them
Step-by-step explanation:
A rational expression is simply a quotient of two polynomials. Or in other words, it is a fraction whose numerator and denominator are polynomials.
. Which equations are true? Choose all that apply.
A. 2 x 0 = 2
B. 5x0=9×0
D.) 1 x 3 = 3
C. 6 x 1= 3x2
Answers
Valerie is 64 inches tall. About how many centimeters tall is Valerie?
(1 inch -2.5 centimeters)
O 25.5
O 30.6
O 160
O 180
Answers
Using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.
What is the conversion factor?A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.
The amount is often expressed as a fraction or ratio with a multiplication factor.
For instance, 12 inches equals one foot when converting between inches and feet.
So, 64 inches in cm is:
We know that:
1 inch = 2.5 cm
Then, 64 inches is:
64 inches = 2.5 × 64
64 inches = 160
Therefore, using the conversion factor, the height of Valerie in centimeters is (C) 160 cm.
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Correct question:
Valerie is 64 inches tall. About how many centimeters tall is Valerie?
(1 inch -2.5 centimeters)
A. 25.5
B. 30.6
C. 160
D. 180
There are 8 roses and 7 daisies in a vase.
(a) What is the ratio of roses to all flowers in the vase?
(b) What is the ratio of daisies to all flowers in the vase?
Answers
b) 7:15
Hope it helps
Two tracking stations are on the equator 163 miles apart. A weather balloon is located on a bearing
of N 43°E from the western station and a bearing of N 17°E from the eastern station. How far, to the
nearest mile, is the balloon from the western station? i got 322 miles
Answers
If the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
Suppose the selling price of a towel is x, according to the given condition,
5 = x - 15% of x
5=x-0.15x
5=0.85 x
x=5/0.85
x=5.88
Thus, if the overhead was 20% of the cost of each towel. The selling price of each towel is 5.88.
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Suppose the number cube was rolled 500 times. Based on the results in the table, about how many times would it land on 5?
Answers
The number of times that the cube will land on 5 if the number cube was rolled 500 times is 83 times.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
It should be noted that in a number cube, we hage numbers from 1 to 6. The probability of getting a 5 is 1/6.
Therefore, when it's rolled 500 times, the possible number will be:
= 1/6 × 500
= 83 times.
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(7x² + 4y²)(5x² - y²)
Answers
Answer:
okay so step by step explanation,
first multiply 7[tex]x^{2}[/tex] with 5[tex]x^{2}[/tex] and -[tex]y^{2}[/tex]
35[tex]x^{4}[/tex]-7[tex]x^{2}[/tex][tex]y^{2}[/tex]
then do the second one
20[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]
take the sum of those,
35[tex]x^{4}[/tex]+13[tex]x^{2}[/tex][tex]y^{2}[/tex]-4[tex]y^{4}[/tex]
good luck<3!
On a farm the ratio of grey goats to white is 4:7 there are 160 grey goats. How many white goats are there
Answers
Answer: 88
Step-by-step explanation:
For every 7 grey goats there are 4 white goats. 160/7=22 4*22=88
15. Tim can finish painting his barn in 10 hours. It takes
his wife JoAnn only 8 hours to do the same job. If they
work together, how long will it take them to complete the
job?
Answers
Answer:
4 4/9
is the time it will take
A little help please i dont know how to do this
Answers
For 90 degrees clockwise, A’=(2,3) B’=(4,-2) C’=(1,-3)
For 90 degrees counterclockwise, A’=(-2,-3) B’=(-4,2) C’=(-1,3)
can somebody please help me
Answers
Answer:
B
Step-by-step explanation:
This is correct because it is the only one in proper set notation.
Hope it helps!
What is the smallest distance between the origin and a point on the graph of y = 1/2*(x^2 - 8)?
Answers
The smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Given, a function
y = 1/2(x² - 8)
We have to find the smallest distance between origin and a point on the graph of y = 1/2(x² - 8).
Now, the point on the graph be,
( x , 1/2(x² - 8) ) and origin be (0 , 0)
Let the function of the distance between both the points be,
D = √(x - 0)² + (1/2(x² - 8) - 0)²
D = √x² + 1/4(x² - 8)²
D² = x² + 1/4(x² - 8)²
On differentiating, we get
2DD' = 2x + x(x² - 8)
x³ + 2x - 8x = 0
x³ - 6x = 0
x(x² - 6) = 0
So, x = 0 , √6 , -√6
and the distance is minimum for x = √6
Therefore, using distance formula, we get
Distance = √(x1 - x2)² + (y1 - y2)²
Distance = √(0 - √6)² + (0 - (-1))²
Distance = √6 + 1
So, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
Hence, the smallest distance between the origin and a point on the graph of y = 1/2(x² - 8) is √7 units.
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A department store buys 400 shirts at a cost of $3,200 and sells them at a selling price of $10 each. What is the percent markup?
Answers
Find the square root of:
441
Answers
It is very easy, we just have to take the square root as it tells us in the problem:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{ \sqrt{441 }} = \orange{21}[/tex]
You may ask ¿why 21?
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \red{21 \times 21} = \orange{441} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf So , \: the \: result \: is \\ \sf \longmapsto \orange{21} [/tex]
a magician charges a $30 fee to cover travel and expenses, plus $19.99 per hour. Write an equation to represent the relationship between h, the number of hours, and t, the total charge for the magician.
Answers
The equation to represent the relationship between h and t is
t = 30 + 19.99h.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the magician charges a $30 fee one time and a $19.99 fee per hour.
The total charge, t, for the magician for h hours is,
t = 30 + 19.99h
Hence, the equation to represent the relationship between h and t is
t = 30 + 19.99h.
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Help to solve this question attached below###
Answers
Consider two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
Answers
The value of the consecutive numbers are 7 and 8.
What are consecutive integers?Consecutive integers simply means the numbers that follow each others. It should be noted that such numbers have the same difference between them.
From the information given, we want to find two consecutive positive integers such that the square of the second integer added to 6 times the first is equal to 106.
Let the numbers be x and x+1.
Therefore, 6x + (x + 1)² = 106
6x + x² + 2x + 1 = 106
Collect like terms
x² + 8x + 1 - 106
x² + 8x - 105
x² + 15x - 7x - 105
x(x + 15) - 7(x - 15) = 0
Therefore x - 7 = 0
x = 0 + 7
x = 7
Therefore x + 1
= 7 + 1
= 8
The numbers are 7 and 8.
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b) The diagram shows a thin square sheet of metal measuring 24 cm by 24 cm. A square of side x cm is cut off from each corner. The remainder is then folded to form an open box, x cm deep, whose square base is shown shaded in the diagram. Write the volume, cm³, of the box as V=4x³-96x² +576x [3]
(ii) Compute the maximum cost paid to fill up the box with sand if RM 0.30 per cubic centimeter of sand charged. [2]
Answers
Answer:
Below
Step-by-step explanation:
Graphing the equation shows local max volume at x = 4 of 1024 cm^3
1024 cm^3 * RM . 30 / cm^3 = RM 307.2
Add.
(-x³-x)+(6x² + 6x -7)
Answers
Answer:
[tex]-x^{3}+6x^{2} +5x-7[/tex]
Step-by-step explanation:
-x^3-x+6x^2+6x-7
Order the polynomial from exponent order to make it easier
-x^3+6x^2+6x-x-7
-x^3+6x^2+5x-7
Hopes this helps please mark brainliest
Answer:
-x^3+6x^2+5x-7
Step-by-step explanation:
open parentheses, collect like terms.
100 pointers! pls answer ASAP!!!!
find the measure of angle A show all your work
Thx
Answers
The value of ∠A in triangle ABC is 40°
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given triangle ABC,
∠A=7x-16°, ∠B=81°
By alternate segment theorem,
∠C=4x+27°
The sum of all the angle of a triangle is 180°.
∠A+∠B+∠C=180°
⇒7x-16+81+4x+27=180
11x=180-92
11x=88
x=8
So the value of ∠A=7×8-16 = 40°
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Answer:
The value of ∠A in triangle ABC is 40°
Pretty much the same as the person that posted before.
What is the constant of proportionality, ?
I
y
30+
28+
26+
-24+
22+
20+
18+
16+
14+
12+
10+
8+
6+
4+
2+
2
3
4
5
6
7
8
I
Answers
Answer:50.8%
Step-by-step explanation:
Heather and her friends want to buy tickets to the Harry Styles concert. Each ticket cost 85$ and parking cost 25$. Write an equation to represent if Heather spends 280$
Answers
answer: 85+85+85+25
Suppose an investment account is opened with an initial deposit of $18,500 earning 6.25% interest, compounded continuously. How much will the account be worth after
25 years? (Round your answer to two decimal places.)
$
Answers
The amount in the account after 25 years be $ 84,216.11
Given, an investment account is opened with an initial deposit of $18,500 earning 6.25% interest, compounded continuously.
We have to find the amount in the account after 25 years.
Now, on using the compound interest amount formula, we get
Amount = P(1 + r/100)^t
Amount = 18500(1 + 6.25/100)^25
Amount = 18500(1.0625)^25
Amount = 18500(4.55)
Amount = 84,216.1137
Hence, the amount in the account after 25 years be $ 84,216.11
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