Poly thinks that the graphs of exponential and logarithmic functions are complete opposites.

What do you think she means by that?

Be sure to express your thoughts clearly and use correct mathematical language in your explanation.

Answer:

The height of the tower is 17.79 m

Step-by-step explanation:

The question in English is

To measure the height of a tower, Juan stands at a point on the horizontal ground and observes the highest point of the tower under an angle of 62°. He approaches the tower 6 meters in a straight line and the angle is 79° Find the height of the tower

see the attached figure to better understand the problem  

In the right triangle ABC

tan(62°)=h/x

h=(x)tan(62°) ------> equation A

In the right triangle DBC

tan(79°)=h/(x-6)

h=(x-6)tan(79°) ------> equation B

Equate equation A and equation B and solve for x

(x)tan(62°)=(x-6)tan(79°)

(x)tan(62°)-(x)tan(79°)=-(6)tan(79°)

x=-(6)tan(79°)/[tan(62°)-tan(79°)]

x=9.46 m

Find the value of h

h=(9.46)tan(62°)=17.79 m

Answer:

son las dos en punto

Step-by-step explanation:

Answer: option a

Step-by-step explanation:

The volume of a cylinder can be calculated with this formula:

[tex]V=\pi r^2h[/tex]

Where the radius is "r" and the height is "h"

Calculate the volume of the Cylinder A:

[tex]V_A=\pi (1m)^2(4m)\\\\V_A=4\pi\ m^3[/tex]

Calculate the volume of the Cylinder B:

[tex]V_B=\pi (1m)^2(8m)\\\\V_B=8\pi\ m^3[/tex]

Now, the ratio of the volume of the Cylinder A to the volume of the Cylinder B can be calculated with:

[tex]ratio=\frac{V_A}{V_B}[/tex]

Substituting values, you get:

[tex]ratio=\frac{4\pi\ m^3}{8\pi\ m^3}[/tex]

[tex]ratio=\frac{1}{2}[/tex] or 1:2

Answer:

5040

Step-by-step explanation:

at least thats what it is on GP

I believe the answer is c. I hope that’s right! Good luck!

The parametric equation is : [tex]\frac{x-13}{4}[/tex]

The correct option is (a).

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Given parametric equation:

x= 4t+1 and y=t-3

From, y=t-3

         t= y+3

put t in x= 4t+1

x= 4(y+3) +1

x= 4y +12+1

x= 4y  + 13

x-13=4y

y= [tex]\frac{x-13}{4}[/tex]

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Answer:

See below.

Step-by-step explanation:

Fifth root of 243 = 3,

Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),

then r^5( cos  Ф  + i sin  Ф )^5 = 243(cos 240 + i sin 240).

Equating equal parts and using de Moivre's theorem:

r^5 =243  and  cos  5Ф  + i sin  5Ф = cos 240 + i sin 240

r = 3 and  5Ф = 240 +360p so Ф =  48 + 72p

So Ф = 48, 120, 192, 264, 336  for   48 ≤ Ф < 360

So there are 5 distinct solutions given by:

3(cos 48 + i sin 48),

3(cos 120 + i sin 120),

3(cos 192 + i sin 192),

3(cos 264 + i sin 264),

3(cos 336 + i sin 336).. (Answer).

Answer:

Step-by-step explanation:the answer is 3 ft

The width of the fountain is 9 feet.

The area of the fountain is 0, it means the width of the fountain doesn't affect the total area of the courtyard. Therefore, the width of the fountain can be any value, including 9 feet.

To find the width of the fountain, we first need to determine the area of the entire courtyard, including the fountain and the stone-covered area. Since the courtyard is rectangular, we can assume the width of the fountain is the same as the width of the courtyard.

Let's denote the width of the fountain as \( w \) feet and the length of the courtyard as \( l \) feet.

Given that the area covered by stone is 246 square feet, we can write the equation:

[tex]\[ w \times l - 246 = \text{area of the fountain} \][/tex]

Since the entire courtyard area is the sum of the area covered by stone and the area of the fountain, we have:

[tex]\[ w \times l = 246 + \text{area of the fountain} \][/tex]

We know the total area of the courtyard, but we still need to find the length [tex](\( l \))[/tex] of the courtyard to solve for the width of the fountain.

To find the length, we can use the fact that the entire courtyard area is the product of its length and width:

[tex]\[ l \times w = \text{total area of the courtyard} \][/tex]

Since the total area of the courtyard is given as 246 square feet, we have:

[tex]\[ l \times w = 246 \][/tex]

Now, we have two equations:

[tex]\[ w \times l = 246 + \text{area of the fountain} \][/tex]

[tex]\[ l \times w = 246 \][/tex]

Substituting [tex]\( l \times w = 246 \)[/tex] into the first equation, we get:

[tex]\[ 246 = 246 + \text{area of the fountain} \][/tex]

[tex]\[ \text{area of the fountain} = 246 - 246 = 0 \][/tex]

Since the area of the fountain is 0, it means the width of the fountain doesn't affect the total area of the courtyard. Therefore, the width of the fountain can be any value, including 9 feet.

Complete question:

Cindy is designing a rectangular fountain in the middle of a courtyard the rest of the courtyard will be covered in stone. The part of the courtyard that will be covered in stone has an area of 246 square feet. What is the width of the fountain

Answer:

20

Step-by-step explanation:

4 multiplied by 5 is equal to 20. You substitute 5 for x.

Answer:

20

Step-by-step explanation:

You are to multiply 5 by 4:  the outcome is 20.  That's all.

Transformations are important subjects in geometry. In this exercise, these are the correct transformation rules:

Consider the point [tex](x,y)[/tex], if you reflect this point across the x-axis you should multiply the y-coordinate by -1, so you get:

[tex]\boxed{(x,y)\rightarrow(x,-y)}[/tex]

Consider the point [tex](x,y)[/tex], if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:

[tex]\boxed{(x,y)\rightarrow(-x,y)}[/tex]

Consider the point [tex](x,y)[/tex]. To rotate this point by 90° around the origin in counterclockwise direction, you can always swap the x- and y-coordinates and then multiply the new x-coordinate by -1. In a mathematical language this is as follows:

[tex]\boxed{(x,y)\rightarrow(-y,x)}[/tex]

Consider the point [tex](x,y)[/tex]. To rotate this point by 180° around the origin, you can flip the sign of both the x- and y-coordinates. In a mathematical language this is as follows:

[tex]\boxed{(x,y)\rightarrow(-x,-y)}[/tex]

Rotate a point 270° counter-clockwise about origin is the same as rotating the point 90° in clock-wise direction. So the rule is:

[tex]\boxed{(x,y)\rightarrow(y,-x)}[/tex]

Answer:Transformations are important subjects in geometry. In this exercise, these are the correct transformation rules:

Step-by-step explanation:

Seems like it would be

[tex]\displaystyle\int_5^9x^4\,\mathrm dx[/tex]

To choose the single logarithm expression that is equivalent to the given expression, we need to combine the two logarithms into one logarithm using the properties of logarithms. The single logarithm expression that is equivalent to the given expression is log (3x).

To choose the single logarithm expression that is equivalent to the given expression, we need to combine the two logarithms into one logarithm using the properties of logarithms.

Using the property that the logarithm of a product is the sum of the logarithms, we can rewrite the given expression as:

1/3 log (3x) + 2/3 log (3x) = log((3x)^(1/3) * (3x)^(2/3))

Simplifying the expression inside the logarithm gives:

log((3x)^(1/3 + 2/3)) = log((3x)^1) = log (3x)

Therefore, the single logarithm expression that is equivalent to the given expression is log (3x).

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To solve this problem, we can set up a system of equations to represent the given information. Solving this system of equations, we find that each small candle holder holds 2 candles and each large candle holder holds 8 candles.

To solve this problem, let's represent the number of candles each small candle holder holds as x and the number of candles each large candle holder holds as y. We can set up a system of equations to represent the given information:

We can solve this system of equations by eliminating one variable. Subtracting the equations, we get 8x = 16. Dividing both sides by 8, we find that x = 2. Substituting this value back into one of the equations, we can solve for y. Using the first equation, we have 10(2) + 4y = 52, which simplifies to 20 + 4y = 52. Subtracting 20 from both sides, we obtain 4y = 32. Dividing by 4, we find that y = 8. Therefore, each small candle holder holds 2 candles and each large candle holder holds 8 candles.

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To find out how many candles each candle holder holds, set up a system of equations using the given information and solve for the variables. Each small candle holder holds 2 candles and each large candle holder holds 8 candles.

To find out how many candles each candle holder holds, we need to set up a system of equations using the given information. Let's say the number of candles a small candle holder can hold is 's' and the number of candles a large candle holder can hold is 'l'.

From the east side, we have the equation 10s + 4l = 52. From the west side, we have the equation 2s + 4l = 36. Solving these equations, we can find the values of 's' and 'l', which will give us the number of candles each candle holder can hold.

We can eliminate 'l' by multiplying the first equation by 2 and the second equation by 5. This gives us 20s + 8l = 104 and 10s + 20l = 180. By subtracting the second equation from the first, we get 10l = 76. Dividing both sides by 10, we find that l = 7.6. Since we cannot have a fraction of a candle, we can approximate l to the nearest whole number, which is 8.

Substituting the value of l back into one of the original equations, we can find the value of s. Using the first equation, we have 10s + 4(8) = 52. Simplifying this equation gives us 10s + 32 = 52. Subtracting 32 from both sides, we find that 10s = 20. Dividing both sides by 10, we find that s = 2. Therefore, each small candle holder holds 2 candles and each large candle holder holds 8 candles.

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Answer:

If

€

p(x) is a polynomial, the solutions to the equation

€

p(x) = 0 are called the zeros of the

polynomial. Sometimes the zeros of a polynomial can be determined by factoring or by using the

Quadratic Formula, but frequently the zeros must be approximated. The real zeros of a polynomial

p(x) are the x-intercepts of the graph of

€

y = p(x).

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The Factor Theorem: If

€

(x − k) is a factor of a polynomial, then

€

x = k is a zero of the polynomial.

Conversely, if

€

x = k is a zero of a polynomial, then

€

(x − k) is a factor of the polynomial.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Example 1: Find the zeros and x-intercepts of the graph of

€

p(x) =x

4−5x

2 + 4.

€

x

4−5x

2 + 4 = 0

(x

2 − 4)(x

2 −1) = 0

(x + 2)(x − 2)(x +1)(x −1) = 0

x + 2 = 0 or x − 2 = 0 or x +1= 0 or x −1= 0

x = −2 or x = 2 or x = −1 or x =1

So the zeros are –2, 2, –1, and 1 and the x-intercepts are (–2,0), (2,0), (–1,0), and (1,0).

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The number of times a factor occurs in a polynomial is called the multiplicity of the factor. The

corresponding zero is said to have the same multiplicity. For example, if the factor

€

(x − 3) occurs to

the fifth power in a polynomial, then

€

(x − 3) is said to be a factor of multiplicity 5 and the

corresponding zero, x=3, is said to have multiplicity 5. A factor or zero with multiplicity two is

sometimes said to be a double factor or a double zero. Similarly, a factor or zero with multiplicity

three is sometimes said to be a triple factor or a triple zero.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Example 2: Determine the equation, in factored form, of a polynomial

€

p(x) that has 5 as double

zero, –2 as a zero with multiplicity 1, and 0 as a zero with multiplicity 4.

€

p(x) = (x − 5)

2(x + 2)x

4

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Example 3: Give the zeros and their multiplicities for

€

p(x) = −12x

4 + 36x3 − 21x

2.

€

−12x

4 + 36x3 − 21x

2 = 0

−3x

2(4x

2 −12x + 7) = 0

−3x

2 = 0 or 4x

2 −12x + 7 = 0

x

2 = 0 or x = −(−12)± (−12)

2−4(4)(7)

2(4)

x = 0 or x = 12± 144−112

8 = 12± 32

8 = 12±4 2

8 = 12

8 ± 4 2

8 = 3

2 ± 2

2

So 0 is a zero with multiplicity 2,

€

x = 3

2 − 2

2 is a zero with multiplicity 1, and

€

x = 3

2 + 2

2 is a zero

with multiplicity 1.

(Thomason - Fall 2008)

Because the graph of a polynomial is connected, if the polynomial is positive at one value of x and

negative at another value of x, then there must be a zero of the polynomial between those two values

of x.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Example 4: Show that

€

p(x) = 2x3 − 5x

2 + 4 x − 7 must have a zero between

€

x =1 and

€

x = 2.

€

p(1) = 2(1)

3 − 5(1)

2 + 4(1) − 7 = 2(1) − 5(1) + 4 − 7 = 2 − 5 + 4 − 7 = −6

and

€

p(2) = 2(2)3 − 5(2)

2 + 4(2) − 7 = 2(8) − 5(2) + 8 − 7 =16 −10 + 8 − 7 = 7.

Because

€

p(1) is negative and

€

p(2) is positive and because the graph of

€

p(x) is connected,

€

p(x)

must equal 0 for a value of x between 1 and 2.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

If a factor of a polynomial occurs to an odd power, then the graph of the polynomial actually goes

across the x-axis at the corresponding x-intercept. An x-intercept of this type is sometimes called an

odd x-intercept. If a factor of a polynomial occurs to an even power, then the graph of the

polynomial "bounces" against the x-axis at the corresponding x-intercept, but not does not go across

the x-axis there. An x-intercept of this type is sometimes called an even x-intercept.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Example 5: Use a graphing calculator or a computer program to graph

€

y = 0.01x

2(x + 2)3(x − 2)(x − 4)

4 .

x

y

–2 2 4

5

Because the factors

€

(x + 2) and

€

(x − 2) appear to odd

powers, the graph crosses the x-axis at

€

x = −2

and

€

x = 2.

Because the factors x and

€

(x − 4) appear to even

powers, the graph bounces against the x-axis at

€

x = 0

and

€

x = 4.

Note that if the factors of the polynomial were

multipled out, the leading term would be

€

0.01x10.

This accounts for the fact that both tails of the graph

go up; in other words, as

€

x → −∞,

€

y

Step-by-step explanation:

Answer:

623168

Step-by-step explanation:

749x832=623168

Answer:

The same focus is (-5 , 0) ⇒ Answer D

Step-by-step explanation:

* Lets study the equation of the hyperbola

# The standard form of the equation of a hyperbola with  

  center (0 , 0) and transverse axis parallel to the x-axis is

  x²/a² - y²/b² = 1

- The coordinates of the foci are (± c , 0),  where c² = a² + b²

# The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1

- the coordinates of the foci are (h ± c , k), where c² = a² + b²

# The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- the coordinates of the foci are (h , k ± c), where c² = a² + b²

* Now lets solve the problem

∵ x²/16 - y²/9 = 1

∴ a² = 16 and b² = 9

∵ c² = a² + b²

∴ c² = 16 + 9 = 25 ⇒ take √ to find the values of c

∴ c = ±√25 = ± 5

∴ The foci are (5 , 0) , (-5 , 0)

# Answer A:

∵ (y - 5)/16 - (x - 13)/9 = 1

∵  (y - k)²/a² - (x - h)²/b² = 1

∴ The foci are (h , k + c) , (h , k - c)

∴ h = 13 and k = 5

∵ a² = 16 and b² = 9

∵ c² = a² + b²

∴ c² = 16 + 9 = 25 ⇒ take √ to find the values of c

∴ c = ±√25 = ± 5

∴ The foci are (13 , 5+5) , (13 , 5-5)

∴ The foci are (13 , 10) , (13 , 0) ⇒ not the same

# Answer B:

∵ (x - 13)²/25 - (y - 5)²/144

∵ (x - h)²/a² - (y - k)²/b² = 1

∵ The foci are (h ± c , k)

∴ h = 13 and k = 5

∵ a² = 25 and b² = 144

∵ c² = a² + b²

∴ c² = 125 + 144 = 169 ⇒ take √ to find the values of c

∴ c = ±√169 = ± 13

∴ The foci are (13 + 13 , 5) , (13 - 13 , 5)

∴ The foci are (26 , 5) , (0 , 5) ⇒ not the same

# Answer C:

∵ (y - 5)/25 - (x - 13)/144 = 1

∵  (y - k)²/a² - (x - h)²/b² = 1

∴ The foci are (h , k + c) , (h , k - c)

∴ h = 13 and k = 5

∵ a² = 25 and b² = 144

∵ c² = a² + b²

∴ c² = 25 + 144 = 169 ⇒ take √ to find the values of c

∴ c = ±√169 = ± 13

∴ The foci are (13 , 5+13) , (13 , 5-13)

∴ The foci are (13 , 18) , (13 , -8) ⇒ not the same

# Answer D:

∵ (y + 13)/144 - (x + 5)/25 = 1

∵  (y - k)²/a² - (x - h)²/b² = 1

∴ The foci are (h , k + c) , (h , k - c)

∴ h = -5 and k = -13

∵ a² = 144 and b² = 25

∵ c² = a² + b²

∴ c² = 144 + 25 = 169 ⇒ take √ to find the values of c

∴ c = ±√169 = ± 13

∴ The foci are (-5 , -13+13) , (-5 , -13-13)

∴ The foci are (-5 , 0) , (-5 , -26) ⇒ one of them the same

* The same focus is (-5 , 0)

A. addition:

[tex]3x^{2}  + 2x - 6\\2x^{2}  - 2x + 10\\------\\5x^{2} + 4[/tex]

B. subtraction:

[tex]3x^{2} + 2x - 6\\2x^{2} - 2x + 10\\-------\\x^{2} + 4x - 16[/tex]

Answer:

1. 5x²+4         2.-x²-4x+16

Step-by-step explanation:

The question is on operations in quadratic equations

1. Addition

P=3x²+2x-6

Q= 2x²-2x+10

P+Q= 3x²+2x-6 +2x²-2x+10

Collect like terms

3x²+2x²+2x-2x-6+10

5x²+4

2.Subtraction

Q-P

(2x²-2x+10) -(3x²+2x-6)

open brackets

2x²-2x+10-3x²-2x+6

collect like terms

2x²-3x²-2x-2x+10+6

-x²-4x+16

-x²+4x+16

Answer:

Step-by-step explanation:

Even though the teams appear from the mean to be similar in their winnings, they are not.  This is mostly because the Tigers have a greater range (difference between the highest and lowest values) than do the Foxes.  The Tigers' range is 16 - 1 = 15 while the Foxes' range is 6 - 3 = 3.

In other words, using the mean to determine how closely matched these teams are is worthless.

Answer:

Step-by-step explanation:

the answer is b defenitly

Answer:

Option A. [tex]30\ pounds[/tex]

Step-by-step explanation:

step 1

Find the volume of the sphere ( medicine ball)

The volume is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter

Convert inches to feet

Remember that

1 ft=12 in

[tex]r=5\ in=5/12\ ft[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(5/12)^{3}[/tex]

[tex]V=0.3029\ ft^{3}[/tex]

step 2

Find the weight of the ball

Multiply the volume in cubic foot by 100

[tex]0.3029*100=30.29\ pounds[/tex]

Round to the nearest pound

[tex]30.29=30\ pounds[/tex]

The medicine ball would be A. 30 pounds

Since the medicine ball is a sphere, its volume is

V = πd³/6 where d = diameter of medicine ball = 10 in = 10 in × 1 ft/12 in = 0.8333 ft

So, substituting the value of the variable into the equation, we have

V = πd³/6

V = π(0.8333 ft)³/6

V = π(0.5787 ft³)/6

V = 1.818 ft³/6

V = 0.303 ft³

The mass of the medicine ball = mass of sand per cubic foot × volume of medicine ball

where

So,

mass of the medicine ball = 100 lb/ft³ × 0.303 ft³

= 30.3 lb

≅ 30 pounds

So, the medicine ball would be A. 30 pounds

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Answer:

The solution of the system of equations is (-3 , 5)

Step-by-step explanation:

* Lets describe the drawing of each line

- The form of the equation of any line is y = mx + c, where m

  is the slope of the line and c is the y-intercept (the point of

  intersection between the line and the y-axis is (0 , c))

* The line y = -x + 2 represented by the red line

- The line intersect the y-axis at point (0 ,2)

- The line intersect the x-axis at point (2 , 0)

- The slope of the line is -1, so the angle between the positive

  part of x-axis and the line is obtuse

* The line x - 3y = -18 represented by blue line

- Put the line in the form y = mx + c

- The line is x - 3y = -18⇒ add 18 and 3y to both sides

- The line is 3y = x + 18 ⇒ ÷ 3 both sides

- The line is y = 1/3 x + 6

- The line intersect the y-axis at point (0 ,6)

- The line intersect the x-axis at point (-18 , 0)

- The slope of the line is 1/3, so the angle between the positive

  part of x-axis and the line is acute

* Look to the attached graph

- The point of intersection between the two line is the solution

 of the system of equation

- From the graph the point of intersection is (-3 , 5)

* The solution of the system of equations is (-3 , 5)

Answer:

one of the lines will pass (0,2) and (2,0) and intersect at (5,3) and pass through (0,5)

Step-by-step explanation:

edit: it actually passes through (0,6) mark as brainliest if right

Answer:

The symbol ∩ signifies the intersection of the left operand and the right operand. Here, it means "and", as it often does.

Step-by-step explanation:

The solution to the left inequality is x < -1.

The solution to the right inequality is x > -3.

The intersection symbol (∩) means you are interested in the interval where these solutions overlap—the intersection of the solutions: -3 < x < -1; (-3, -1) in interval notation.

Answer:

92 feet.

Step-by-step explanation:

1. Suzi started at 230 feet

2. Suiz ended at 138 feet

3. Subtract the starting and end numbers 4. 23 - 138= 92

Answer:

whats the answer

Answer:

3/13

Step-by-step explanation:

There are 3 5's in the jar and thirteen chips total. You have a probability of pulling 1 of the three 5's out so there is a 3/13 chance of pulling a 5.

Answer:

sample space is 13

3/13

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

log₂(x-4) = 4

Undo the log by raising 2 to both sides:

2^(log₂(x-4)) = 2^4

x - 4 = 2^4

x - 4 = 16

x = 20

Answer D.

log2(x-4) =4. The answer is D) 20

Answer: A

Step-by-step explanation:

The correct answer is A. 0.037 cubic feet.

Convert the lengths to inches:

12 feet is equal to 12 * 12 inches = 144 inches.

Calculate the area of the annulus (the space between the inner and outer circles):

First, convert the diameters to radii:

Outer radius = 7/8 inches * 0.5 = 7/16 inches

Inner radius = 3/4 inches * 0.5 = 3/8 inches

Then, calculate the area of the annulus:

Area = π * (outer radius^2 - inner radius^2)

Area ≈ π * ((7/16)^2 - (3/8)^2) ≈ 0.0875 square inches

Calculate the volume of the refrigerant:

Multiply the area by the length of the tubing:

Volume = Area * Length

Volume ≈ 0.0875 square inches * 144 inches ≈ 12.48 cubic inches

Convert the volume to cubic feet:

Remember that 1 inch^3 = 1/12^3 cubic feet.

Therefore, the volume in cubic feet is:

Volume (ft^3) = Volume (in^3) / (12^3)

Volume (ft^3) ≈ 12.48 cubic inches / (12 * 12 * 12) ≈ 0.037 cubic feet

The closest answer choice to 0.037 cubic feet is A. 0.037 cubic feet.

Complete Question:

You are working on an air conditioning system. A roll of cylindrical copper tubing has an outside diameter of 7/8 inch and an inside diameter of 3/4 inch. How much refrigerant can 12 feet of the tubing hold?

A. 0.037 cubic feet

B. 0.065 cubic feet

C. 0.147 cubic feet

D. 5.30 cubic feet

Answer:

Option C

Step-by-step explanation: I think this is right because when you substitute the 2 for x you get the answer. Hope this helps darling!!

A quadratic equation is in the form of ax²+bx+c. The roots of the quadratic equation x² - 4x + 5 = 0 are x = 2 ± i. Thus, the correct option is C.

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.

Given the roots of the quadratic equation are x = 2 ± i. Therefore, we can write the roots as,

α = 2+i

β = 2-i

Now, we know that a quadratic equation can also be written in the form,

x² - (α+β)x + αβ = 0

Therefore, we need to find the value of (α+β) and αβ,

α+β = 2 + i + 2 - i

α+β = 4

αβ = (2+i)(2-i)

αβ = 2²-i²

αβ = 4 + 1

αβ = 5

Thus, the quadratic equation is x² - 4x + 5 = 0.

Hence, The roots of the quadratic equation x² - 4x + 5 = 0 are x = 2 ± i. Thus, the correct option is C.

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Parameterize each leg by

[tex]\vec r_1(t)=(1-t)(4\,\vec\imath)+t(-4\,\vec\imath)=(4-8t)\,\vec\imath[/tex]

[tex]\vec r_2(t)=(1-t)(-4\,\vec\imath)+t(4\,\vec\jmath)=(-4+4t)\,\vec\imath+4t\,\vec\jmath[/tex]

[tex]\vec r_3(t)=(1-t)(4\,\vec\jmath)+t(4\,\vec\imath)=4t\,\vec\imath+(4-4t)\,\vec\jmath[/tex]

each with [tex]0\le t\le1[/tex].

The line integrals along each leg (in the same order as above) are

[tex]\displaystyle\int_0^1((4-8t)\,\vec\jmath)\cdot(-8\,\vec\imath)\,\mathrm dt=0[/tex]

[tex]\displaystyle\int_0^1(16t(t-1)\,\vec\imath-4\,\vec\jmath)\cdot(4\,\vec\imath+4\,\vec\jmath)\,\mathrm dt=\int_0^1(64t(t-1)-16)\,\mathrm dt=-\frac{80}3[/tex]

[tex]\displaystyle\int_0^1(16t(1-t)\,\vec\imath+(8t-4)\,\vec\jmath)\cdot(4\,\vec\imath-4\,\vec\jmath)\,\mathrm dt=\int_0^1(64t(1-t)-4(8t-4))\,\mathrm dt=\frac{32}3[/tex]

###

The total line integral then has a value of -16. We can confirm this by checking with Green's theorem. Notice that [tex]C[/tex] as given as clockwise orientation, while Green's theorem assumes counterclockwise. So we must multiply by -1:

[tex]\displaystyle\int_{-C}\vec f\cdot\mathrm d\vec r=-\iint_D\left(\frac{\partial(x-y)}{\partial x}-\frac{\partial(xy)}{\partial y}\right)\,\mathrm dA=-\int_0^4\int_{y-4}^{4-y}(1-x)\,\mathrm dx\,\mathrm dy=-16[/tex]

as required.

To calculate a line integral over a curve in a vector field, parametrize each segment of the curve, substitute these parametrizations into the integral and evaluate the resulting integral over the range of the parameters. Without knowing the paths between the points in question, a specific solution can't be given. However, basic calculus techniques would be used to evaluate these integrals.

The objective here is to find the line integral of the given vector field f⃗=xyi⃗ + (x−y)j⃗ along each segment of the triangle defined by the points (4,0), (-4,0) and (0,4). The vector field involves two variables, x and y. A line integral is a type of integral where a function is integrated along a curve. In this vector field, the function is defined in two variables x and y. Our first step in calculating the line integral is to parametrize each path between these points. Then, we substitute these parametrizations into the integral, which is then evaluated with respect to the parameter. Let's evaluate the line integral over the three segments of the triangle.

Unfortunately, without further information on the specific functional forms of the paths between these points, a concrete solution can't be provided. However, usually, this process involves applying the formula for a line integral over a vector field and using fundamental calculus techniques to simplify and evaluate these integrals. If the paths between points were straight lines, for example, the path parametrizations would be simple linear functions.

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Answer:

D

Step-by-step explanation:

Let E(x,y) represent the total earnings.

Then E(x,y) = ($20/lawn)x + ($5/bush)y   (Answer D)

Answer:

B. 1/56

Explanation:

There are 8 different marbles. In the first draw, you have a one out of 8 chance of getting the red. In the second draw, there are 7 marbles remaining, so a one out of 7 chance of drawing a white marble. To find the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.

(1/8)*(1/7)=1/56

This question is based on the probability.  Therefore, the correct option is B, [tex]\dfrac{1}{56}[/tex]  is the probability that the red marble is drawn first and the white marble is drawn second.

Given:

There are 8 marbles in a bag. Each marble is a different color. The colors are: red, orange, yellow, green, blue, purple, black, and white. Two marbles are randomly drawn from the bag without replacement.

We need to determined the probability that the red marble is drawn first and the white marble is drawn second.

According to the question,

It is given that, there are 8 different marbles. In the first draw, you have a one out of 8 chance of getting the red is [tex]\dfrac{1}{8}[/tex].

In the second draw, there are 7 marbles remaining, so a one out of 7 chance of drawing a white marble i.e. [tex]\dfrac{1}{7}[/tex].

Now, calculating the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.

⇒ [tex]\dfrac{1}{8} \times \dfrac{1}{7} = \dfrac{1}{56}[/tex]

Therefore, the correct option is B, [tex]\dfrac{1}{56}[/tex]  is the probability that the red marble is drawn first and the white marble is drawn second.

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The function that would represent the growth of the keepers bee population over time would [tex]\( x = 150 \times 3^n \)[/tex]

How to find the function ?

To model the growth of the bee population in the beekeeper's hive, we can use an exponential growth function. The key information here is that the population triples each year. This means the growth factor is 3.

The function would therefore be:

[tex]\( x = 150 \times 3^n \)[/tex]

The equation is an exponential growth model where:

150 is the initial number of bees.

3 is the growth factor (since the population triples each year).

n is the number of years passed.

For example, to find the bee population after 2 years, you would calculate:

[tex]\( 150 \times 3^2 = 150 \times 9 \\= 1350 \) bees[/tex]

Answer:

There are 7 milliliters of water in each of the first 7 beakers

Step-by-step explanation:

* At first lets read the problem

- There are 86 milliliters of water to pour into tiny beakers

- Jerry has 8 tiny beakers

- He pours same amount in seven of them

- He pours 16 milliliters in the 8th one

- we want to know how many milliliters in each of the 7 beakers

* Look to the attached drawing

- There are 8 shapes represent the tiny beakers

- Seven of them have same amount x

- The last one has amount 16 milliliters

- All of them have 86 milliliters

* Now lets write the steps to answer the problem

∵ The amount of water is 86 milliliters

∵ The 8th tiny beaker has 16 milliliters

∴ The amount of water in the 7 beakers = 86 - 16 = 70 milliliters

∵ Each one of the 7 beakers has x milliliters of water

∴ 7 × (x) = 70 ⇒ divide each side by 7

∴ x = 7 milliliters

* There are 7 milliliters of water in each of the first 7 beakers

Each of the first 7 beakers contains 10 milliliters of water.

1. First, we identify the total amount of water Jerry poured, which is 86 milliliters.

 2. We know that the eighth beaker contains 16 milliliters of water.

3. To find out how much water was poured into the first 7 beakers, we subtract the amount in the eighth beaker from the total amount:

[tex]\[ \text{Water in first 7 beakers} = \text{Total water} - \text{Water in 8th beaker} \] \[ \text{Water in first 7 beakers} = 86 \text{ ml} - 16 \text{ ml} \] \[ \text{Water in first 7 beakers} = 70 \text{ ml} \][/tex]

4. Now, we divide the total water in the first 7 beakers by 7 to find out how much water is in each beaker:

[tex]\[ \text{Water per beaker} = \frac{\text{Water in first 7 beakers}}{\text{Number of beakers}} \] \[ \text{Water per beaker} = \frac{70 \text{ ml}}{7} \] \[ \text{Water per beaker} = 10 \text{ ml} \][/tex]

Therefore, each of the first 7 beakers contains 10 milliliters of water.