Answer:
[tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesGeometry
Volume of a Cone: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]Calculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{r}{h} = \frac{2}{3} \\\frac{dV}{dt} = 5 \ cm^3/s\\h = 15 \ cm[/tex]
Step 2: Rewrite Cone Volume Formula
Find the volume of the cone with respect to height.
Define ratio: [tex]\displaystyle \frac{r}{h} = \frac{2}{3}[/tex]Isolate r: [tex]\displaystyle r = \frac{2}{3} h[/tex]Substitute in r [VC]: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{2}{3}h)^2h[/tex]Exponents: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{4}{9}h^2)h[/tex]Multiply: [tex]\displaystyle V = \frac{4}{27} \pi h^3[/tex]Step 3: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{27} \pi \cdot 3 \cdot h^{3-1} \cdot \frac{dh}{dt}[/tex]Simplify: [tex]\displaystyle \frac{dV}{dt} = \frac{4}{9} \pi h^{2} \frac{dh}{dt}[/tex]Step 4: Find Height Rate
Find dh/dt.
Substitute in known variables: [tex]\displaystyle 5 \ cm^3/s = \frac{4}{9} \pi (15 \ cm)^{2} \frac{dh}{dt}[/tex]Isolate dh/dt: [tex]\displaystyle \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} } = \frac{dh}{dt}[/tex]Rewrite: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (15 \ cm)^{2} }[/tex]Evaluate Exponents: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{\frac{4}{9} \pi (225 \ cm^2) }[/tex]Evaluate Multiplication: [tex]\displaystyle \frac{dh}{dt} = \frac{5 \ cm^3/s}{100 \pi cm^2 }[/tex]Simplify: [tex]\displaystyle \frac{dh}{dt} = \frac{1}{20 \pi} \ cm/s[/tex]PLEASE ANSWER! WILL GIVE BRAINLIEST!
ardith has 3/71 x 10^7 bytes of space remaining on a flash drive. she needs to copy some files each of which is about 8.2 x 10^4 bytes in size, onto the flash drive. about how many files can ardith copy onto the flash drive?
Answer:
5
Step-by-step explanation:
Given that:
Space left on flash drive = 3/71 * 10^7 bytes = 0.0422535 * 10^7 = 422535.21 bytes
Size of each file = 8.2 * 10^4 bytes = 82000 bytes
Number of files that can be copied :
(422535.21) / (82000)
= 5.1528684
Number of files that can be copied = 5 files
In the figure shown below, lines j and k are parallel. Which equation can be used to find the value of x in the figure?
Answer:
Step-by-step explanation:
D b/c you know that the two angles add to 180°
The solution is Option D.
The value of x can be calculated from the equation
( x + 40 ) + ( 2x + 20 ) = 180
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles
Given data ,
Let the parallel lines be j and k
The transversal line is m
Now , the value ( 2x + 20 )° lies on one side of the transversal line
And the value ( x + 40 )° lies on one side of the transversal line
The total angle of a line is 180°
So ,
The sum of ( 2x + 20 )° and ( x + 40 )° will be 180°
Therefore , The solution is ( x + 40 ) + ( 2x + 20 ) = 180
Hence , The value of x can be calculated from the equation
( x + 40 ) + ( 2x + 20 ) = 180
To learn more about angles in parallel lines click :
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Consider a sample with data values of 9, 20, 17, 21, 16, and 13. Round your answers to 1 decimal place.
a. Compute the mean.
b. Compute the median.
Answer:
16 ; 16.5
Step-by-step explanation:
Given the data:
X = 9, 20, 17, 21, 16, 13
1.) The mean of the data:
Σ(X) / n
n = sample size ; n = 6
(9 + 20 + 17 + 21 + 16 + 13) / 6
= 96 / 6
= 16
2.) The median :
Rearranged data : 9, 13, 16, 17, 20, 21
1/2 (n + 1)th term
1/2 (6 + 1)th term
1/2 (7) th term
The 3.5 th term is the median:
(3rd + 4th) / 2
(16 + 17) / 2
33 /2 = 16.5
Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a
congruence statement,
If no, justify your answer.
Answer:
Yes, there is enough information to prove that the triangles are congruent.
ASA POSTULATE
Step-by-step explanation:
[tex] In\:\triangle PQR \: and \triangle TSR\\[/tex]
[tex] \angle PQR \cong \angle TSR...(given) \\[/tex]
[tex] QR\cong SR..... (given) \\[/tex]
[tex] \angle PRQ \cong\angle TRS\\(Vertical \: \angle s) \\[/tex]
[tex] \therefore \triangle PQR \cong \triangle TSR\\(ASA\: postulate) [/tex]
Answer:
YesStep-by-step explanation:
Given
One angle and a side of one triangle are congruent to same on another triangleAlso angle R is vertical and therefore equal for both trianglesWe have two angles and included side congruence which is ASA
If the balance at the end of eight years on an investment of $196 that has been invested at a rate of 9% is $337.12, how much was the interest
Answer:
$141.12
Step-by-step explanation:
Initial investment = $196
After 8 years with 9% interest rate it becomes: $337.12
The amount of interest will be:
= $337.12 - $196
= $141.12
A town in east Texas received 10 inches of rain in two DAYS. If it kept raining at this rate for a 31 day month, how much rain did the town receive? 11
This is equivalent to approximately 12.917 feet.
===================================================
Work Shown:
(10 inches)/(2 days) = (x inches)/(31 days)
10/2 = x/31
10*31 = 2*x ... cross multiply
310 = 2x
2x = 310
x = 310/2
x = 155
Keep in mind that this water is being drained on a fairly continuous basis. This means that not all of the water is sticking around (we'd hope not anyway) at the same moment in time.
Note: 155 inches = 155/12 = 12.917 feet approximately.
--------------------------
Alternative method:
If the town got 10 inches in 2 days, this means it rains at a unit rate of 10/2 = 5 inches per day.
Multiply that by 31 days and we get 5*31 = 155 inches of total rain.
the grade point average for 10 students are listed below. find the range of the data set.
0.8, 0.9 1.8, 2.0, 2.9, 3.2, 3.3 ,3.6, 4.0
Answer:
might be 22.5 i think but i'm not sure correct me if i'm wrong
Step-by-step explanation:
Answer:
Step-by-step explanation:
the range is the difference between the largest and the smallest value
4.0-0.8=3.2
Consider the following ordered data.6 9 9 10 11 11 12 13 14(a) Find the low, Q1, median, Q3, and high.(b) Find the interquartile range.
Answer:
6 ; 9 ; 11 ; 12.5; 14
B.) 3.5
Step-by-step explanation:
Given the data:
6 9 9 10 11 11 12 13 14
a.) The low = 6 (lowest value in the dataset)
b.) Q1 = Lower quartile
Q1 = 1/4(n + 1)th term
n = sample size = 9
Q1 = 1/4(9 + 1) ; 1/4(10) = 2.5th term
Q1 = (2nd + 3rd term) / 2 = (9 + 9) / 2 = 9
Median Q2:
Q2 = 1/2(9 + 1) ; 1/2(10) = 5th term = 11
Upper Quartile Q3:
Q3 = 3/4(9 + 1) ; 3/4(10) = 7.5th term
Q3 = (7th + 8th term) / 2 = (12 + 13) / 2 = 12.5
Interquartile range (Q3 - Q1)
(12.5 - 9) = 3.5
The high = 14 (highest value in the dataset)
I really think it’s a good question and my homework
Answer:
77.245 i used me brane and paper and give brainliest and your in shcool why why why cheat
Step-by-step explanation:
Answer:
680.745
Step-by-step explanation:
hope this helps.
The repeating decimal, 0.ModifyingAbove 27 with bar, is converted to the fraction 0.ModifyingAbove 27 with bar = StartFraction 3 Over x EndFraction.
What is the value of x in the fraction?
9514 1404 393
Answer:
x = 11
Step-by-step explanation:
A 2-digit repeating decimal fraction will have two 9s as the denominator. In this case the fraction can be reduced.
[tex]0.\overline{27}=\dfrac{27}{99}=\dfrac{3}{11}[/tex]
Comparing this to 3/x, we see that x = 11.
Answer:
11
Step-by-step explanation:
sorry if im wrong
1. Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 during her retirement. She wants to save enough money so that the payments lasts for 30 years. A financial advisor has told her the she can expect to earn 5% interest on her funds, compounded annually.
2. Yejin has just turned 28 years old. She currently has no retirement savings. She wants to save part of her salary each month into her annuity fund. Calculate the amount Yejin needs to save each month, to meet her retirement goal.
9514 1404 393
Answer:
$3891.10
Step-by-step explanation:
This question is a bit unusual in that the interest is compounded annually, but payments and withdrawals are made monthly. The effective monthly rate is ...
1.05^(1/12) -1 = 0.407412378% = i
We assume that payments to the annuity are made at the end of the month, and that withdrawals are made at the beginning of the month. (The last payment and the first withdrawal are made on the same day.)
The amount of money required in the fund is ...
A = $4000(1 -(1.00407^-360))/(1 -1.00407^-1) = $757,712.88
The amount of money needed each month to be put into the fund is P, where ...
$757,712.88 = P(1 -1.00407)^(-12(60-28))/(1 -1.00407^-1) = 194.7297P
P = $757,712.88/194.7297 = $3891.10
Yejin needs to save $3891.10 each month to meet her retirement goal.
_____
Sanity check
Yejin wants payments for 30 years from the fund to which she has contributed for 32 years. The similarity of the time periods means that Yejin's monthly contribution will need to be very similar to the amount she plans to withdraw.
The only ways to reduce the required contribution are to earn a higher interest on deposits, or to adjust the relative time periods (retire later).
help with geometry pleasee
Answer:
Angle E
Step-by-step explanation:
What is the value of the expression? (10 1/4 +61) – (3 3/5 - 3 1/2) Enter your answer in the box as a mixed number in simplest form.
Answer:
71 3/20Step-by-step explanation:
This is easy. The first step here is to simplify the numbers inside the parentheses.
10 1/4 + 61 = 71 1/4
3 3/5 - 3 1/2 = 3 6/10 - 3 5/10 (We needed to get both with like denominators, so we raised the fractions to an equivalent denominator.)
3 6/10 - 3 5/10 = 1/10
Now, we will do the operation outside of the parentheses.
71 1/4 - 1/10 = 71 5/20 - 2/20 = 71 3/20
Answer is 71 3/20
Anna bought 120 feet of copper
wire. She cut it into 16 pieces of
the same length. How long is one
piece of copper wire?
Answer:
7 1/2 feet
Step-by-step explanation:
The number of points scored by a basketball player in the first eight games of a season are shown below. 15, 35, 18, 30, 25, 21, 32, 16 What would happen to the data distribution if she scored 24, 22, 27, and 28 points in her next four games?
Answer:
im not sure how the data should be interpreted but here is the distribution. It goes up by .416
Step-by-step explanation:
the average of the first 8 games is 24
the average of the 12 games is 24.416
Find the slope of the line that contains the following points:
(5, 4) and (3, -4)
Answer:
slope = 4
Step-by-step explanation:
y2-y1/x2-x1 = slope
-4 - 4 / 3 - 5 = slope
-8/-2 = slope
8/2 = slope
4/1 = slope
4 = slope
Which points are on the graph of g(x) = (1/5)^x
Choose all answers that are correct.
A.(-1,5)
B.(3,1/125)
C.(1,0)
D.(-2,1/25 )
Answer:
A) The point( -1 , 5) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
B) The point( 3 , 1/125) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Step-by-step explanation:
Explanation:-
Given graph
y = [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Put the point ( -1 , 5)
Put y =5 and x =-1
[tex]5 = (\frac{1}{5} )^{-1} = 5[/tex]
The point( -1 , 5) is satisfies the given graph
ii)
Given graph
y = [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
[tex]\frac{1}{125} = (\frac{1}{5} )^{3} = \frac{1}{125}[/tex]
The point( 3 , 1/125) is satisfies the given graph [tex]g(x) = (\frac{1}{5} )^{x}[/tex]
Solve -9 < 4x+3 5 11.
A. x>-3 and xs 2
B. x>3 or xs 2
C. x>-3 or xs 2
D. x > 3 and xs3
3 tiles are red 6 tiles are green 3 tiles are blue a tile will be randomly selected from the bag. What is the probability that the tile selected will be green?
Answer:
80 percent
Step-by-step explanation:
Because there are green tiles so the possibility is 80 percent
calculate the nth term for the following sequences:
1: 3,6,12,24,48
2: 4,9,16,25,36,49
3: 5,10,17,26,37,50
4: 8,3,-2,-7,-12
5: 6,11,18,27,38,51
Answer:
1:96
2:64
3:65
5:66
Answer:
1:56...................
Simplify the following expression.
12a376c5
3a284c5
O A 4a6²c
OB.
9a62
OC. 4a62
OD. 9ab2cC
Answer:
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]
Required
Simplify
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex]
To solve this, we apply the following law of indices:
[tex]\frac{m^x}{m^y} = m^{x-y}[/tex]
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}[/tex] becomes
[tex]\frac{12}{3}a^{3-2}b^{6-4}c^{5-5}[/tex]
[tex]\frac{12}{3}a^{1}b^{2}c^{0}[/tex]
[tex]c^0 = 1[/tex]; So, we have
[tex]\frac{12}{3}a^{1}b^{2}*1[/tex]
Finally,
[tex]4ab^{2}[/tex]
Hence:
[tex]\frac{12a^3b^6c^5}{3a^2b^4c^5}=4ab^{2}[/tex]
⚠️please help!!!⚠️
find the value of x then find the measure of the labeled angle
x°=.......°
(x-35)°=......°
Step-by-step explanation:
x° + (x - 34)° = 180°. (C-angles)
Thereforr 2x - 34 = 180 and x = 107.
x° = 107°.
(x - 34)° = 73°.
you need to raise at least $400 in order to go on a field trip. you are selling magazines for $12 each. you have already raised $124. how many magazines must you sell to meet your goal? write, solve and graph the inequality for this situation.
Answer:
44 magazines need to be sold
Step-by-step explanation:
Y=Mx+b
400=12x-124
524=12x
43.6667 or 43 (2/3)
round up since you cant sell 2/3 of a magazine
Answer:
the inequality is 124+12x≤400
Step-by-step explanation:
x=23
hope this helps
All functions have a domain of R (all real numbers).
True
Or False
Answer:
True
Step-by-step explanation: Trust me
I have three marbles in a bag. One is purple and the other two are green. What is the probability of pulling a green marble out of the bag?
Answer:
1/3 would be the chances you'd pick purple, because there's only 1 in 3 that's purple out of all 3 marbles.
With green it would be 2/3 because there's twice the number of green marbles than purple.
If there's 1 of purple and 1 of green, the probability would then be 1/2 of picking either colour.
A trombone acts like an open pipe of length 2.96 m .On a cold day it plays,its 4th harmonic at 221 hz what is the speed of the sound waves in the horn that day?
Answer:
327.08 m/s
Step-by-step explanation:
Given that:
Length of pipe = 2.96m
4th harmonic frequency = 221 Hz
Speed of wave in the horn :
Speed of wave (v) = fλ
For 4th harmonic :
Wavelength, λ = (2/4)L
λ = L/2 ; 2λ = L
2λ = 2.96
λ = 2.96 / 2
λ = 1.48 m
Hence, speed of wave in the horn = 221 * 1.48 = 327.08 m/s
Please help! I’m begging you. Give the answers!
Answer:
4lb and 6oz
Step-by-step explanation:
number one is
An armount of nitrogen undergoes a physical change and increases its volurme, What can be knoW) about this
physical change?
O The boiling point of the nitrogen increased.
O The mass of nitrogen increased.
O The color changed.
O The density changed.
Answer:
d
Step-by-step explanation:
Give three points that lie on a line with a
slope of -2/5
Answer:
The three points that lie on a line y = -2/5x with a slope -2/5 will be:
(0, 0)(5, -2)(10, -4)Please check the attached graph also.
Step-by-step explanation:
We know that the slope-intercept form of the line equation is
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Given
slope = m = -2/5
We suppose the line passes through the origin.
so b = 0
substituting m = -2/5 and b = 0 in the slope-intercept form
[tex]y = mx+b[/tex]
y = -2/5x + 0
y = -2/5x
Thus, the equation of line with the slope m = -2/5 and passes through the origin (0, 0) will be:
y = -2/5x
As the equation of line passes through (0, 0), thus the point (0, 0) lies on the line.
Putting x = 0 in the equation y = -2/5x
y = -2/5 × (0)
y = 0
Thus, (0, 0) is the point which also passes through the line
Putting x = 5 in the equation y = -2/5x
y = -2/5 × 5
y = -2
Thus, (5, -2) is the point which also passes through the line
Now, putting x = 10 in the equation y = -2/5x
y = -2/5 × 10
y = -4
Thus, (10, -4) is the point which also passes through the line.
Thus, the three points that lie on a line y = -2/5x with a slope -2/5 will be:
(0, 0)(5, -2)(10, -4)Please check the attached graph also.
HELP ME PLS I REALLY NEED HELP THIS MAH LAST QUESTION
Answer:
number 1
Step-by-step explanation: