Find the volume of the cylinder shown using the formula in the box below. Round your answer to the nearest tenth. Show your work

Let [tex]A(t)[/tex] = amount of salt (in pounds) in the tank at time [tex]t[/tex] (in minutes). Then [tex]A(0) = 11[/tex].

Salt flows in at a rate

[tex]\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}[/tex]

and flows out at a rate

[tex]\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}[/tex]

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

[tex]\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}[/tex]

which I'll solve with the integrating factor method.

[tex]\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95[/tex]

[tex]-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}[/tex]

[tex]\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}[/tex]

Integrate both sides. By the fundamental theorem of calculus,

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}} [/tex]

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right) [/tex]

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}[/tex]

[tex]\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}[/tex]

[tex]\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}[/tex]

After 1 hour = 60 minutes, the tank will contain

[tex]A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131[/tex]

pounds of salt.

Answer:

22

I remember this question in school

Answer: third store

Step-by-step explanation:

1

First store: 95

Second store: 0.8*115=92

Third store: 0.9*105=94.5

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

By using distance formula :

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(4 - ( - 1)) {}^{2} + (4 - ( - 1)) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{(4 + 1) {}^{2} + (4 + 1) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{2(5) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: 5 \sqrt{2 }\: \: units[/tex]

[tex] \rm{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]

Proof:

[tex] \rm{Let \: X'OX \: and \: YOY' \: be \: the \: z-axis \: and \: y-axis \: respectively. Then, O \: is \: the \: origin.}[/tex]

[tex] \rm{Let \: A(x_1,y_1) \: and \: B(x_2,y_2) \: be \: the \: given \: points.}[/tex]

[tex] \rm{Draw \: AL \perp \: OX, BM \perp \: OX \: and \: AN \perp BM }[/tex]

Now,

[tex] \rm{OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2}[/tex]

[tex]\rm\therefore{AN=LM=(OM-OL)=(x_2-x_1)}[/tex]

[tex] \: \: \: \: \rm{BN=(BM-NM)=(BM-AL)=(y_2-y_1)}[/tex]

[tex] \rm{In \: right \: angled \: \triangle ANB, by \: Pythagorean \: theorem,}[/tex]

We have,

[tex] \: \: \: \: \rm{AB^2=AN^2+BN^2}[/tex]

[tex] \rm{or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex] \rm\therefore AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]

The Given question,

Find the distance of AG if A (4,4) and G (-1,-1).

Solution,

The given points are A(4,4) and G(-1,-1).

Then,

[tex] \rm{(x_1=4,y_1=4) and (x_2=-1,y_2=-1)}[/tex]

We know that,

The distance formula,

[tex] \rm{AG= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]

[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 1 - 4)}^{2} + {( - 1 - 4)}^{2} } [/tex]

[tex] \: \: \: \: \: \: \: \: = \sqrt{ {( - 5)}^{2} + {( - 5)}^{2} } [/tex]

[tex] \: \: \: \: \: \: \: \: = \sqrt{25 + 25} [/tex]

[tex] \: \: \: \: \: \: \: \: = \sqrt{50} [/tex]

[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(25)} [/tex]

[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)(5)(5)} [/tex]

[tex] \: \: \: \: \: \: \: \: = \sqrt{(2)( {5}^{2}) } [/tex]

[tex] \rm \: \: \: \: \: \: \: \: = 5 \sqrt{2} \: units[/tex]

Answered by:

[tex]\frak{\red{moonlight123429}}[/tex]

Answer:3 - x/4

Step-by-step explanation: quotient of x and 4 = x/4. 3 minus x/4 = 3 - x/4.

The expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

We have a sentence - "3 minus the quotient of x and 4".

We have to determine the expression that represents the sentence.

The expression representing the above statement is -

x - y = π.

According to the question, we have -

3 minus the quotient of x and 4.

Using the Division Algorithm -

x = 4q + r

Substituting r = 0 by introducing decimals in the quotient, we get -

q = [tex]$\frac{x}{4}[/tex]

Therefore -

[tex]$3 -\frac{x}{4}[/tex]

Hence, the expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

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A statement which does not describe a characteristic of the line of best fit for a scatter plot is that: A. the line of best fit should be the average of all the data points.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

The statements which describe a characteristic of the line of best fit for a scatter plot include the following:

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The mean of the set is : 16

The Slandered deviation of set : 5.8689389538863

Moderation is the quality of falling at or close to a medium point, whether it is in terms of location, period of time, quantity, or rate. 2 is the arithmetic mean. 3 denotes a plural noun: a tool for achieving one's goals. Attempt to locate it using all available techniques.

The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.

An indicator of how much a group of numbers vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, but when it is large, the values tend to deviate from that mean more.

Average x = 16

Count n = 9

Sum     Sum =144

Average = Sum / Count

= 144 / 9

= 16

Standard Deviation, σ: 5.8689389538863

Count, N = 9

Sum, Σx: = 144

Mean, μ:  = 16

Variance, σ²: = 34.444444444444

Calculating slandered devotion:

[tex]\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}[/tex]

[tex]\sigma^{2}=\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}[/tex]

[tex]=\frac{(16-16)^{2}+\ldots+(24-16)^{2}}{9}[/tex]

= 310/9

=  34.444444444444

σ =  √34.444444444444

σ =   5.8689389538863

The mean of the set is : 16

The Standard deviation of set : 5.8689389538863

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Answer:

3.75

Step-by-step explanation:

3/4 times 5 =3 3/4

3%

Answer:

Selling price with VAT {15%} = Rs 41400

S.P +15% of S.P =Rs 41400

S.P(1+15%)=Rs 41400

S.P=Rs 41400/1.15

Selling price without VAT =Rs 36000

Again

Discount = 10%

M.P =S.P+ Discount % of M.P

M.P-Discount% of M.P= S.P

M.P(1-Discount%)=Rs 36000

M.P(1-10%)=Rs 36000

M.P=Rs 36000/0.9

Marked Price = Rs 40,000

again

Discount =Discount % of M.P

=10% of 40000

=Rs 4,000

Again

Profit=20%

For 20% profit

Cost price = (S.P*100)/(100+profit%)

=(36000*100)/(100+20)

= Rs 30000

For 24% profit

selling price = (100+profit%)*C.P/100

=(100+24)*30000/100

=Rs 37200

Again

Discount = 40000–37200 = Rs2800

Discount % = discount/M.P*100%

=2,800/40,000* 100 = 7%

Finally

Discount percent to be reduced =10%–7%= 3%

Answer:

5040 ways

Step-by-step explanation:

7! = 5040

7 choices on day 1

6 choices on day 2

5 choices on day 3

4 choices  on day 4

3

2

1                                 7 x 6 x 5 x 4 x 3 x 2 x1 = 5040

The length of the altitude AD is 12 units.

The height of the triangle can be found as follows:

We have to find an angle using cosine law before  we can find the height.

Therefore,

20² = 13² + 21² - 2 × 21 × 13 cos B

400 = 169 + 441  - 546 cos B

400 - 610 = - 546 cos B

-210 = - 546 cos B

cos B = -210 / -546

cos B = 0.38461538461

B = cos⁻¹ 0.38461538461

B = 67.3810899783

B = 67.38°

Hence,

sin 67.38° = opposite / hypotenuse

sin 67.38° = AD / 13

cross multiply

AD = 13 sin 67.38°

AD = 11.9999882145

AD = 12 units

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Using the combination formula, it is found that he can make 4 different stacks.

The order in which the balls are selected is not important, as stated in the problem. hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, he has four flavors, and will choose three of them for the stacks, hence the number of different stacks is given as follows:

[tex]C_{4,3} = \frac{4!}{3!1!} = 4[/tex]

He can make 4 different stacks.

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Answer:

now we know that

book is 120page

__6785

The extremum of f(x,y) is subject to the given constraint, There is a global minimum (x,y,z.) (4,2,-8).

An instance of a constraint is the fact that there are only so many hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. one which restricts, limits, or regulates; a test.

A constraint is something that limits or controls what you may do. Their decision to abandon the ride turned into made due to economic constraints. Water shortages in the location could be the main constraint on development. Synonyms: limit, drawback, scale back, rein more Synonyms of constraint.

predicament or restriction. repression of herbal emotions and impulses: to exercise constraint. unnatural restraint in manner, communique, and many others.; embarrassment. Something that constrains.

By lagranier multi plur

of = hog

(2x, is, 22>= 25-47

8x=42

10x + 2 = 42

2

28

2x=4, 4= 2

=2

722 (4)

(4.9,2) = (4.2-8)

(4,2-8)= 84

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The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

From the function [tex]B(t) = 182(1.065)^t[/tex]:

b = 1.065

Growth rate = 1.065 - 1 = 0.065 = 6.5%

The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.

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Step-by-step explanation:

proof from r.h.s to l.h.s

(cot(a)-tan(a))(cot(a)+tan(a))

cot(a)=cos(a)/sin(a)

tan(a)=sin(a)/cos(a)

(cot(a)-tan(a))=cos(a)/sin(a) - sin(a)/cos(a)

=cos²(a)-sin²(a)/sin(a)cos(a)

from trigonometry identity cos²(a)-sin²(a)=cos2(a)

so we have cos2(a)/sin(a)cos(a)

(cot(a)+tan(a))=cos(a)/sin(a) +sin(a)/cos(a)

=cos²(a)+sin²(a)/cos(a)sin(a)

from trigonometry identity cos²(a)+sin²(a)=so we have 1/cos(a)sin(a)

(cot(a)-tan(a)) ÷(cot(a)+tan(a))

=cos2(a)/cos(a)sin(a) ÷ 1/cos(a)sin(a)

=cos2(a)/cos(a)sin(a) * cos(a)sin(a)

=cos2(a)

proved

Answer:

25/81.

Step-by-step explanation:

(27/8)^-4/3

= 8^4/3 / 27^4/3

= (∛8)^4 / (∛27)^4

= 16 / 81

(64/125)^-2/3

= (125)^2/3 / (64)^2/3

= (∛125)^2 / (∛64)^2

=  5^2 / 4^2

= 25/16

So the answer is

16/81 * 25/16

= 25/81.

Answer:

25 / 81(25 by 81) is your answer.

Answer:

  5x^4 -37x^3 -6x^2 +41x -6

Step-by-step explanation:

We simplify this expression by removing parentheses and combining like terms. Parentheses are removed using the distributive property.

The product of the final pair of polynomials in parentheses is ...

  (-4x^3 +5x -1)(2x -7) = (-4x^3 +5x -1)(2x) +(-4x^3 +5x -1)(-7)

  = -8x^4 +10x^2 -2x +28x^3 -35x +7

  = -8x^4 +28x^3 +10x^2 -37x +7

  = (5x^4 -9x^3 +7x -1) + (-8x^4 +4x^2 -3x +2) - (-8x^4 +28x^3 +10x^2 -37x +7)

  = (5 -8 -(-8))x^4 +(-9 -28)x^3 +(4 -10)x^2 +(7 -3 -(-37))x +(-1 +2 -7)

  = 5x^4 -37x^3 -6x^2 +41x -6

Answer:

Robert bought 13 colored pencils and 2 pencils

Step-by-step explanation:

13 x 0.60 = 7.8
2 x 0.45 = 0.9

7.8 + 0.9 = 8.70

13 colored pencils are $7.80

2 pencils are $0.9

15 total is $8.70

Answer: negative slope

constant slope

decreasing function

B-C-E

Step-by-step explanation:negative slope

constant slope

decreasing function

Answer: False

Step-by-step explanation:

The base is more than 1, so the function is increasing.

The multiplication property of equality has been used in the second step when both sides of the equation have been multiplied by 5/3.

State the Multiplication Property of Equality:

The Multiplication Property of Equality states that multiplying both sides of the equation with the same number, expression, or variable, the equation remains unchanged, i.e. equality is maintained.

Use of Multiplication Property of Equality in the Second Step:

The given equation was,

3x/5 + 5 = 20

In the first step, subtraction property of equality is applied as follows,

3x/5 + 5 - 5 = 20 - 5

3x/5 = 15

Now, for isolating x on the left hand side, we must apply multiplication property of equality by multiplying both sides of the equation by 5/3.

We get,

3x/5 × 5/3 = 15 × 5/3

x = 25

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The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.

According to the statement

we have given that the

Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0)

And we have to find that the which terms are corrected from the given options when Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

So, For this purpose we know that the

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

And According to the given statement

when parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

Then the conditions A, C, E are applicable because on rotation these things are applicable.

So, The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Figure 2 was constructed using figure 1.

On a coordinate plane, 2 parallelograms are shown.

Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0).

Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

For the transformation to be defined as a rotation, which statements must be true? Select three options.

A. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).

B. The transformation is rigid.

C. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

D.Segment CP is parallel to segment CP'.

E. If figure 1 is rotated 180° about point C, it will be mapped onto itself.

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Answer:

B. 10/13

Step-by-step explanation:

There are 52 cards in a deck. Divide that by 4 and get 13, thats how many diamonds there are. There are 36 number cards. Since 9 of the cards in diamonds are numbers, we dont count those ones. 13-9 is 4, so we add that to our total to get 40. 40/52 is the same as 10/13.

Answer: 10/13

Step-by-step explanation:

There are 52 cards in a deck. Every 13 cards, 9 will be number cards so there are 36 number cards. There are 13 diamond cards. There are 9 diamond cards that are number cards. So the probability of the following is (36+13-9)/52 = 40/52 = 10/13

Answer:

90

Step-by-step explanation:

First, we should find the area of the trapezoid, and then subtract the area of the removed triangle in order to find the shaded area.

Area of the trapezoid

1) Area of the rectangle in the middle.

Base Length: 10

Height Length: 10

Area: 10 x 10 = 100

2. Area of the triangles on the side

Base Length: (14 - 10)/2 = 2

Height Length: 10

Area: 2 x 10 x 1/2 = 10

There are two triangles: 10 x 2 = 20

Area of the trapazoid: 100 + 20 = 120

Area of the triangle that's been removed

Base Length: 10

Height Length: 10 - 4 = 6

Area: 10 x 6 x 1/2 = 30

Shaded area

Area of the trapezoid - Area of the triangle

120 - 30 = 90

Area of the shaded region is 90.

Answer:

2, 0, 2, 3, 5

1, 2, 4, 0, 5

Step-by-step explanation:

(ax + b)(cx² + dx + e)

acx³ + adx² + aex + bcx² + bdx + be

2(2)x³ + 2(3)x² + 2(5)x + 0 + 0 + 0

4x³ + 6x² + 10x

a = 2

b = 0

c = 2

d = 3

e = 5

1(4)x³ + 1(0)x² + 1(10)x + 2(4)x² + 0 + 10

4x³ + 8x² + 10x + 10

a = 1

b = 2

c = 4

d = 0

e = 5

Answer:

[tex] \blue{b < 8}[/tex]

Answer 1 is correct

Step-by-step explanation:

[tex] \frac{3}{2} b + 5 < 17[/tex]

Take 5 to the right side.

[tex] \frac{3}{2} b < 17 - 5 [/tex]

[tex]\frac{3b}{2} < 12 [/tex]

Multiply both sides by 2.

[tex]3b <12 \times 2[/tex]

[tex]3b < 24[/tex]

Divide both sides by 3.

[tex]b < 8[/tex]

The total surface area of this shaded region is 1000 units²

An equation is an expression that shows the relationship between two or more numbers and variables.

The total surface area of a polygon is the sum of the individual areas of each surface.

Total area of the figure = 2(20 * 10) + 2(10 * 10) + 2(20 * 10) = 1000 units²

The total surface area of this shaded region is 1000 units²

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