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).


A round cylinder with a circle top and base with radius r and a height of h




Part a: Assume that the height of your cylinder is 8 inches. Consider A as a function of r , so we can write that as A(r)=2πr2+16πr. 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 8 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)=

Preview Change entry mode

Hints:


To calculate an inverse function, you need to solve for r. Here, you would start with A=2πr2+16πr. This equation is the same as 2πr2+16πr−A=0 which is a quadratic equation in the variable r , and you can solve that using the quadratic formula. You will want to keep A as a variable when you plug the values into the quadratic formula.

If you want to type in 3π+1x+1 in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.



Part c: If the surface area is 100 square inches, then what is the radius r ? In other words, evaluate r(100). Round your answer to 2 decimal places.


Hint: To compute a numeric square root such as 17. 3−−−−√ , you could


Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17. 3)

Use a browser to connect to the Internet and type in sqrt(17. 3) into a search field

Use a calculator



The radius is

inches if the surface area is 100 square inch

Answer:

Step-by-step explanation:

in the above question we have to do addition and subtraction method. Therefore, u is equal to 3.

Addition in math is a process of combining the two or more numbers. Addends are the numbers added, and the result or final answer we get after the process is called the sum. It is one of essential mathematical functions we use in our everyday activities. There are many situations in which we use to add the numbers. One of the most common everyday uses for adding the numbers is when we work with time or money—for example, adding up the bills and receipts.

An addition sentence is a mathematical expression that shows the two or more values added together and their sum. The two or more values that are added are called the addends. The parts of an addition sentence are the two or more addends, plus symbol(s), equal sign, and the sum.

From above question, it is given that:

u+4=7

so, u= 7-4= 3

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The required simplified value of the given expression h(-1) = 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
As given that,
h (x)=2x+4

Put x = -1
h(-1) = 2(-1) +4
h(-1) = 2

Thus, the required simplified value of the given expression h(-1) = 2.

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The square root of 11 and 62 to the nearest tenth is 7.9 and 3.3 .

Given, the numbers are 11 and 62.

we are asked to determine the square root of the given numbers to the nearest tenth.

a. 11

Since the given number is not an even number, hence we can't get a whole number as the square root of 11.

we need to find the number whose square root is nearest to the number 11.

3 × 3= 9

9 is nearer to 11 whereas 4 × 4 = 16 gets greater than 11.

then dividing the number 11 by 3.we get:

√11 = 3.31662479  × 3.316622479

√11 = 3.31662479

√11 = 3.4 (rounding off to the nearest tenth)

b.  62

since we can't get the square root as a whole number so ,

we need to find the number whose square root is nearest to the number 62.

8 × 8 = 64

which gets greater than 62, hence we take 7 × 7 = 49

therefore, √62 = 7.874007874 × 7.874007874

√62 = 7.874007874

√62 = 7.9 (rounding off to the nearest tenth)

hence we get the square root of 11 and 62 as 3.3 and 7.9 respectively.

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The vector function, r(t) that represents the curve of intersection of the two surfaces, the paraboloid and the parabolic cylinder is given by < t, 3t2, 8t2 + 9t4 >. It is attained by applying the concept of vectors to the assigned problem.

What is a vector?

A vector is any quantity that contains both magnitudes as well as direction. Geometrically, one can imagine a vector as a directed line segment, whose length denotes the magnitude of the vector and the direction is shown by the arrow, which is generally taken from its tail to its head. Using an arrow with a line specifies that it is not only scalar but also has some direction.

Calculation of the vector function representing the curve of intersection of the paraboloid and parabolic cylinder

A vector function r(t) is represented as: r(t) = < x, y, z >

Given: y = 3x2                         – 1

z = 8x2 + y2                             – 2

Let,

x = t

Using x = t in equations 1 and 2

y = 3t2

z = 8t2 + y2

Putting the value of y in z, we get,

z = 8t2 + (3t2)2

z = 8t2 + 9t4

Substitute  these values of x, y, and z in vector representation to obtain the result, i.e. < t, 3t2, 8t2 + 9t4 >

Hence, the value of vector function r(t) is: < t, 3t2, 8t2 + 9t4 >

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Cavitation reduces a tree's ability to conduct water due to the formation of air bubbles in water, thereby reducing the hydraulic conductance of the tree.

Cavitation, also known as embolism, is said to occur when the tracheid or vessels of the xylem is being filled with bubbles of air. Cavitation is what is said to occur when air bubbles form in water during transpiration.

The effect of cavitation is the prevention of the upward pull of water, leading to a degradation of hydraulic conductance, such that the xylem water potential is reduced.

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The numerical form of the statement the product of 9 and a number is

9n - 9.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given statement is 9 is subtracted from the product of 9 and a number.

Let the number be 'n'.

Therefore, The statement 9 is subtracted from the product of 9 and a number can be numerically written as,

9n - 9.

We can also take 9 as a common factor,

9(n - 1).

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Answer:

2x+y=-2

-9x-3y=18

So what you would do is see which one you would like to get rid of (either x, or y in this situation get rid of y)

multiply y by postive 3

3(2x+y=-2)

6x+3y=-6

-9x-3y=18          (both y's cross out since 3y+-3y is equal to zero)

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

-3x=-24 (divide both sides by -3)

---     ---

-3      -3

x= 8 (neg/neg=positive)

Then figure out the x so use either the first or second equation

so in this case I will use the first equation (plug in the x for 8)

2(8)+y=-2

16+y=-2

-16    -16

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

y=-18

Check:

2x+y=-2

2(8)+y(-18)=-2

16+-18=-2

-2=-2 (therfore you know that you are right)

Ansers:

y=-18

x=8

Hope this helps!

Answer:

length = 2ft

width = 1 ft

height = 4 ft

Step-by-step explanation:

V = LWH

V = (1/2)y × y × 2y

V = y³ = 8 ft³

y = 2

length = 2ft

width = (1/2)(2 ft) = 1 ft

height = 2(2 ft) = 4 ft

Answer:

30/32

Step-by-step explanation:

15×2=30

16×2=32

30/32

Answer:

5:2 , 30:12 , 60:24 , etc.

Step-by-step explanation:

To identify ratios equivalent to 15:6, all you need to do is multiply or divide both numbers in the ratio by the same amount to find an equivalent ratio.

So, for example:

1:2 --> 1*2 : 2*2 = 2:4 Both one half, so equal.

Now for 15:6...

Let's divide by the least common denominator ( 3 )

15 / 3 and 6 / 3 = 5 and 2

So 15:6 = 5:2

And we can also multiply the ratio by any constant as well...

For example 15 * 2 and 6 * 2

So 30:12 = 15:6

Hope this helped!

Answer:

a

Step-by-step explanation:

The commutative property is related to both addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result.

Since the question specifically asked for multiplication, the answer is a.

The equation of straight line in the cartesian plane with slope and y-intercept of -1 is  y+x+1=0

A straight line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.

Given the slope = y-intercept= -1

Therefore m = -1 and c = -1 .

Substituting the values of m and c in the general equation of a straight line we get :

y = -x - 1

or, y + x+ 1 = 0

Therefore the equation of the straight line is y + x+ 1 = 0.

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The interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).

We are given the function:

f ( x ) = - ( x + 8 )² - 1

We will first simplify the expression:

f ( x ) = - x² - 64 - 16 x - 1

f ( x ) = - x² - 16 x - 65

Now, we will plot the function on a graph.

Now, we can see that, the function is decreasing at [-8, ∞) from the graph of the function.

Therefore, the interval at which the function f ( x ) = - ( x + 8 )² - 1 is decreasing is [-8, ∞).

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The distance between -2 3/5 and -1​ on a number line is -1 3/5.

A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction in which the numerator is less than the denominator. An example of a mixed number is -2 3/5.

In order to determine the distance, -1 would be subtracted from -2 3/5

[tex]-2\frac{3}{5} - (-1)[/tex]

[tex]-2\frac{3}{5} + 1[/tex]

[tex]-\frac{13}{5} + \frac{5}{5}[/tex]

[tex]\frac{5 - 13}{5}[/tex]

-8/5 = -1 3/5

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Based on the fact that town is 2 miles away, the time it took Trinity to travel to town and back was 33 minutes

The time taken can be found as:

= Distance / Speed

Trinity's trip to town took:
= 2  / 4

= 0.5 hours

Trinity's trip back took:

= 2  / 40

= 0.05 hours

The total time it took Trinity to travel to and from town was:

= (0.5 + 0.05) x 60 minutes per hour

= 0.55 hours x 60

= 33 minutes

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The mean is 590.45 and the variance is 0.053.

What is arithmetic mean and variance?

Now,

=> Sum of all the values = 590.1+590.2+590.3+590.4+590.5+590.6+590.7+590.8 = 4723.6

=> Since 8 data values are present,

=> Mean = 4723.6/8 = 590.45

=> 590.1 - 590.45 = -0.35;

=> (-0.35)² = 0.1225

=> 590.2 - 590.45 = -0.25;

=> (-0.25)² = 0.0625

=> 590.3-590.45 = -0.15;

=> (-0.15)² = 0.0225

=> 590.4-590.45 = -0.05;

=> (-0.05)² = 0.0025

=> 590.5-590.45 = 0.05;

=> (0.05)² = 0.0025

=> 590.6-590.45 = 0.15;

=> (0.15)² = 0.0225

=> 590.7-590.45 = 0.25;

=> (0.25)² = 0.0625

=> 590.8-590.45 = 0.35;

=> (0.35)² = 0.1225

Thus, variance = [tex]\frac{(0.1225+0.0625+0.0225+0.0025+0.0025+0.0225+0.0625+0.1225)}{8}[/tex] = 0.42/8 = 0.0525 ≈ 0.053

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There are 3 cars to be needed for the remaining 15 persons in Ethel club.

Unitary method:

Unitary method used to find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Given,

27 people will travel for bowling.

As there is only one van.

and in that one van only 12 people can go.

so remaining people will go by car

no. of people that they will go by car

=> 27 - 12 = 15

in one car 5 people can go

no. of cars needed to take people=no. of people/no. of cars

=> 15 / 5 = 3

Therefore 3 cars will be needed.

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Answer:

22) -3jk+12k^2---------24)-3xy^4-7xy^3

Step-by-step explanation:

The scale is 1 inch represent 20 miles.

The new scale is 1 inch represents 10 miles

The distance on the map would be 11.8 inches.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. A map is a scale drawing of a city.

The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image.

Scale of the drawing = original dimensions / dimensions of the scale drawing

Initial scale = 65 ÷ 3 1/4

65 X 4/13 = 20

1 inch ; 20 miles

New scale = 65 / 6.5 = 1 10

1 inch : 10 miles

Length of the map = (2 x 65) / 11 = 11,8 inches

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Answer:

20.

Step-by-step explanation:

Well, Multiplication is simple. 4*5 is 20, because you're basically writing and solving 5+5+5+5. 5 added to itself 4 times.

Hope this helps!

Side Note
If you have trouble with Division, the way to do it with this equation is:
You know our answer is 20 now, so what is 20/5? (20 divided by 5) This would be 4. This is the Inverse Property of Multiplication.

The volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.

According to the given question.

Length of the edge of the cube = 0.843 cm.

As we know that, a cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.

And the volume of cube is calcualted by the formula

V = a^3

Where,

V is the volume of cube

And, a is the length of the edge of cube

Therefore,

The volume of the cube whose edge length is 0.843 cm

= (0.843cm)^3

= 0.599 cubic centimeters

Hence, the volume of cube whose edge length is 0.843 is 0.599 cubic centimeters.

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Initial velocity=0

Height=45m

G=10m/s^2

By the 2 nd equation of motion …(Under free fall)-

H = ut + 1/2 g t^2

45 = 0 + {1/2 * 10 * (t^2)} •: [0*t=0]

45 = 5 t^2

45/5 = t^2

9 = t^2

√9=t

3=t

Answer-: The time taken would be 1.3 seconds to reach the ground.

Answer: software, hardware, input device, operating system

Step-by-step explanation:

Answer:

windows-software

mouse-input device

microsoft word-operating system

motherboard-hardware

Step-by-step explanation:

Answer:

$3.53

Step-by-step explanation:

$30.01- the eggs $5.30= $24.71

24.71÷7= 3.53

Answer:

Angle BOC = 120°

Angle DOC = 60°

Angle ODC = 90°

Step-by-step explanation:

Triangle ABC is an equilateral triangle, therefore Angle BAC = 60°.

Now that we know Angle BAC, we can find Angle BOC: 2 × 60 = 120°

Angle DOC = ½ Angle BOC ( Radius drawn from centre to midpoint of chord, bisect the angle)

So Angle DOC = ½ (120) = 60°

Angle = 90° because D is the midpoint of chord BD and OD is a radius.

Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.

We are given that:

Pamela wants to make a three legged stool.

She has two pieces of wood: 36 inches and 21 inches.

Length of each leg = 16 inches.

Now, she cut 1 leg from each piece of the wood.

Length of wood pieces left will be given by the expression:

36 inches - 16 inches = 20 inches

and

21 inches - 16 inches = 5 inches.

Yes, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.

Therefore, Pamela will have enough wood for making the third leg as she has a 20 inch piece still left with her.

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Answer:

x = 12

AB = 39

AC = 24

Step-by-step explanation:

The sum of AB and BC is equal to the length of AC.

We can write the following equation based on this information :

AB + BC = AB rewrite the equation using given values

4x - 9 + 3x - 12 = 63 add like terms

7x - 21 = 63 add 21 to both sides

7x = 84 divide both sides by 7

x = 12 replace x with 12 in each expression to find the lengths

AB = 4x-9

AB = 4•12 - 9 and

AB = 39

BC = 3x -12

BC = 3•12-12 and

BC = 24

Answer: 17.5

Step-by-step explanation:

Si un circulo tiene un diametro de 35 centimetros entonces para encontrar el radio se divide en 2. 35 /2 = 17.5