A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r be the radius of the top of the can and let h be the height. The surface area of the cylinder, A , is A=2πr2+2πrh (two circles, one for the top and one for the bottom plus a rolled up rectangle for the sides).

Part a: Assume that the height of your cylinder is 6 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+12πr . What is the domain of A(r) ? In other words, for which values of r is A(r) defined?

Part b: Continue to assume that the height of your cylinder is 6 inches. Write the radius r as a function of A . This is the inverse function to A(r) , i.e., to turn A as a function of r into r as a function of A .

r(A)=

Part c: If the surface area is 175 square inches, then what is the radius r ? In other words, evaluate r(175) . Round your answer to 2 decimal places.

The radius is ? inches if the surface area is 175 square inches

Answer:

A. (2,3)

It is rather simple the 9 points between a and B 2/3 of that is 6

Final answer:

The difference of the elevations is 30347 feet.

Step-by-step explanation:

Step 1

The highest elevation is 29028 feet.

Step 2

The lowest elevation is -1319 because it is below the sea level.

Step 3

The difference of the elevations is:

29028 - (-1319)

Step 4

Evaluate the value of expression:

29028 - (-1319) = 30347

If Erica earned a total of $15450 last year from both the jobs then he earns $2840 from college if she earned 1250 more than four times the amount from college from store.

Given Total amount earned=$15450,Amount earned from store is 1250 more than 4 times earned from college.

Amount from store forms an equation.

let the amount earned from college is x.

According to question:

Amount earned from store=4x+1250

Amount earned from college=x

Total amount earned=4x+1250+x

5x+1250=15450

5x=15450-1250

5x=14200

x=14200/5

x=2840

Put the value of x in 4x+1250 to get amount earned from store=4(2840)+1250=$12610.

Hence the amount earned by Erica from college is $2840.

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Answer:

First one

Step-by-step explanation:

First one ....pick a point ....say C    for 'x'   add 8    for y   subtract 3  and you will be at C'

Answer:

200

Step-by-step explanation:

it was found that the ratio of people who liked Arithmetic and Algebra is 9 : 8. If 25% liked the both, 80 liked none of these and 20% liked arithmetic only, find the total number of people participated in the survey. Ans: 200

Answer:

g(x)=-32x

Step-by-step explanation:

When something is reflected over the x-axis. The x doesn't change, it's the y that changes. So let's just generally say you have the point (x, y). Reflecting this over the x-axis means the y is changing, so it becomes (x, -y). And since the g(x) represents the y, you multiply the entire thing by -1. So the new equation becomes: g(x) = -(8(4x)) = -8(4x) = -32x. So the equation is g(x) = -32x or -8(4x) if you want to leave it like how it was before.

The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)

An expression is defined as a mathematical statement consisting of variables , constants and mathematical operators.

The expression given is

28w⁴x²y⁷+12w⁹x⁸

Factors of the given expression will be the common terms in both the terms

w⁴x² is common in the variable term

The HCF of 28 and 12 is 4

4w⁴x² (7y⁷ + 3w⁵x⁶)

The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)

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The perimeter of the rectangle is 1 1/7 units

The formula for calculating the perimeter of a rectangle is given as:

P = 2(l + w)

Given the following

length. = 1/7 units

width = 1/2 units

Substitute

P = 2(1/7 + 1/2)

P = 2(9/14)

P = 9/7 = 1 1/7

Hence the perimeter of the rectangle is 1 1/7 units

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The correct option based on the paralel line given is that the corresponding angles are congruent.

Given that a student was told to consider the diagram and asked to prove that angle 1 ≅ angle 2.

We are to find the reason for the second step in the following proof. Since lines A and B are parallel and cut by a transversal, so angles 1 and 3 are corresponding angles. That is, ∠1. ≅ ∠3

Also, angles 2 and 3 are vertically opposite angles, so ∠2 ≅ ∠3.

And, therefore we get ∠1 ≅ ∠2.

Thus, the reason in the second step will be angles 1 and 3 are corresponding angles and corresponding angles are congruent.

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By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and

[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].

Trigonometric Identities exist as the equivalencies that apply trigonometry operations and have true for all the values of variables shown in the equation. There exist different trigonometric identities concerning the side length as nicely as the angle of a triangle.

How to simplify the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]?

Given:

[tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]

General solution for [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex]

then from the general equation, we get

[tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] and

[tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]

Solve [tex]$\frac{\pi}{2}-x = \frac{\pi}{6}+2n\pi[/tex] then [tex]$x= -2n\pi +\frac{\pi}{3}[/tex]

Solve [tex]$\frac{\pi}{2}-x = \frac{5\pi}{6}+2n\pi[/tex]then [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Therefore, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Radians, [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and [tex]$x= -2n\pi -\frac{\pi}{3}[/tex]

Degree, [tex]$x = 60 \degrees- 360\degree n[/tex], [tex]$x = -60\degree- 360\degree n[/tex]

By simplifying the equation [tex]$\:sin\left(\frac{\pi }{2}-x\right)=\frac{1}{2}[/tex], we get [tex]$x= -2n\pi +\frac{\pi}{3}[/tex] and

[tex]$x= -2n\pi -\frac{\pi}{3}[/tex].

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Using proportions, the value of x is given as follows: x = 16

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

We are given this following proportion:

[tex]\frac{n}{4} = \frac{k}{x}[/tex]

In this problem, we have that n = 15 and k = 60, hence:

[tex]\frac{15}{4} = \frac{60}{x}[/tex]

Applying cross multiplication:

15x = 60 x 4

Simplifying by 15:

x = 4 x 4

x = 16.

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Answer:

B ∩ (A ∪ C)'

Step-by-step explanation:

It's the B part excluding A and C union. Hence,

(A ∪ C)' ∩ B

There are two interpretations we could go for:

Check out the diagram below.

Point A on the red line y = x has two locations it could end up. If we follow method 1, then point A shifts upward to point B. Do this to every point on the red line and the entire red line shifts up 4 units.

Or if you decide to shift 4 units to the left (method 2), then point A moves to point C's location. Doing this to every point on the red line shifts the entire line 4 units to the left.

the probability that in bot rolls we have a sum of, at most, 8, is:

P = 47/ 1,296 = 0.036

The pair is tossed twice. A pair of dice has 36 possible outcomes, so if we toss twice the pair, the total number of outcomes is:

36*36 = 1,296

Now if we define the outcomes as:

{dice 1 (roll1), dice2(roll1), dice 1 (roll2), dice2(roll2) }

The outcomes that give at most a sum of 8 are:

{1, 1, 1, 1}

{2, 1, 1, 1} ( 3 permutations)

{2, 2, 1, 1} ( 6 permutations).

{2, 2, 2, 1} ( 3 permutations)

{3, 1, 1, 1} ( 3 permutations)

{3, 2, 1, 1} ( 12 permutations)

{3, 3, 1, 1} (6 permutations)

{4, 1, 1, 1} (3 permutations)

{4, 2, 1, 1} (6 permutations)

{5, 1, 1 , 1} (3 permutations)

{2, 2, 2, 2}

These are all the outcomes that give a sum of, at most, 8.

If we add all the outcomes we get 47 outcomes.

Then the probability that in bot rolls we have a sum of, at most, 8, is:

P = 47/ 1,296 = 0.036

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The ratio of the measurements written as a fraction is 8/9.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.

In order to convert the ratio to fraction, the units of measurements have to be the same. So, pounds would be converted to ounces.

3 x 16 = 48 ounces

48 / 54 = 8/9

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Answer:

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space.

The equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.

The given coordinates are (3,0) and (4,4).

The formula to find the slope of an equation is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex].

Now, slope[tex]=\frac{4-0}{4-3} =4[/tex].

The equation of the line is [tex](y-y_{1} )=m(x-x_{1} )[/tex]

⇒(y-3)=4(x-0)

⇒y-3=4x

⇒4x-y+3=0

Therefore, the equation for the given coordinates (3,0) and (4,4) is 4x-y+3=0.

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Hence, the inverse of the given function is [tex]{(\frac{x}{10})}^5 - 2[/tex]

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function has three parts, a set of inputs, a set of outputs, and a rule that relates the elements of the set of inputs to the elements of the set of outputs in such a way that each input is assigned exactly one output.

given function,

                 q(x) = 10[tex]\sqrt[5]{x-2}[/tex]

say y=q(x)

now we have,

                y = 10[tex]\sqrt[5]{x-2}[/tex]

                [tex]\frac{y}{10}[/tex] = [tex]\sqrt[5]{x-2}[/tex]

raising to 5th power on both sides,

               [tex](\frac{y}{10})^5[/tex] = x - 2

               x =  [tex](\frac{y}{10})^5[/tex] + 2

               [tex]q^{-1}(x) =[/tex] [tex]{(\frac{x}{10})}^5 - 2[/tex]

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Answer:

I think 5m is the correct answer

Answer:

Hello! The answer to your question is [tex]\sqrt{29}[/tex], or approximately 5.39.

Step-by-step explanation:

(Two methods)

Method 1:

To solve this problem, we will use the Pythagorean theorem. To create the triangle, you can connect all the points with lines. This will leave you with the base of the triangle as 2 and the leg as 5. We do not know the hypotenuse. Now, we can use the Pythagorean theorem formula:

[tex]a^2 + b^2 = c^2[/tex]

[tex]\sqrt{2^2 + 5^2 } \\= \sqrt{4 + 25} \\= \sqrt{29}\\or 5.39[/tex]

Now, we can substitute our values:

Method 2:

To solve this problem, we will use the distance formula:

[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

Our points are:

A(-3, 1) and B(-1, -4)

Now, we substitute our values into the distance formula provided:

[tex]\sqrt{(-1 - (-3))^2 + (-4 - 1)^2} \\= \sqrt{(-1 + 3))^2 + (-5)^2} \\= \sqrt{(2)^2 + (-5)^2} \\= \sqrt{4 + 25} \\= \sqrt{29} \\or 5.39[/tex]

Among all the given equations 6(x+3)+x=7x+9+9 is having many solutions.

Given Equations :

6(x+3)+x=7x+2+1

6(x+3)+3=7x+5

6(x+3)+x=6x+3+15

6(x+3)+x=7x+9+9

We have to find the equation having many solutions.

The equation whose both sides are equal to each other is supposed to have many solutions. For determining all equations needs to be solved.

Equation 1

6(x+3)+x=7x+2+1

6x+18=7x+3

No the above equation is not having many solutions.

Equation 2

6(x+3)+3=7x+5

6x+18+3=7x+5

6x+21=7x+5

No the above equation is not having many solutions.

Equation 3

6(x+3)+x=6x+3+15

6x+18+x=6x+18

7x+18=6x+18

No the above equation is not having many solutions.

Equation 4

6(x+3)+x=7x+9+9

6x+18+x=7x+18

7x+18=7x+18

Yes the above equation is having many solutions.

Hence the equation which is having many solutions is 6(x+3)+x=7x+9+9.

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The options given in the question are wrong and the correct options are as under:

1) 6(x+3)+x=7x+2+1

2)6(x+3)+x=7x+5

3)6(x+3)+x=6x+3+15

4) 6(x+3)+x=7x+9+9

Answer:

.

Step-by-step explanation:

A parallelogram has two pairs of parallel lines so if AD // BC and that AD//BC, Then it is indeed a parallelogram

Answer:

The first step in solving the equation should be to add 3 to both sides.

Step-by-step explanation:

Adding 3 to both sides will cancel out the -3 on the left hand side of the equation, leaving only the 2x term. On the right hand side, adding 3 will cancel out the -6, leaving only 0. This will give you the equation 2x = 0, which is much easier to solve.

The system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

From the question, we are to determine the system of inequalities that represents the graph

The equation of the solid line is  y = -x +4

Since the lower part of the graph was shaded

Then,

The inequality that represents the solid line is

y ≤ -x +4

The equation of the dotted line is  y = 3x -1

Since the lower part of the graph was shaded,

Then,

The inequality that represents the solid line is

y < 3x-1

Hence, the system of inequalities that represent the graph is

y ≤ -x +4

y < 3x-1

The correct option is the third option

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Answer:

Hope it helps!!

Answer:

[tex]a < 0[/tex]   False

[tex]|a| > 0[/tex] True

[tex]|a|=0[/tex]  False

________________________________________________

a is on the right side of 0,

which means a is positive.

The absolute value is the distance to zero (always positive)

Which means the absolute value of a is also positive.

[tex]a < 0[/tex]   is wrong because a is positive

[tex]|a| > 0[/tex]  is correct because a is larger than 0

[tex]|a|=0[/tex]  is wrong because [tex]a[/tex] ≠ [tex]0[/tex]

________________________________________________

Hope this helps :)

Answer:

y=-0.012x(x-200).

Step-by-step explanation:

1) the given parabola has two zeros: 0 and 200. It means, the required equation is: y=ax(x-200), where a - unknown number;

2) according to the given graph the vertex is (100; 120). It is possible to substitute the coordinates of it into the equation y=ax(x-200) and calculate the value of 'a':

120=a*100(100-200); ⇒ a=-0.012.

3) finally, the required equation is:

[tex]y=-0.012x(x-200).[/tex]

Answer:

             x     +             6      ≥        15

Step-by-step explanation:

Add any number greater than equal to 9 to the number 6 and you get a result of at least 12. Any number less than 9 produces a result that is not at least 15.

Just saying the question was not that descriptive so I don't know if this is what you asked for... Sorry!

Answer: The absolute values of 7 and -7 are equal because they are both a distance of 7 units from 0 on the number line.

The thing that's wrong with the equation is that 2 shouldn't be multiplied by 4 but should have been added.

From the information given, it can be seen that the equation is:

(3x²)(-2x⁴) = 3(-2)x² × x⁴ = 6x^8

Based on the information above, this calculation is incorrect. The correct calculation will be:

(3x²)(-2x⁴) = 3(-2)x² × x⁴

= -6x^6

Therefore, the multiplication should be an addition of the power.

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Answer:

14.8 feet

Step-by-step explanation:

since this is creating a right triangle you can use the Pythagorean theorem which is a^2 + b^2 = c^2, and by plugging in the one leg length and the hypotenuse length you get 14.8324 which rounds up to 14.8

The  distance between the ground and the top of the ladder is 14.8 feet.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

Hypotenuse= 16 foot,

Base = 6 feet

Using Pythagoras theorem,

H² = B² + P²

16² = 6² + P²

256 = 36 +P²

P² = 256-36

P= 14.83 feet

Hence, the distance between the ground and the top of the ladder is 14.8 feet.

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