The soot produced by a garbage incinerator spreads out in a circular pattern. The depth, H(r), in millimeters, of the soot deposited each month at a distance r kilometers from the incinerator is given by H(r)=0.116eâ2.3r.Write a definite integral (with independent variable r) giving the total volume of soot deposited within 5 kilometers of the incinerator each month.

Answer: First choice

Sq rt of 3 X sq rt of 2 = sq rt of 6 which is irrational

Sq rt of 12 and sq rt of 3 = sq rt of 36 which = 6 rational

Sq rt of 5 plus sq rt of 2 is irrational

Sq rat of 9 plus sq rt of 4 is 3+2=5 rational

Step-by-step explanation:

Answer:

slope of AB = 1-(-3)/0-(-3)

= (1+3)/3 = 4/3

Slope of CD = -1-(-5)/3-0

=(-1+5)/3 = 4/3

Both AB and CD are parallel because their slopes are equal.

Answer:

The answer is 19

Step-by-step explanation:

2 + 2 = 4

3 + 5 = 8

4  + 8 = 12

12 + 7 = 19

Answer:

68.2°

Step-by-step explanation:

AC is the longest side which means 90° is at B

SinA = BC/AC

sinA = 5/sqrt(29)

sinA = 0.9284766909

A = 68.19859051

A = 68.2°

To find the measure of angle A, we used the tangent function, which is the ratio of the side opposite the angle to the side adjacent to it. Using a calculator, the inverse tangent of the ratio BC/AB equals approximately 68.2 degrees.

In order to solve for angle A in a right triangle, we can use the concept of trigonometry. Specifically, we'll use the tangent (tan) function, which in a right triangle is the ratio of the side opposite the angle to the side adjacent to it. Since angle A is between sides AB and AC, the tangent of A would be defined as tan(A) = opposite side/adjacent side = BC/AB = 5/2.

After calculating the ratio, typically, we would use a calculator to find the arctan or inverse tangent of this ratio, which should give the angle A in degrees. In this case, the arctan(5/2) equals about 68.2 degrees when rounded to the nearest tenth.

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Answer: 18π units³ or 56.52 units³

Step-by-step explanation: Notice that the figure shown here is a cylinder. To find the volume of a cylinder, start with the formula for the volume of a cylinder which is shown below.

Volume = πr²h

Here, notice that our cylinder has a radius

of 3 units and a height of 2 units.

So we have (π)(3 units)²(2 units).

Start by simplifying the exponent.

(3 units)² is (3 units)(3 units) or 9 units².

So we have (π)(9 units²)(2 units).

Now, (9 units)²(2 units) is 18 units³.

So we have 18π units³.

So the volume of the cylinder shows here is 18π units³.

Remember that π is approximately equal to 22/7 or 3.14. So we can estimate the value of the volume by plugging in 3.14 for π.

So we have (18)(3.14) which is equal to 56.52.

So the value of the volume is approximately 56.52 units³.

Answer:

D. There are zeros between x = 1 and x = 2, x = 0 and x = –1.

Step-by-step explanation:

A zero point is inside an interval where value of y changes from positive to negative or viceversa. The curve is evaluated in the given points hereafter:

f(-3) = - 909, f(-2) = -192, f(-1) = -9,f(0) = 18, f(1) = 3, f(2) = -204, f(3) = -1017

There two zero, one between x = -1 and x = 0 and other between x = 1 and x = 2. Hence, the answer is D.

Answer:

Percentage of decrease in Sales = 11.04% or 11 %

Step-by-step explanation:

Decrease Percentage = [(Original Value - New Value) ÷ Original Value] × 100 

Percentage = [(145,000 - 129,000) ÷ 145,000] × 100

Percentage = [(16,000) ÷ 145,000] × 100

Percentage = (0.1104) × 100

Percentage of decrease in Sales = 11.04% or 11 %

The line y = 0 will be having an infinite number of x-intercepts thus a line can cross the x-axis infinite times.

A line section that can connect two places is referred to as a segment.

The line extends endlessly in both directions.

A line segment is just part of a big line that is straight and going unlimited in both directions.

If two lines intersect each other at a point then the number of intersections will be only one,

It is because the line away from the intersection goes away with the line.

But if two lines are on each other having an infinite number of intersections.

For example the intersection of line y = 0 with the x-axis.

Hence "The line y = 0 will be having an infinite number of x-intercepts thus a line can cross the x-axis infinite times".

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Answer:

13.18% or 0.1318

Step-by-step explanation:

please see the attached files for explanation

Answer: 5.2752

Well, whenever you are working with fractions with different denominators, you would multiply both the top and the bottom of the fraction with the smaller number as the denominator. (You could also divide the larger denominator number.) So let's see what number we can multiply by 5 to get 10. That would be 2. Then we would multiply the numerator by two as well. So what is 3 times 2? 6. Once you've done that, you get 6/10 or 0.6 in decimal form. The difference would be 0.3 or 3/10. :)

Answer:

y = 15x

11x + y = 286

where

y = number of miles driven by the truck driver

x = number of hours the truck driver drives

Solving this gives, x = 11 hours and y = 165 miles.

Step-by-step explanation:

Let the number of hours the truck driver drives be x.

Let the number of miles driven by the truck driver be y.

Since the truck driver drives at 15 miles per hour, the number of miles covered by the driver y, can be given from the speed equation.

Speed = (distance/time)

15 = (y/x)

y = 15x.

And the drivers are paid $11 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance.

Meaning that on a day that the truck driver drives y miles for x hours, the total pay, C, is given as

C = 11x + 1y = 11x + y

So, on this fateful day, the total amount paid to a truck driver was $286

So, C = $286

11x + y = 286.

So, the two equations for the scenarios are

y = 15x

11x + y = 286

Solving this gives, x = 11 hours and y = 165 miles.

Hope this Helps!!!

The system of a linear equation that could be used to determine the number of hours the driver worked and the number of miles the truck drove is : (11x + y = 286) and (y = 15x).

Given :

The following steps can be used in order to determine the system of linear equations:

Step 1 - Let the total number of miles be 'x' and the total number of hours be 'y'.

Step 2 - The linear equation that represents the total expenses for the driver, gas, and truck maintenance is given by:

11x + y = 286

Step 3 - The linear equation that represents the situation that the driver drove an average of 15 miles per hour is given by:

y = 15x

So, the system of a linear equation that could be used to determine the number of hours the driver worked and the number of miles the truck drove is : (11x + y = 286) and (y = 15x).

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Answer:

3.06 megawatts

Step-by-step explanation:

Firstly, we write the proportionality equation.

wind power varies directly as the square of the length r of one of the blades;

P ∝ r^2

Let’s introduce a constant of proportionality k; This means;

P = kr^2

Now let’s calculate the value of k when 1.5 megawatts and r is 35m

1.5 mw = 35^2 * k

k = 1.5/35^2 = 1.5/1225 = 0.001224489796 MW/m^2

Now we want to calculate the amount of megawatts to be produced by a turbine with 50m blades.

That would be;

P = 0.001224489796 * 50^2 = 3.06 megawatts

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that P varies directly with r², if we introduce a constant of proportionality, k, the expression becomes

P = kr²

If P = 1.5 when r = 35, then

1.5 = k × 35²

k = 1.5/35² = 1.5/1225

Therefore, the direct variation function is

P = 1.5r²/1225

When r = 50, then

P = 1.5 × 50²/1225

P = 3.06 megawatt

Answer:

y = 4x

Step-by-step explanation:

Given that y and x vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition that x = 2, y = 8

8 = 2k ( divide both sides by 2 )

4 = k, thus

y = 4x ← equation of variation

Correct Question:

John works as a tutor for $12 an hour and as a waiter for $8 an hour. This month, he worked a combined total of 86 hours at his two jobs.

Let be the number of hours John worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answer:

Total hours = 86

Let t is the hours he spent on tutoring

then (86-t) is hours spent on waiting

Let Y is the total amount in dollars which is required .

Now;

y = (tutoring hours x 12$) + (waiting hours x 8$)

Y = 12t + 8(86-t)

Answer:(4,-1.5)

Step-by-step explanation:

You’d be adding 5,-0.5 to the respective coordinates. Point F’ is located at -1,-1 so you’d be adding 5 to -1 for the x coordinate and -0.5 to -1 for the y coordinate.

Answer:

Answer: b. 20.8 ft-lb

Step-by-step explanation:

Answer:

Step-by-step explanation:

10^2 + b^2 = 26^2

100 + b^2 = 676

-100 -100

b^2 = 576

square root of b equals b

square root of 576 equals 24

The other leg equals 24

Answer:

24mm

Step-by-step explanation:

Using Pythagoreans Theorem, a^2+b^2=c^2

a^2+10^2=26^2

a^2+100=676

a^2=576

a= sqrt 576

a=24mm

Answer:

a) Q = 0 or 9

b) Q = 5

c) Q = 7

d) Q = 8

Step-by-step explanation:

We assume the postal money order to be of the United State. A smudged digit is calculated using the following algorithm.

1. Add first 10 digits of 11-digit number.

2. Divide the sum of the 10 numbers by 9.

3.The remainder is the smudged digit.

4.The smudged digit is appended to the end of the ID number or anywhere in the number.

It is calculated as:

[tex]x_{11} = (x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} + x_{8} + x_{9} + x_{10} )mod 9[/tex]

a) 493212Q0688

[tex]8 = (4 + 9 + 3 + 2 + 1 + 2 + Q + 0 + 6 + 8) mod 9\\8 = (Q + 35) mod 9\\8 = Q mod 9 + 35 mod 9\\8 = Q mod 9 + 8\\Q mod 9 = 8 - 8\\Q mod 9 = 0\\Q = 0 or 9[/tex]

Therefore, Q is either 0 or 9.

b) 850Q9103858

[tex]8 = (8 + 5 + 0 + Q + 9 + 1 + 0 + 3 + 8 + 5) mod 9\\8 = (Q + 39) mod 9\\8 = Q mod 9 + 39 mod 9\\8 = Q mod 9 + 3\\Q mod 9 = 8 - 3\\Q mod 9 = 5\\Q = 5[/tex]

Therefore, Q is 5 because from Q mod 9 = 5, we have Q = 5 mod 9.

c) 2Q941007734

[tex]4 = (2 + Q + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3) mod 9\\4 = (Q + 33) mod 9\\4 = Q mod 9 + 33 mod 9\\4 = Q mod 9 + 6\\Q mod 9 = 4 - 6\\Q mod 9 = -2\\Q = -2 mod 9\\Q = 7[/tex]

Therefore, Q is 7 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -2 + 9 = 7.

d) 66687Q03201

[tex]1 = (6 + 6 + 6 + 8 + 7 + Q + 0 + 3 + 2 + 0) mod 9\\1 = (Q + 38) mod 9\\1 = Q mod 9 + 38 mod 9\\1 = Q mod 9 + 2\\Q mod 9 = 1 - 2\\Q mod 9 = -1\\Q = -1 mod 9\\Q = 8[/tex]

Therefore, Q is 8 because we have to cancel out the negative sign by adding the modulo base (9) to the negative number: -1 + 9 = 8.

For the given postal money order scenarios, the smudged digit, Q, is determined as follows: Scenario a - either 0 or 9, Scenario b - 5, Scenario c - 5, and Scenario d - 3.

Let's analyze the given postal money order scenarios and determine the smudged digit, Q, using the provided algorithm:

Scenario a:

ID number: 493212Q0688

Sum of the first 10 digits: 4 + 9 + 3 + 2 + 1 + 2 + 0 + 6 + 8 + 8 = 43

43 divided by 9 equals 4 with a remainder of 7.

Therefore, the smudged digit, Q, is either 0 or 9.

Scenario b:

ID number: 850Q9103858

Sum of the first 10 digits: 8 + 5 + 0 + 9 + 1 + 0 + 3 + 8 + 5 + 8 = 47

47 divided by 9 equals 5 with a remainder of 2.

Therefore, the smudged digit, Q, is 5.

Scenario c:

ID number: 2Q941007734

Sum of the first 10 digits: 2 + 7 + 9 + 4 + 1 + 0 + 0 + 7 + 7 + 3 = 40

40 divided by 9 equals 4 with a remainder of 4.

To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -4 + 9 = 5.

Therefore, the smudged digit, Q, is 5.

Scenario d:

ID number: 66687Q03201

Sum of the first 10 digits: 6 + 6 + 6 + 8 + 7 + 0 + 3 + 2 + 0 + 1 = 33

33 divided by 9 equals 3 with a remainder of 6.

To cancel out the negative sign in the remainder, we add the modulo base (9) to the negative number: -6 + 9 = 3.

Therefore, the smudged digit, Q, is 3.

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Answer:

1. 23.55 in

2. 102.36 mm

Step-by-step explanation:

The circumference of a circle is calculated by the formula: [tex]C=\pi d=2\pi r[/tex] , where d is the diameter and r is the radius.

We can use this to answer both problems.

1. Since the diameter is 7.5 inches, then d = 7.5. Substitute this into the equation: [tex]C=\pi *7.5=3.14*7.5=23.55[/tex]. So, the circumference is 23.55 inches.

2. Here, the radius is 16.3 mm, so r = 16.3. Substitute this into the equation: [tex]C=2\pi r=2*3.14*16.3=102.364=102.36[/tex]. So, the circumference is 102.36 mm.

Hope this helps!

Answer:

1) 23.55 inches

2) 102.36 mm

Step-by-step explanation:

C = pi × d

1) C = 3.14 × 7.5

= 23.55

C = 2 × pi × r

2) C = 2 × 3.14 × 16.3

= 102.364 mm

Answer:

3:4

Step-by-step explanation:

Before we start to deal with the ratio, we need all lengths in the same units.

The width is 18 inches.

The height is 2 feet.

Let's convert the height to inches. Then we will have both dimensions in the same units, inches.

2 ft * (12 in.)/ft = 24 in.

Now we have:

width = 18 in.

height = 24 in.

ratio of width to height = 18 in. to 24 in. = 18/24 = 3/4 = 3:4

Answer:

D. 4821 years

Step-by-step explanation:

A = A0e-0.000124t

A/A0 = e^-0.000124t

0.55 = e^-0.000124t

ln(0.55) = ln(e^-0.000124t)

ln(0.55) = -0.000124t × lne

t = ln(0.55)/-0.000124

4821.266135

Height MT of the pyramid will be 8.9 cm

    Given in the question,

Since, diagonals of a rectangle bisect each other, point M will be the midpoint of the diagonal AC.

By applying Pythagoras theorem in right triangle ΔABC,

AC² = AB² + BC²

AC = [tex]\sqrt{AB^2+BC^2}[/tex]

AC = [tex]\sqrt{6^2+7^2}[/tex]

AC = [tex]\sqrt{85}[/tex]

Therefore, AM = [tex]\frac{\sqrt{85} }{2}[/tex]

AM = 4.61 cm

Apply Pythagoras theorem in right triangle ΔAMT,

AT² = AM² + TM²

TM = [tex]\sqrt{AT^2-AM^2}[/tex]

TM = [tex]\sqrt{(10)^2-(4.61)^2}[/tex]

     = [tex]\sqrt{78.7479}[/tex]

     = 8.874

     ≈ 8.9 cm

    Therefore, height MT of the pyramid will be 8.9 cm.

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Answer:

m = - 3

Step-by-step explanation:

- 19 + 7 = -12

- 12 ÷ 4 = -3

Answer:

[tex]\frac{21}{4}[/tex]

Step-by-step explanation:

So to start, you need to make 3 [tex]\frac{3}{4\\}[/tex] into an improper fraction, which will give you [tex]\frac{15}{4}[/tex]. Then to make it easier, instead of dividing it by [tex]\frac{5}{7}[/tex], multiply it by the reciprocal ( [tex]\frac{7}{5}[/tex] )

Your new expression should look like this:

    [tex]\frac{15}{4}[/tex] x [tex]\frac{7}{5}[/tex]

To make it even easier, you can simplify this expression even further. Looking at the numerators and denominators, we see that we have a 15 on top and a 5 on the bottom. Cross out the 5 and put a 1 in its place since 5 goes into 5 one time! Now we have to do it to the 15... Cross out the 15 and put a 3 since 5 goes into 15 three times!

Your simplified expression should look like this:

    [tex]\frac{3}{4}[/tex] x [tex]\frac{7}{1}[/tex]

Now, just multiply the numerators and the denominators to get your final answer of

    [tex]\frac{21}{4}[/tex]

Since you cannot simplify this anymore, that is your answer!!!

Answer:

3/28

Step-by-step explanation:

Answer:

If it is asking for the order of the letters, it would be: Δ J H E

Explanation:

You have to put the letters in the same order that they were on the first triangle.

Hope this helps!!  :)

Answer:

There will be 50 bacteria remaining after 28 minutes.

Step-by-step explanation:

The exponential decay equation is

[tex]N=N_0e^{-rt}[/tex]

N= Number of bacteria after t minutes.

[tex]N_0[/tex] = Initial number of bacteria when t=0.

r= Rate of decay per minute

t= time is in minute.

The sample begins with 500 bacteria and after 11 minutes there are 200 bacteria.

N=200

[tex]N_0[/tex] = 500

t=11 minutes

r=?

[tex]N=N_0e^{-rt}[/tex]

[tex]\therefore 200=500e^{-11r}[/tex]

[tex]\Rightarrow e^{-11r}=\frac{200}{500}[/tex]

Taking ln both sides

[tex]\Rightarrow ln| e^{-11r}|=ln|\frac{2}{5}|[/tex]

[tex]\Rightarrow {-11r}=ln|\frac{2}{5}|[/tex]

[tex]\Rightarrow r}=\frac{ln|\frac{2}{5}|}{-11}[/tex]

To find the time when there will be 50 bacteria remaining, we plug N=50, [tex]N_0[/tex]= 500 and  [tex]r}=\frac{ln|\frac{2}{5}|}{-11}[/tex] in exponential decay equation.

[tex]50=500e^{-\frac{ln|\frac25|}{-11}.t}[/tex]

[tex]\Rightarrow \frac{50}{500}=e^{\frac{ln|\frac25|}{11}.t}[/tex]

Taking ln both sides

[tex]\Rightarrow ln|\frac{50}{500}|=ln|e^{\frac{ln|\frac25|}{11}.t}|[/tex]

[tex]\Rightarrow ln|\frac{1}{10}|={\frac{ln|\frac25|}{11}.t}[/tex]

[tex]\Rightarrow t= \frac{ln|\frac{1}{10}|}{\frac{ln|\frac25|}{11}.}[/tex]

[tex]\Rightarrow t= \frac{11\times ln|\frac{1}{10}|}{{ln|\frac25|}}[/tex]

[tex]\Rightarrow t\approx 28[/tex] minutes

There will be 50 bacteria remaining after 28 minutes.

Final answer:

To solve this problem, we use the formula for exponential decay and solve for the time when there are 50 bacteria remaining.

Explanation:

To solve this problem, we can use the formula for exponential decay: A = A0 * e^(kt), where A is the final population, A0 is the initial population, e is Euler's number (approximately 2.71828), k is the decay constant, and t is the time in minutes.

First, let's determine the value of k. We know that after 11 minutes, the population is 200 bacteria, so we can substitute these values into the formula to solve for k: 200 = 500 * e^(11k).

Divide both sides of the equation by 500: 0.4 = e^(11k).

Take the natural logarithm of both sides to solve for k: ln(0.4) = 11k.

Divide both sides by 11 to find the value of k: k ≈ -0.07761.

Now we can use the formula to solve for t when there are 50 bacteria remaining: 50 = 500 * e^(-0.07761t).

Divide both sides by 500: 0.1 = e^(-0.07761t).

Take the natural logarithm of both sides to solve for t: ln(0.1) = -0.07761t.

Divide both sides by -0.07761 to find the value of t: t ≈ 13.857 minutes.

Therefore, after approximately 14 minutes (rounded to the nearest whole number), there will be 50 bacteria remaining.

Answer:

20.4°C

Step-by-step explanation:

Initial temperature 't1'= -4.8°C

Final temperature 't2'= 15.6°C

In order to find change in temperature, take the difference of above two temperatures. So,

Change in temperature 'ΔT' = t2 - t1

ΔT= 15.6 - (-4.8)

ΔT= 20.4 °C

Therefore, the change in temperature was 20.4°C

Answer:

It would be 8.

Step-by-step explanation:

Since in the first answer the man was 6 feet and his shadow was 3, you divide 16 by 2. After dividing you get 8 feet.

Answer:

it would be 8 because 6/3 is 2 and 16/2 is 8

Answer:

x=40

Step-by-step explanation:

Since a circle has a total of a 360 degree angle the equation is

(x+40)+(2x+60)+(3x+20)=360

to simplify this we can bring all the variables(x) together and the numbers together.

(x+2x+3x)+(40+60+20)=360

6x+120=360

6x=360-120

6x=240

6x/6=240/6

x=40

The sum of all the degrees in a circle is 360 degrees. Knowing this you can make a equation:

(x + 40) + (2x + 60) + (3x + 20) = 360

x + 40 + 2x + 60 + 3x + 20 = 360

(x + 2x + 3x) + (40 + 60 + 20) = 360

Now you must combine like terms  This means the numbers with the same variables must be combined...

(x + 2x + 3x) + (40 + 60 + 20) = 360

x + 2x + 3x = 6x

(6x) + (40 + 60 + 20) = 360

Now combine the terms without variables (on the left side of the equation) together

(6x) + (40 + 60 + 20) = 360

40 + 60 + 20 = 120

(6x) + 120 = 360

Now we must isolate x. To do this first bring 120 to the right side by subtracting 120 to both sides (what you do on one side you must do to the other). Since 120 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

6x + 120 - 120 = 360 - 120

6x + 0 = 240

6x = 240

To further isolate x  you must divide 6 to both sides. Since x is being multiplied by 6 you must divide 6 to both sides to make 6 one on the left side and bring it over to the right side

6x / 6 = 240 / 6

1x = 40

x = 40

Check:

(40 + 40) + (2(40) + 60) + (3(40) + 20)

(80) + (80 + 60) + (120 + 20)

80 + 140 + 140

360

Hope this helped! Let me know if you have any further questions or want anything clarified.

~Just a girl in love with Shawn Mendes