The rate of the change of the volume of the pile, in cubic feet per hour, when the circumference of the base is 8x feet, for this case, is 40x²/π³ cubic ft/ hour.
How to calculate the instantaneous rate of change of a function?Suppose that a function is defined as;
[tex]y = f(x)[/tex]
Then, suppose that we want to know the instantaneous rate of the change of the function with respect to the change in x, then its instantaneous rate is given as:
[tex]\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}[/tex]
What is chain rule of differentiation?If a variable z depends on the variable y, which itself depends on the variable x, then we have:
[tex]\dfrac{dz}{dx} = \dfrac{dz}{dy} \times \dfrac{dy}{dx}[/tex]
(assuming all these derivatives exist).
For this case, we're given that:
[tex]V = \dfrac{r^3}{3}[/tex] (in cubic ft)
Assuming the cross section being circular, expressing radius 'r' in terms of circumference, we get:
[tex]C = 2\pi r\\\\r = \dfrac{C}{2\pi}\\\\V = r^3/3\\\\V = \dfrac{C^3}{24\pi^2} \: \rm ft^3[/tex]
It is given that rate of change of circumference with respect to time is 5.
Thus, symbolically, we get:
[tex]\dfrac{dC}{dt} = 5[/tex]
Finding rate of change of volume with respect to time:
[tex]\dfrac{dV}{dt} = \dfrac{d\left (\dfrac{C^3}{24\pi^2}\right) }{dC} \times \dfrac{dC}{dt} = \dfrac{3C^2}{24\pi^3} \dfrac{dC}{dt} = \dfrac{5C^2}{8\pi ^3} \: \rm ft^3/hour[/tex]
(using chain rule of differenciation).
At C = 8x ft, we get:
[tex]\dfrac{dV}{dt} = \dfrac{5C^2}{8\pi ^3} \: \text{ft}^3\text{/hour}\\\\\dfrac{dV}{dt} |_{C = 8x} = \dfrac{5(8x)^2}{8 \pi^3} = \dfrac{40x^2}{\pi^3} \: \rm ft^3/hour[/tex]
Thus, the rate of the change of the volume of the pile, in cubic feet per hour, when the circumference of the base is 8x feet, for this case, is 40x²/π³ cubic ft/ hour.
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Answer number 1 please thank you
1 point
2. Write the equation of a line through the point (4, 6) that
is perpendicular to the line 2x - y = 15.
Enter the equation in slope-intercept form. Use fractions if necessary. NO SPACES.
Answer: 2x-y=15
Step-by-step explanation: can u be more detailin
Find the length of the unknown side
SOMEONE PLEASE HELP ME WITH THESE! ILL GIVE YOU BRAINLIST ANSWER!!
Answer:
1. 676 2. 10,000 3. 2,500 4. 1,681
Step-by-step explanation:
1. Using the Pythagorean Theorem (a sqaured + b sqaured = c sqaured) you do 10 sqaured plus 24 squared which equals 676.
2. By using the same Theorem, you do 60 sqaured plus 80 sqaured which equals 10,000.
3.By using the same Theorem, you do 30 sqaured plus 40 sqaured which equals 2,500
4.By using the same Theorem, you do 40 sqaured plus 9 sqaured which equals 1,681.
Solve the inequality x − y < z for x
Answer:
Resolver para x
⎩
⎪
⎨
⎪
⎧
x<
1−z
y
,
x∈R,
x>
1−z
y
,
z<1
y>0 and z=1
z>1
Step-by-step explanation:
The solution of the inequality x − y < z is x < z + y.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality,
x − y < z.
To solve for x:
Add y to both sides,
x < z + y
Therefore, the solution is x < z + y.
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help please!!!! it makes so sense
Answer:
(- [tex]\frac{1}{5}[/tex] , 0 )
Step-by-step explanation:
to find where the line crosses the x- axis, let y = 0 in the equation and solve for x
5x - 2(0) + 1 = 0
5x - 0 + 1 = 0
5x + 1 = 0 ( subtract 1 from both sides )
5x = - 1 ( divide both sides by 5 )
x = - [tex]\frac{1}{5}[/tex]
the line crosses the x- axis at (- [tex]\frac{1}{5}[/tex], 0 ) or ( - 0.2, 0 )
Answer:
(-1/5, 0).
Step-by-step explanation:
Where the line crosses the axis the value of y = 0.
5x - 2y + 1 = 0
Let y = 0, then:
5x - 2(0) + 1 = 0
5x + 1 = 0
5x = -1
x = -1/5.
So the point is (-1/5, 0).
It costs $112 to turf a lawn of area 56m squared. How many dollars would it cost to turf a lawn of area 77m squared.
[tex]Cost\:of\:56m^2lawn=$112\\Cost\:of\:1m^2 lawn=$(112/56)\\=$2Cost\:of\:99m^2=$(99\:x\:2)=$198\\=14166.9rs /14167 rs[/tex]
Found answer here: https://brainly.in/question/12501706
Answer:
$154
Step-by-step explanation:
You have to divide 112/56 to get the amount of money each m squared is which is 2
Then you subtract 77-56 to get the difference, which is 21 and then you multiply 21•2 which is 42
Then you add 42+112 which will be 154
what is 2+2 divided by 50
Answer: 2.04
Step-by-step explanation:
2+2=4
4/50 = 2.04
i need help with question 28;
Answer:
Hope this helps!
(help very much needed asap)
Pls help me solve the equation. Show steps.
Pasos
5
3
k+
10
7
=
15
11
k−
5
2
Resta
15
11
k en los dos lados.
5
3
k+
10
7
−
15
11
k=−
5
2
Combina
5
3
k y −
15
11
k para obtener −
15
2
k.
−
15
2
k+
10
7
=−
5
2
Resta
10
7
en los dos lados.
−
15
2
k=−
5
2
−
10
7
El mínimo común múltiplo de 5 y 10 es 10. Convertir −
5
2
y
10
7
a fracciones con denominador 10.
−
15
2
k=−
10
4
−
10
7
Como −
10
4
y
10
7
tienen el mismo denominador, reste sus numeradores para restarlos.
−
15
2
k=
10
−4−7
Resta 7 de −4 para obtener −11.
−
15
2
k=−
10
11
Multiplica los dos lados por −
2
15
, el recíproco de −
15
2
.
k=−
10
11
(−
2
15
)
Multiplica −
10
11
por −
2
15
(para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).
k=
10×2
−11(−15)
Realiza las multiplicaciones en la fracción
10×2
−11(−15)
.
k=
20
165
Reduzca la fracción
20
165
a su mínima expresión extrayendo y anulando 5.
k=
4
33
Answer:
33/4
Step-by-step explanation:
3k/5 +7/10 = 11k/15 - 2/5
11k/15 - 3k/5 = 7/10 +2/5
11k/15 - 9k/15 = 7/10 + 4/10
2k/15 = 11/10
2k = 165/10
2k = 33/2
k = 33/4
Help!?!? Find the area of the shaded region. Round your answer to the nearest hundredth.
Check the picture below.
so if y = 2, then 2y = 4, thus
[tex]\textit{area of a segment of a circle}\\\\A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}~~ - ~~sin(\theta ) \right)~~\begin{cases}r=radius\\\theta =\stackrel{degrees}{angle}\\[-0.5em]\hrulefill\\r=4\\\theta =60\end{cases}\\\\\\A=\cfrac{4^2}{2}\left(\cfrac{\pi (60) }{180}~~ - ~~sin(60^o ) \right)\implies A=8\left( \cfrac{\pi }{3}~~ - ~~\cfrac{\sqrt{3}}{2} \right)\\\\\\A=\cfrac{8\pi }{3}~~ - ~~4\sqrt{3}\implies A\approx 1.45[/tex]
3w+1≥19 Solve the inequality
Step-by-step explanation:
group like terms
[tex]3w \geqslant 19 - 1[/tex]
solve
[tex]3w \geqslant 18[/tex]
divide the number with the variable by both sides
[tex] \frac{3w}{3} \geqslant \frac{18}{3} [/tex]
solve
[tex]w \geqslant 6[/tex]
Answer:
w ≥ 6
Step-by-step explanation:
Given:
3w+1≥19
Solve:
3w+1≥19
Subtract 1 from both sides
3w+1≥19
-1 -1
-----------------
3w≥18
Divide both sides by 3
3w/3 ≥18/3
w ≥ 6
Hence, the answer is:
w ≥ 6
Kavinsky
Answer number 2 please
Make x the
Subject
4(x +t) = M
Answer:
x = (M-4t)/4
Step-by-step explanation:
First we expand the brackets:
4(x+t) =M
4x +4t = M
Subtract 4t from both sides:
4x +4t -4t = M -4t
Simplify:
4x = M -4t
Divide both sides by 4 :
4x÷4 = (M-4t)/4 = (M-4t)÷4
x = (M-4t)/4
Hope this helped and brainliest please.
Need help with this quickly . Will give brainliest.
Answer:
A
Step-by-step explanation:
(Not sure if this is completely right but this should be it)
How many times does the graph cross the x-axis for this equation y = -2x2 + 4x -
5? *
A quadratic equation is in the form of ax²+bx+c. The graph of the equation y = -2x² + 4x -5 will not intersect the x-axis at any point.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The given equation is a quadratic equaion, therefore, to know if the equation will intersect with the x-axis we need to find the roots of the equation.
Since the value of the discriminant is negative for this equation, the roots of the equation will be imaginary. Plotting the graph, we will observe that the graph will not intersect the x-axis at any point.
Hence, the graph of the equation y = -2x² + 4x -5 will not intersect the x-axis at any point.
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A number exceeds 47,56,908 by 16,34,096 .Find the number
Answer:
6391004
Step-by-step explanation:
hope this helps
Answer:
6391004
Step-by-step explanation:
The question is basically saying that a number is more than 47,56,908 by 16,34,096.
So that number will be 4756908+1634096 =
6391004
Therefore that number is 6391004
A circule has a diameter of 28 ft what is the circumference
Answer:
Circumference of a 28 Foot Diameter Circle ; 87.965, feet ; 1,055.6, inches ; 87′ 11.6″, feet and inches ; 26.812, meters ; 2,681.2, centimeters .
Step-by-step explanation:
Will give 5 stars on your answer and a thank you.
Answer:
the variable term is (t)
the answer is 13.50t
Answer:
it will be 13.50t
Step-by-step explanation:
it says 13.50 for EACH Ticket so it is the last one
Hope it helps <333
Mr. Schultz is randomly distributing 15 rulers with centimeter markings and 10 rulers without centimeter markings to his class. What is the probability that the first ruler he hands out will have centimeter markings and the second one does not have the markings?
The probability that the first ruler he hands out will have centimeter markings and the second one does not have the markings is 9/40.
Probability of distributing the rulers
The probability of distributing the rulers is calculated as follows;
Total outcome = 15 rulers with centimeter markings + 10 rulers without centimeter markings
Total outcome = 25
The probability that the first ruler he hands out will have centimeter markings and the second one does not have the markings;
P = (R with M) and (R without M)
P = (15/25) x (9/24)
P = (3/5) x (3/8)
P = 9/40
Thus, the probability that the first ruler he hands out will have centimeter markings and the second one does not have the markings is 9/40.
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Combine these radicals.
-V5 -3v5
[tex]-\sqrt 5 -3\sqrt 5\\\\\\=(-1-3)\sqrt 5\\\\\\=-4\sqrt 5[/tex]
Answer:
b
Step-by-step explanation:
Many bird species populate a forest. Researchers
conducting a study need to estimate the number of each
species that live in the forest. in They divide the forest into
equal sections and then record the species of the first 25
birds they see in each section.
What is the population in this study?
O A. The
first 25 birds in each section of the forest
O B. The species with the greatest number
• C. All the birds in the forest
• D. The species that are native to the area that contains the forest
Please help first to answer and is correct I will give brainlist please hurry!!!
The population in the study are the species that are all the birds in the forest.
What is population in research?The term population in reasearch refers to the entire participants in a study. Sometimes a fraction of these partcipants are selected in such a way that the entire population is depicted. This is called sampling.
In this case, the population in the study are the species that are all the birds in the forest.
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Answer:
O A. The first 25 birds in each section of the forest
Step-by-step explanation:
Test approved
Which two sets of angles are corresponding angles?
∠a and ∠d; ∠b and ∠c
∠a and ∠e; ∠b and ∠d
∠a and ∠c; ∠b and ∠d
∠a and ∠e; ∠b and ∠c
Answer:
∠a and ∠d; ∠b and ∠c
Step-by-step explanation:
The two triangles as similar triangles and the scale factor is 2 : 1
The sides measuring 6 and 3 are corresponding sides
The sides measeuring 8 and 4 are ocrreposnding sides
⇒ ∠a and ∠d are corresponding angles
The sides measuring 8 and 4 are corresponding sides
The sides measeuring 4 and 2 are ocrreposnding sides
⇒ ∠b and ∠c are corresponding angles
An above ground pool is shaped like a cylinder. It is 5.5 feet tall and has a diameter of 20 feet. If the pool is filled to 5 feet, what is the volume of the water? If the pool is filled to the top, what is the volume of the water?
First, we must know the formula for solving the volume of a cylinder, which is [tex]V = \pi r^2 h[/tex]. Since the water is only being filled to 5 feet, we do not care about the 0.5 feet of the height.
Using the formula, we need to plug-in the numbers for the radius (20 divided by 2 is 10) and height. Doing this, the equation should now look like this: [tex]V = 3.14 * 10^2 * 5[/tex]. When solving, the volume of the water is 1570 feet cubed.
Answer:
1570.796 feet cubed
Step-by-step explanation:
First you find the surface area of the base of the cylinder which should look like this:
(10^2)(π)
Next you multiply that by the height (5 feet) because 3d shapes are bases stacked on each other which should look like this:
314.1592654(5)
After that arithmetic you will get 1570.796 or 1570.8 rounded as your answer!
Consider two events, P and Q. The probability of event P occurring is 16. The probability of event Q occurring is 23. Which statement is true?
The event "P and Q" is a compound event in the probability, and the true statement about the probability is P(P and Q) = 1/9
How to determine the true statement?The probabilities are given as:
P(P) = 1/6
P(Q) = 2/3
The probability of the event P and Q is calculated using:
P(P and Q) = P(P) * P(Q)
This gives
P(P and Q) = 1/6 * 2/3
Evaluate the product
P(P and Q) = 1/9
Hence, the true statement about the probability is P(P and Q) = 1/9
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Use a net to find the surface area of the cylinder. Use 3.14 for pi.
The surface area of the cylinder is about cm^2
(Round to the nearest tenth as needed.)
Which expression is equivalent to log18 – log(p 2)?
The expression which is equivalent to the provided logarithmic equation log18 – log(p +2) is log[18/(p+2)].
What is the equivalent expression?Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.
The given logarithmic expression is,
[tex]\log18 -\log(p+ 2)[/tex]
Let the expression which is equivalent to above expression is f(p). Thus,
[tex]f(p)=\log18 -\log(p+ 2)[/tex]
With the help of Quotient Rule of logarithmic, the above expression can be written as,
[tex]f(p)=\log18 -\log(p+ 2)\\f(p)=\log\left(\dfrac{18}{p+2}\right)[/tex]
Thus, the expression which is equivalent to the provided logarithmic equation log18 – log(p +2) is log[18/(p+2)].
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Twelve hungry teenagers can devour a very large pizza in $20$ minutes. How many teenagers would it take to finish a very large pizza in $15$ minutes
Answer:
9 teenagers
Step-by-step explanation:
12/20 = x/15
180/20 = x
9 = x
-----------------------
9 teenagers would take to finish the large pizza in 15 mins
Find the length of the third side. If necessary, round to the nearest tenth.
23
30
Answer:
37.80
Step-by-step explanation:
a^2 + b^2 = c^2
=> 23^2 + 30^2 = x^2
=> 1429 = x^2
=> 37.80
Hope this heps :)
I need help pleaseeeee
[tex] \qquad\qquad\huge\underline{{\sf Answer}}{} [/tex]
Surface area of a cube is :
[tex]\qquad \tt \dashrightarrow \:6 {a}^{2} [/tex]
where, a represents side length of each edge.
[tex]\qquad \tt \dashrightarrow \:a = 6(6.4) {}^{2} [/tex]
[tex]\qquad \tt \dashrightarrow \:a = 6(40.96)[/tex]
[tex]\qquad \tt \dashrightarrow \:a = 245.76 \: \: unit {}^{2} [/tex]
it can be taken as an approximate of :
[tex]\qquad \tt \dashrightarrow \:a \approx245.8 \: \: unit {}^{2} [/tex]
Answer:
The answer is D. 245.8 unit^2