A cylindrical can has a height of 19 cm and a radius of 6 cm. The volume of the cylindrical can is decreasing at a rate of 563 cubic cm per second, with the height being held constant. What is the rate of change of the radius, in cm per second, when the radius is 6 cm?
Round your answer to the nearest hundredth.
Answers
The rate of change of radius at radius 6cm is 0.79 cm/sec.
The rate of change of a function is simply the derivative of the function with respect to the changing parameter in the function i.e. variable in the function.
So for calculating the rate of change of radius, we calculate the rate of volume change as volume is the function of radius.
As we know volume of the cylinder is given by V=πr²h
where r is the radius and h is the height of the cyclinder.
Given that rate of change of volume = 563 cm/sec
⇒ dV/dt =563 cm/sec
⇒ d(πr²h)/dt =563
taking πh outside the derivative as π and h is constant term
⇒ πh dr²/dt =563
⇒ πh (dr²/dr)(dr/dt)= 563 (applying chain rule dy/dx = (dy/du)(du/dx))
⇒ πh(2r)(dr/dt) =563
⇒dr/dt= 563/(2πhr)
given height of the cylinder h= 19cm
rate of change of radius at radius r =6cm= dr/dt= 563/(2πhr)= 563/(2*π*19*6)= 0.79 cm/sec
Therefore rate of change of radius at radius 6cm is 0.79 cm/sec.
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Related Questions
54-90.27-90.22-90.87-90
Answers
Answer: -307.36 I think
Step-by-step explanation:
The graph of y=x−2−−−−√ is is transformed to become y=x+3−−−−√−2. Which of the following statements best describes the effect this transformation has on the graph of y=x−−√
Answers
Answer:
The graph is translated 5 units left and 2 units down
Step-by-step explanation:
transformation =
initially the equation of graph [tex]y=\sqrt{x-2} = f(x)[/tex]
after transformation the equation becomes [tex]y = \sqrt{x+3} -2 = g(x)[/tex]
transformation done [tex]f(x) = \sqrt{x-2}[/tex] → [tex]g(x) = \sqrt{x+3} -2[/tex]
The horizontal shift of graphit depends on the value of h. The horizontal shift is described as:
g(x) = f(x + h) - The graph is shifted to the left h units.
g(x) = f(x - h) - The graph is shifted to the right h units.
if h=0, means that the graph is not shifted to the left or right
the vertical shift of graphThe vertical shift depends on the value of k. The vertical shift is described
as:
g(x) = f(x) +k - The graph is shifted up k units.
g(x) = f(x)- k - The graph is shifted down k units.
so here in the question the graph is shifted 5 units left and then 2 units down
you can see the graph of initial equation and transformed equation below.
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Write an expression that can be used to produce vector b from vector a, and explain how you determined that expression.
Answers
Answer:
Expression that can be used to produce vector b from vector a
= T× magnitude of vector a × vector 'a'
Step-by-step explanation:
Given question is based on the concept of vectors
Vectors:- Vectors is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point. Various operations can be applied to vectors such as addition, subtraction, and multiplication
To produce an another vector form a given vector we increase its magnitude only not its direction as we have to produce another vector 'b' with increased magnitude from a given vector 'a'.
its clear from the question that only the magnitude of vector a is increased to produce another vector b
hence we multiply any constant ('T') with the magnitude of vector a to increase its magnitude.
and finally multiply the increased magnitude with the vector 'a' itself to get the answer.
so, the final expression that can be used to produce vector b from vector a is = T× magnitude of vector a × vector 'a'.
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What does each decreasing portion of the graph represent? bouncing a ball
Answers
Each decreasing portion of the graph indicates the ball has been thrown upward and is traveling toward the ground.
What is a graph?A graph can be defined as a type of chart that is used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate i.e x-axis and y-axis.
By critically observing the graph attached in the image below, we can infer and logically deduce that each decreasing portion of the graph indicates the ball has been thrown upward and is traveling toward the ground.
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A snack bar offers chili and/or cheese on its hot dogs for an additional fee.
The owner kept track of the hot dog orders over the course of a week. His
data are shown in a relative frequency table.
Answers
Answer:
the answer is c. the row is chili, the column is no cheese
Maximiza a: z=5x+2y
Sujeta a: x+2y≤12
x+y≥4
x,y ≥0
Answers
Answer:
hi
Step-by-step explanation:
no
Which degenerate conic is formed when a double cone is sliced through the a pex by a plane parallel to the slant edge of the cone?
Circle
Parabola
One line
Two lines
Answers
One line will be formed which will be parallel to the slant edge option third is correct.
What is a conic section?It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (circle is a special type of ellipse).
We have a statement:
Which degenerate conic is formed when a double cone is cut through the top by a plane parallel to the slant edge of the cone?
As we can see in the attached picture if the double cone is cut through the top by a plane parallel to the slant edge of the cone one line will be formed which will be parallel to the slant edge.
Thus, one line will be formed which will be parallel to the slant edge option third is correct.
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Need number 2 please!!
Answers
Answer:
A
Step-by-step explanation:
note that i = [tex]\sqrt{-1}[/tex]
given
- 1 + 2i[tex]\sqrt{3}[/tex]
= - 1 + [tex]\sqrt{2^2(-1)3}[/tex]
= - 1 + [tex]\sqrt{-12}[/tex]
Use the point–slope formula to write an equation of the line that passes through(-5, -16 )and has a slope of m=3. Write the answer in slope–intercept form (if possible).
Answers
Answer:
Slope-intercept form: y = 3x - 1
Step-by-step explanation:
We are given that a line passes through the point (-5, -16) and has a slope of 3
We want to write the equation in point-slope form, and simplify it to slope-intercept form (if it is possible to do so).
First, point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point
We have both the slope and a point, but let's label the values of everything to avoid confusion + mistakes:
m = 3
[tex]x_1=-5\\y_1=-16[/tex]
Now substitute into the formula (remember: we have NEGATIVE numbers, and the formula uses SUBTRACTION):
[tex]y--16=3(x--5)[/tex]
The equation can be simplified
[tex]y+16=3(x+5)[/tex]
We can also write this in slope-intercept form
Start by distributing 3 to both x and 5 (multiply both x and 5 by 3)
[tex]y+16=3x + 15[/tex]
Subtract 16 from both sides
y = 3x - 1
a) Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable
Answers
Answer:
175
Step-by-step explanation:
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
find the value of x
d:6
Answers
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \: 5x = 3x + 12[/tex]
[ by vertical opposite angle pair ]
[tex]\qquad \sf \dashrightarrow \: 5x - 3x = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 12[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 12 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 6[/tex]
Therefore, the correct choice is D. 6
Step-by-Step Solution:
We know, (5x)° and (3x + 12)° are Vertically Opposite Angles and Vertically Opposite Angles are Equal.
Therefore,
5x = 3x + 12
5x - 3x = 12
2x = 12
x = 12/2
=> x = 6
Therefore, x = 6
Find the interval in which the function f(x) = |x + 4| is increasing.
Answers
[tex]f { }^{ - } (x) = \frac{2(x + 4)}{2 |x + 4| {}^{} } = \frac{x + 4}{ |x + 4| } [/tex]
[tex] |x + 4| \: is \: always \: positive[/tex]
[tex]solve \: x + 4 > 0[/tex]
[tex]x > - 4[/tex]
[tex]f(x) \: is \: incresing \: from \\[/tex]
]-4,∞[Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3
Answers
Answer:
[tex](x,y) = (5,-6)[/tex]
Step-by-step explanation:
[tex]\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\[/tex]
[tex]~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)[/tex]
[tex]\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\[/tex]
[tex]\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5[/tex]
[tex]y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6[/tex]
[tex]\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)[/tex]
the polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity at x=-2.
find a possible formula for P(x)
P(x)=
Answers
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
Given the roots of the polynomial, therefore, the following details can be written as,
The polynomial has a root of multiplicity 2 at x=2, (x-2)²The polynomial has a root of multiplicity 2 at x=0, (x-0)²The polynomial has a root of multiplicity 1 at x=-2, (x+2)¹Therefore, the polynomial will become,
P(x) = (x-2)²(x-0)²(x+2)¹
= (x²+4-4x) (x)² (x+2)
= (x²+4-4x) (x³+2x²)
= x⁵ + 2x⁴ + 4x³ + 8x² - 4x⁴ -8x³
= x⁵ - 2x⁴ - 4x³ + 8x²
Hence, the possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².
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Bob has saved $535 each month for the last 3 years to make a down payment on a house. The account earned an interest rate of .34 percent per month. How much money is in Bob's account?
Answers
Answer:
The account has $18,795.02.
Step-by-step explanation:
The account has $18,795.02.
3 years * $535 = $1,605
$1,605 * .0034 = $5.481
$5.481 * 36 (months) = $197.146
$18,795.02 = $1,605 + $197.146
only 2/3 of the school districts kindergarten teachers are women. if 59 are men, how many kindergarten teachers in all are employed by the school district
Answers
Answer:
177
Step-by-step explanation:
2/3 are women.
that means the remainder, 1/3, are men.
59 = 1/3 of all kindergarten teachers (3/3 = 1 representing the "whole").
so,
59×3 = 177
is the number of all kindergarten teachers employed by the school district.
What linear function can be represented by the set of ordered pairs?
{(−1,−10),(3,2),(5,8),(7,14)}
Enter your answer in the box.
Answers
just find the slope then use two point and point slope form to solve for slope intercept form
12x² + 9x² =
A. 21x²²
B. 21x
C. 22x²
D. 22xA
Answers
Answer:
21x²
Step-by-step explanation:
hopefully A is a typo
Answer: A (if it's just a typo) or [tex]21x^{2}[/tex]
Step-by-step explanation:
Since it's the same variable and same exponent, you just need to add the whole numbers and put the same variable and exponent.
12 + 9 = 21
[tex]21x^{2}[/tex]
Given a_4=135\;and\;a_6=1215a
4
=135anda
6
=1215, find the explicit rule for the geometric sequence, given that the common ratio is positive.
Answers
Answer:
Step-by-step explanation:
let a be first term and r be c.r.
a_{n}=ar^{n-1}
a_{4}=ar^{4-1}=ar^3=135
a_{6}=ar^{6-1}=ar^5=1215a_{4}=1215 \times 135
divide
r^2=1215
r=√1215=35
a_{n}=35 a_{n-1}
P(-4, 6), Q(2, 5), R(3, -1), S(-3, 0)
Use slope to determine whether the following is a parallelogram. Explain why or why not.
Find the slope of PQ
Find the slope of QR
Find the slope of RS
Find the slope of SP
Use this information to determine if the quadrilateral a parallelogram.
Answers
From the slopes it is confirmed that PQ || RS OR|| SP and therefore it is a parallelogram .
What is a Parallelogram ?A parallelogram is a quadrilateral in which the opposite sides are parallel.
The coordinates of a quadrilateral is given
To prove that it is a parallelogram
PQ || RS
OR|| SP
The slope of a straight line is given by
[tex]\rm m = \dfrac{y_2 -y_1}{x_2- x_1}[/tex]
For PQ
m = (-1/6) = -1/6
For QR
m = -6/1 = -6
For RS
m = 1/(-6) = -1/6
For SP
m = -6
From the slopes it is confirmed that
PQ || RS
OR|| SP
and therefore it is a parallelogram
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considering the inequality -5x-4y<12 , the shaded area of its graph is described by
Answers
The shaded area for the inequality y > -3-(5/4)x is given below.
The inequality is the relation between two expressions showing the relationships such as greater than, lower than, greater than equals to, and lower than equals to.
The given inequality is -5x-4y<12
solving this inequality for y
-5x-4y<12
⇒ -4y<12+5x
⇒y > (12+5x)/(-4)
⇒y > -3-(5/4)x
the line y= -3-(5/4)x has y intersection at (0,-3) and x intersection at (-12/5,0).
The inequality y > -3-(5/4)x show that this will be above the straight line y = -3-(5/4)x as if we put (0,0) in the inequality, the inequality will be 0>-3 which is true that shows that the region contains (0,0).
Therefore the shaded area for the inequality y > -3-(5/4)x is given below.
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The scale on a map says 1 inch = 25 miles. If two towns are 3 1/2
apart on the map, what actual distance separates them?
Answers
Answer:
87.5 miles
Step-by-step explanation:
Distance between points = 3 1/2 × 25 = 87.5 miles
Make sure you click the image for full picture
Answers
Answer:
See below.
Step-by-step explanation:
19.
The spinner has 12 equal-sized sections.
1/3 of 12 = 4
A number that appears in exactly 4 sections has a probability of 1/3. The number 3 appears exactly 3 times.
A number that appears more than 4 times has a probability greater than 1/3. The number 0 appears exactly 5 times.
A number that appears fewer that 4 times has a probability of less than 1/3.
Both 1 and 2 appear fewer than 4 times.
Answer:
Probability greater than 1/3: 0
Probability equal to 1/3: 3
Probability less that 1/3: 1, 2
20.
The amount of concentrate is 12 gallons.
The total amount of drink is 40 gallons.
The fraction of the concentrate out of the total is 12/40.
12/40 = 0.3
0.3 of each gallon is concentrate.
Color the bottom up to 0.30
Graph A: A horizontal line goes from (1, 0.5) to (2, 0.5). Another horizontal line goes form (2, 0.2) to (7, (0, 2). Graph B: A curve starts at (0, 0), curves up to (1, 1), and then curves down to (2, 0).
Which graph represents a density curve, and why?
graph A only, because the curve is above the horizontal axis, and the area under the curve from 2 to 7 is 1
graph B only, because the curve is above the horizontal axis, and the area under the curve is equal to 1.57
both graph A and graph B, because both curves are above the horizontal axis, and both areas are positive
neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Pictures posted below
Answers
Answer: neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Step-by-step explanation:
Areas under the graphs:
Graph A
[tex](1)(0.5)+(7-2)(0.2)=1.5\\\\[/tex]
Graph B
[tex]\frac{\pi}{2}(1^{2})=\frac{\pi}{2}[/tex]
As neither of these graphs have an area of 1, neither of them are density curves.
The statement - "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
A few fundamental principles apply to density curves:
A density curve's area beneath it represents probability.A density curve's area under it equals one.Base x height in a uniform density curve equals one.The likelihood that x = a will never occur.The likelihood that x < a is the same as that of x ≤ a.Neither curve of Graph A nor of Graph B has the area under the curve summed up as 1, though the curve is above the horizontal axis.
Hence, because neither graph has an area of 1, even if both curves are above the horizontal axis, the statement "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
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A 450-pound circus tiger eats 15 pounds of meat per day. How many pounds of meat would you expect a 360-pound tiger to eat per day? A 450 - pound circus tiger eats 15 pounds of meat per day . How many pounds of meat would you expect a 360 - pound tiger to eat per day ?
Answers
This kind of question is purely based upon proportionality. We are going to be using the cross product method to assess it.
First-hand, it can always help to write down the information that you do have, and the one that is missing.
Here;
450-pound tiger — > 15 pounds of meat
360-pound tiger — > ?? pounds of meat
The calculation you’ll want to use is the following:
360 x 15 / 450
The answer is 12 pounds.
Therefore, you would expect a 360-pound tiger to eat 12 pounds of meat per day.
I hope this helps! Have a nice day :)
Find the area of the shaded portion of the
figure. All angles are right angles.
Dimensions are in inches.
3
8
5
Answers
Answer:
22 [in.²]
Step-by-step explanation:
1. the required area can be calculated as
A=A1-A2, where A1- area of big quadrilateral, A2-area of the small quadrilateral;
2. A=5*8-3*6=40-18=22 [in²].
Please help me solve this
Answers
A function assigns the values. The value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given p(x)= x²+5x, therefore, the value of (p·p)(x) can be written as,
(p·p)(x) = p(p(x))
= (x²+5x)²+5(x²+5x)
= x⁴ + 25x² + 10x³ + 5x² + 25x
= x⁴ + 10x³ + 30x² + 25x
Hence, the value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.
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If the line segment AB is on a number line, and point A is at 6 and Point B is at 13, then the length of AB is ____.
Answers
Answer:
7
Step-by-step explanation:
The length of AB is the distance between A and B which is B-A -> 13-6= 7
f(x)=1/x at x=1 find slope of tangent
Answers
Answer:
f'(1)=-1
Step-by-step explanation:
You can just find the derivative using the power rule for d/dx (x^-1)=-1x^-2=-1/x^2 then find f'(1)=-1.
I used the limit definition of the derivative to find the slope in the picture attached
The volume of the above solid is
Answers
V=pi•radius•^2•height
V=pi•36•5
V=180 pi
