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a) The function of h in terms of r is h=1400/(πr²).

b) The surface area of the can in terms of r is 2800/r+2πr².

c) The corresponding values of r and h that minimize the amount of required material are r≈14.04 cm and h≈2.98 cm.

a) The volume of a cylinder is given by

V = πr²h.

In this case, the volume of the can is

1400 cm³

So we have

1400 = πr²h.

Solving for h, we get

h = 1400/(πr²).

b) The surface area of a cylinder is given by

A = 2πrh+2πr².

Using the expression we obtained for h in part (a), we can substitute it in the equation and get

A = 2πr(1400/(πr²))+2πr²

= 2800/r+2πr².

c) To minimize the amount of required material, we need to find the value of r that minimizes the surface area.
To do this, we take the derivative of the surface area expression with respect to r and set it equal to zero:

dA/dr = -2800/r²+4πr = 0.

Solving for r, we get

r = √(700/π), which is approximately 14.04 cm.

Substituting this value in the expression for h that we obtained in part (a), we get

h = 1400/(π(14.04)²), which is approximately 2.98 cm.

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Answer:

78°F

Step-by-step explanation:

If the temperature was 75.5°F, and it rose by 6°F on Sunday, then the temperature on Sunday was:

75.5°F + 6°F = 81.5°F

If the temperature on Sunday was 81.5°F, and it dropped by 3.5°F on Monday, then the temperature on Monday was:

81.5°F - 3.5°F = 78°F

Therefore, the temperature on Monday was 78°F.

The rectangular block of wax can make approximately 2 candles.

To calculate the number of candles, we use the formula

V of wax = l x w x h = 10 cm x 9 cm x 20 cm = 1800 cubic cm

V of candle = l x w x h = 9 cm x 9 cm x 12 cm = 972 cubic cm

1800 / 972 = 1.85

The above answer is based on the full question below;

you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm.

The height of the candle is 12cm and the base width is 9cm

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The thickness of the said metal piece is 560 micrometers

Solving this question would require us to switch the thickness of the metal from meters to micrometers.

So, 1 meter is equivalent to 1,000,000 micrometers; and when 0.00053 meters is multiplied by 1,000,000, we get:

0.00053 m * 1,000,000 = 560 µm

Consequently, the thickness of the said metal piece is 560 micrometers.

A metal piece's thickness is defined as the distance, measured perpendicular to its opposing surfaces, between those surfaces. It is a crucial aspect in determining the strength and longevity of the metal object and is often stated in length measures like millimeters, inches, or micrometers.

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What is the thickness of the metal piece in micrometers, given that it is 0.00053 meters thick?

Answer:

9ft

Step-by-step explanation:

From the left side, you know one length is 4ft abd the one below is 5ft, when you add them together its the answer of 9ft, which is the missing side.

it's 9ft

its 9ft because when you add 4 +5 you get 9. two rectangles a present in the diagram. the 4ft and 5ft are apart of the rectangle where the missing side is, adding those two together would give you 9 and in a rectangle sides facing each other are epual therefore the missing side is 9

the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.

what is  vertical asymptotes  ?

Vertical asymptotes are vertical lines on a graph where a function approaches infinity or negative infinity as the input (x) approaches a certain value. In other words, vertical asymptotes occur when the denominator of a function becomes zero and the function is undefined at that point

In the given question,

To find the horizontal and vertical asymptotes of the function f(x) = 3x²/[(x+1)(x-4)], we need to analyze the behavior of the function as x approaches infinity or negative infinity and as x approaches the vertical asymptotes (if any).

Vertical asymptotes occur at the values of x that make the denominator of the fraction equal to zero. In this case, we have vertical asymptotes at x = -1 and x = 4.

To find the horizontal asymptote, we need to divide the leading term of the numerator by the leading term of the denominator when x approaches infinity or negative infinity. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. However, we can use long division or synthetic division to write the function in the form of a polynomial plus a proper fraction:

f(x) = 3x²/[(x+1)(x-4)] = (3x + 15)/(x² - 3x - 4)

As x approaches infinity or negative infinity, the fraction approaches the value of 3/1 (the ratio of the leading terms of the numerator and denominator), but there is no horizontal asymptote.

Therefore, the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.

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The equation of the circle is determined as (x + 3)²  + (y - 9)² = 25.

The equation of the circle is calculated as follows;

For the equation;

y = 3/4x+5

Slope = 3/4,  the slope of the line perpendicular to the line = -4/3.

it is pass through the (0, 5).

The equation of the line: y - 5 = -4x/3

For the equation;

3x + 4y = 38

4y = -3x + 38

y = -3x/4 + 38

slope = -3/4, the slope of the line perpendicular to the line = 4/3

it is pass through the (6, 5)

The equation of the line: y - 5 = 4/3(x - 6)

Solve the two equations together to find the point of intersection;

(-4/3)x + 5 = (4/3)(x - 6) + 5

-4x/3 = 4x/3 - 8

8x/3 = -8

8x = -24

x = -3

y - 5 = -4x/3

y - 5 = -4(-3)/3

y - 5 = 4

y = 9

The center of the circle = (-3, 9)

The radius of the circle is calculated as;

r = √ (-3 -0)² + (9 - 5)²

r = √(9 + 16)

r = 5

The equation of the circle becomes;

(x - a )² + (y - b)² = r²

(x + 3)²  + (y - 9)² = 5²

(x + 3)²  + (y - 9)² = 25

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Answer:

FALSSOO

Step-by-step explanation:

lol srry I pretty sure its false I did teh math

Hope its right and it helps! c:

Using the exponential decay equation, we can see that after 1000 years we will have  178.43 mg  of Ra₂₂₆

The decay of a radioactive substance, such as Radium-226, can be modeled by the exponential decay equation:

N(t) = N₀ * (1/2)^(t / T)

where:

N(t) is the amount of the substance remaining after time t

N₀ is the initial amount of the substance

t is the time elapsed

T is the half-life of the substance

Given that the half-life of Radium-226 is 1590 years and the initial amount is 500 mg, we can plug in these values into the equation and solve for N(1000), which represents the amount remaining after 1000 years.

N(1000) = 500 * (1/2)^(1000 / 1590)

N(1000) ≈ 178.43 mg

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Answer:

Sure, I can help you with that.

Given:

   * The box is 24 inches long.

   * The width of the box is seven inches less than the height.

   * The volume of the box is 2,880 cubic inches.

To solve:

   * Complete the equation that models the box's volume in terms of its height, x, in inches.

   * Determine if the height of the box can be 15 inches.

Solution:

Let's define the following variables:

* $h$ = the height of the box (in inches)

* $w$ = the width of the box (in inches)

* $l$ = the length of the box (in inches)

We are given that  l=24 and w=h−7. We can use these values to find the volume of the box:

[tex]V = lwh = 24(h - 7)h[/tex]

We can simplify this expression to get the following equation:

[tex]V = 24h^2 - 168h[/tex]

To determine if the height of the box can be 15 inches, we can substitute 15 for $h$ in the equation and see if we get a positive value for the volume.

[tex]V = 24(15)^2 - 168(15) = 2160 - 2490 = -330[/tex]

Since the volume is negative, the height of the box can't be 15 inches.

Therefore, the equation that models the box's volume in terms of its height, x, in inches is [tex]$V = 24x^2 - 168x$[/tex]. Consequently, the size of the box can't be 15 inches.

Answer:

Yes

Step-by-step explanation:

The only answer is height = 15 because the -8 will be rejected

The only expression that is not equivalent to the given fraction expression is: D (2 x 1/3) + (4 x 1/3)

The correct procedure that we will use to multiply fractions is:

- find a common denominator

- multiply the numerators

- multiply the denominators

- Simplify if necessary.

- Add the numerators and add the denominators

Looking at the options and comparing with the given fraction multiplication problem 2/3 * 4, we see that only option D is not equivalent to it because:

(2 x 1/3) + (4 x 1/3) = 6/3 = 2

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Complete question is:

Which expression is NOT equivalent to 2/3 x 4

A (2x4) /3

B 1/3 x (2x4)

C (4 x 1/3) x 2

D (2 x 1/3) + (4 x 1/3)

The value of measure of ∠A would be,

⇒ ∠ A = 38.68 degree

We have to given that;

In triangle ABC,

AB=32, AC= 22, and BC= 20

Hence, We can formulate;

⇒ sin A = BC / AB

⇒ sin A = 20 / 32

⇒ sin A = 0.625

⇒ A = 38.68 degree

Thus, The value of measure of ∠A would be,

⇒ ∠ A = 38.68 degree

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The solution to the given equation is ( 8 , 1 )

Given data ,

To determine whether (8, 1) is a solution to the system, we need to check whether it satisfies both equations:

x - 3y = 5: 8 - 3(1) = 5, which is true

y = x - 7: 1 = 8 - 7, which is true

Since (8, 1) satisfies both equations, it is a solution to the system. Therefore, the correct answer is:

Hence , (8, 1) is a solution to both equations, so it is a solution to the system

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Answer:Therefore, f(-x) = -x^3 - 3x^2 - 2x + 2.

Step-by-step explanation:o find f(-x), we replace every instance of x in the function f(x) with -x:

f(-x) = (-x)^3 - 3(-x)^2 + 2(-x) + 2

Simplifying, we get:

f(-x) = -x^3 - 3x^2 - 2x + 2

Since the line splits the square into two regions with equal area, it goes through center of square.

Equation of line through point (12,12)

with slope 5

y−12=5(x−12)

y=5x−2

y-intercept=(0,−2)

Since line passes through points (0.4,0)

and (0.6,1)

it divides both the bottom and top of squares in the same ratio, to that the line divides the square into 2

trapezoids with height =1

and bases =0.4

and 0.6

. Therefore, they have the same area.

Answer:

-8√3

Step-by-step explanation:

[tex] - 2 \sqrt{48} \\ = - 2 \sqrt{16 \times 3} \\ = - 2 \sqrt{16} \times \sqrt{3} \\ = - 2 \times 4\sqrt{3} \\ = - 8 \sqrt{3} [/tex]

Note tha given the above trigonometric expression, the solution is

x = 2π/3 or 4π/3

We will start by simplifing the equation by moving all the terms involving sin (x/2) to one side..

2sin (x  /2) = √(3)

Then, we can solve for sin(x/2) by dividing both sides by  two  

sin (x /2) = √(3)/2

This is true when x/2 is π /3 or 2π/3, since these are the values where

sin  (  π/3) = √(3)/2 and

sin  (2π/3) = √(3)/2.

To find the values of x, we multiply these solutions by two

x = 2pi/3 or 4pi/3

Since we need to make sure that these solutions are in the given interval (0, 2π)

 both solutions are in the interval, so our final answer is  

x = 2π/3 or 4 π/3

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7:

To find 6% of 45.50=

0.06x45.50= 2.73

and than 17% of 45.50

0.17x45.50= 7.735

so add 2.73 and 7.735= 10.465

than add 10.465 to $45.50 = $55.965 So the answer is $55.965.

8:

again the same thing but with the different numbers.

0.06x105.75= 6.345

0.20x105.75= 21.15

21.15+6.345= 27.495

so than 105.75-27.495= $78.255

9:

same thing again

146.75x0.25= 36.6875

0.09x146.75= 13.2075

But this time add the tax (13.2075)= 146.75+13.2075= 159.9575

but than you subtract the discount which is 25% so 159.9575-36.6875=123.7

So that is the price! $123.7

I hope that helps!

The domain of g(x) = log (7x - 10) is all real numbers greater than 10/7.

Set-builder notation: x > 10/7. Interval notation: (10/7,∞)

Given the function in the question:

g(x) = log( 7x - 10 )

For the function g(x) = log (7x - 10), the domain consists of all the possible values of x that can be plugged into the function without resulting in an undefined expression.

Here, the logarithm (in this case, (7x - 10) must be greater than zero, since the logarithm of zero or a negative number is undefined in the real numbers.

So we set the argument of the logarithm to be greater than zero, and solve for x:

7x - 10 > 0

Solve for x

7x - 10 + 10 > 0 + 10

7x > 10

Dividing both sides by 7:

7x/7 > 10/7

x > 10/7

Therefore, the domain of g(x) = log (7x - 10) is x > 10/7

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Answer:

1. A trend that gives me interest is the 1, 2 buckle my shoes 3, 4 buckle some more- The reason is why does it even exist and why did it get so popular is such a fast amount of time, and the way people get distracted on technology which we are using all over the world and it takes us away from the real world and makes us stay there.

2. Cocaine Bear it looks good and funny, I watched it with all my friends and they all enjoyed it with me.

Step-by-step explanation:

The value of angle JKN is 73°.

Given that the m ∠JKM = 106 degrees, m ∠LKM = 66, and KN bisects LKM.

So we need to find the value of ∠JKN,

So, using the angles addition postulate,

∠LKM = ∠LKN + ∠MKN

Therefore,

∠LKN = 66/2 [definition of bisector]

∠LKN = 33°

Again, using the angles addition postulate,

∠JKM = ∠JKL + ∠LKM

∠JKL = 106 - 66

∠JKL = 40°

Therefore,

∠JKN = ∠JKL + ∠LKN

∠JKN = 40 + 33

∠JKN = 73°

Hence, the value of angle JKN is 73°.

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Answer:

x^3 + x^2 - 5x + 3

The specified scalar or vector 5u(3v - 4w) is equal to -420i + 250j.

We can begin by distributing the scalar 5 to the vector 3v - 4w:

5u(3v - 4w) = 5u(3v) - 5u(4w)

Next, we can find the scalar multiples:

5u(3v) = 5(-4i + 2j)(3(3i - j)) = 5(-36i + 10j)

5u(4w) = 5(-4i + 2j)(4(-6j)) = 5(48i - 40j)

Now we can substitute these values back into the original expression:

5u(3v - 4w) = 5(-36i + 10j) - 5(48i - 40j)

Simplifying:

5u(3v - 4w) = -420i + 250j

Therefore, 5u(3v - 4w) = -420i + 250j.

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If an avocado costs $1 per pound, the cost of 9 pounds, using multiplication, is $9.

Multiplication is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication involves the multiplicand, the multiplier, and the product.

The cost per pound of an avocado = $1

The total quantity considered = 9 pounds

Proportionately, the total cost of 9 pounds = $9 ($1 x 9)

Thus, based on multiplication operation, the total cost of 9 pounds is $9.00.

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Answer:

x = 45°

Because there are 180° in a triangle

The value c = 3 is not a solution to the inequality

From the question, we have the following parameters that can be used in our computation:

122 c

Express properly

So, we have

1 ≥ c

When this inequality is rewriiten. we have

c ≤ 1

This means that the values of c do not exceed 1

The number 3 exceeds 1

So, it means that c = 3 is not a solution to the inequality

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Deviance is a term used in sociology to describe behavior that violates social norms or expectations. It refers to any behavior that is considered outside of the established rules and expectations of a society or culture.

Informal negative sanctions are the social disapproval or punishment that people receive for violating social norms. An example of informal negative sanctions could be a group of friends ostracizing another friend for breaking a social rule, such as not showing up to a planned event.

In terms of the act of deviance, it could be anything from breaking a minor social norm to committing a serious crime. The reaction of informal negative sanctions is often an attempt to maintain social control by encouraging conformity to the established norms of the group or society.

While physical violence is not necessary to maintain social control, the threat of punishment is an important part of any functioning society. People follow the rules and norms of society because they know that if they do not, there will be consequences. However, it is important to note that violence and punishment should not be the only means of social control. Positive reinforcement, such as rewards for good behavior, can also be an effective way of encouraging conformity to social norms.

In summary, deviance refers to behavior that violates social norms, and informal negative sanctions are a way of enforcing social norms. The threat of physical violence is not necessary to maintain social control, but consequences for deviant behavior are essential for any functioning society.

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