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.

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

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}

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

From the slopes it is confirmed that PQ || RS OR|| SP and therefore it 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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Answer:

the answer is c. the row is chili, the column is no cheese

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.

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]

it 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 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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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]

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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[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]

Answer:

7

Step-by-step explanation:

The length of AB is the distance between A and B which is B-A -> 13-6= 7

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]

Answer:

hi

Step-by-step explanation:

no

Answer: -307.36 I think

Step-by-step explanation:

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

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,

Therefore, 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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A function assigns the values. The value of (p·p)(x) is x⁴ + 10x³ + 30x² + 25x.

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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One line will be formed which will be parallel to the slant edge option third is correct.

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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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

[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

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]

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

Answer:

87.5 miles

Step-by-step explanation:

Distance between points = 3 1/2 × 25 = 87.5 miles

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].

Each decreasing portion of the graph indicates the ball has been thrown upward and is traveling toward the ground.  

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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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

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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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:

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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