A circular pan has a diameter of 8 inches. What is the exact area of the pan? A. 256π square inches B. 8π square inches C. 64π square inches D. 16π square inches

QUESTION POSTED AT 14/01/2020 - 03:05 PM

Answered by admin AT 14/01/2020 - 03:05 PM

D/2=r
area=pir^2
d=8
8/2=4=r
area=pi4^2
aera=16pi
answer is D
Post your answer

Related questions

What is the greatest possible error when measuring to the nearest quarter of an inch?

Using a scale that has increments that are somewhat large, you could get an error if you reach half of the measuring unit. This is because when you arrive at a measurement greater than half of the measuring unit, you would have to round it up. Therefore, the greatest possible error when measuring to the nearest quarter of an inch is 1/8 inch.

ANSWERED AT 21/01/2020 - 10:45 AM


QUESTION POSTED AT 21/01/2020 - 10:45 AM

Ethan is using his compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is he in the process of constructing?. . A circle with a diameter is drawn with two arc markings shown.. . An equilateral triangle. . A square. . A regular pentagon. . A regular hexagon

Answer:

I'm doing the test the correct answer is he is making a square

Step-by-step explanation:

you can look at it and see that hes making a square because the square is the only one with the line through the center of the circle

ANSWERED AT 21/01/2020 - 10:44 AM


QUESTION POSTED AT 21/01/2020 - 10:44 AM

Which of the following best describes a square?. A.A square is equilateral.. B.A square is equiangular.. C.A square is equiangular and equilateral.. D.A square is a parallelogram.

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we know that

A square is a quadrilateral whose all sides are equal and all angles are equal too.

So, A square is equilateral.

A square is equiangular both.

Since a square is also a parallelogram.

But we need the statement which best describes a square.

So, Option 'c' is correct., i.e. A square is equiangular and equilateral.

ANSWERED AT 21/01/2020 - 10:39 AM


QUESTION POSTED AT 21/01/2020 - 10:39 AM

Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that particular vanilla powder has a mass of 128 grams. He added two over three of a cup of vanilla powder to the flour. Should Jeff add more vanilla powder to make the exact recipe or did he go over and by what amount?

The situation above described that Jeff added two - thirds of 128 to the flour. The numerical value of (2/3)(128) is 85.33 grams. The recipe says to add only 32 grams of vanilla powder. Hence, Jeff went over the prescribed amount.

To determine the excess amount, subtract 32 from 85.33 which has a numerical value of 53.33 grams. 

ANSWERED AT 21/01/2020 - 10:38 AM


QUESTION POSTED AT 21/01/2020 - 10:38 AM

. What is the distance from axis about which a uniform, balsa-wood sphere will have the same moment of inertia as does a thin-walled, hollow, lead sphere of the same mass and radius R, with the axis along a diameter, to the center of the balsa-wood sphere?

Parallel axis thm says that about a point of rotation not the center of mass a distance d away from the center of mass

I=Icm+Md^2

For a hollow lead sphere

IH=2/3MR^2

and the moment of inertia about the center of mass for the balsa sphere is

Icm=2/5MR^2

So to set them equal to each other

IH=Icm+Md^2

2/3MR^2=2/5MR^2+Md^2

M(2/3R^2)=M(2/5R^2+d^2)

cancel out the M

d^2=(2/32/5)R^2
answer is 
 \sqrt{4/15}


ANSWERED AT 21/01/2020 - 10:37 AM


QUESTION POSTED AT 21/01/2020 - 10:37 AM

Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?. . [1 foot = 12 inches; 1 yard = 3 feet]. a. 0.5 feet. b. 1.5 feet. c. 3 feet. d. 6 feet

Convert first the cost of $98 /yd³ by the conversion factor that 1 yd³ = 27 ft³.
                           ($98 /yd³) (1 yd³ / 27 ft³) = $ 3 17/27/ft³
Let x be the width, the volume of the rectangular portion of the driveway is,
                           V = (8 ft) (1/3 ft) x = 8x/3 ft³
Using the given total cost of the protion,
                                  C = $58.07 = (8x/3 ft³)($ 3 17/27/ft³) 
x = 5.99957 ft
Thus, the answer is d. 6 feet.

ANSWERED AT 21/01/2020 - 10:36 AM


QUESTION POSTED AT 21/01/2020 - 10:36 AM

. A lizard needs to stay a safe distance from a cactus. The diameter of the cactus is 14 inches. If the lizard is 8 inches from a point of tangency, find the direct distance between the lizard and the cactus (x). If necessary, round to the hundredths place.. . A.. x = 3.63 in.. B.. x = 4.57 in.. C.. x = 7.26 in.. D.. x = 17.63 in..

We will use Pythagorean theorem:
x - The direct distance between the lizard and the cactus;
r = 7 - radius of the cactus;
x + 7 - the distance between the lizard and the center of the cactus:
( x + 7 )² = 7²  + 8²
( x + 7)² = 49 + 64
( x + 7 )² = 113
x + 7 = √ 113 
x + 7 = 10.63
x = 10.63 - 7
x = 3.63
Answer: A)  

ANSWERED AT 21/01/2020 - 10:35 AM


QUESTION POSTED AT 21/01/2020 - 10:35 AM

You are asked to build an open cylindrical can with volume 180.5 cubic inches. You will cut the bottom from a square of metal and form the curved side by bending a rectangular sheet of metal. . . Find the exact value of the radius and height of the can that will minimize the total amount of material required for the square and the rectangle.

The volume of cylinder is

 V=\pi r^2h=180.5.

Express h from this expresiion:

 h=\dfrac{180.5}{\pi r^2}.

The full surface area of this cylinder is

 A=2\pi r^2+2\pi rh.

Then in terms of r the area is

 A(r)=2\pi r^2+2\pi r\cdot \dfrac{180.5}{\pi r^2}=2\pi r^2+\dfrac{361}{r}.

Find the derivative  \dfrac{dA}{dr}:

 \dfrac{dA}{dr} =4\pi r-\dfrac{361}{r^2}.

Equate  \dfrac{dA}{dr} to zero:

 4\pi r-\dfrac{361}{r^2}=0,\\ \\4\pi r^3=361,\\ \\ r=\sqrt[3]{\dfrac{361}{4\pi}} \approx 28.74.

When  r<\sqrt[3]{\dfrac{361}{4\pi}}, the derivative   \dfrac{dA}{dr} is <0 (area is decreasing) and when  r>\sqrt[3]{\dfrac{361}{4\pi}}, the derivative   \dfrac{dA}{dr} is >0 (area is increasing). This means that   r=\sqrt[3]{\dfrac{361}{4\pi}} is point of minimum.

Thus,

 h=\dfrac{180.5}{\pi r^2}=\dfrac{180.5}{\pi (\sqrt[3]{\dfrac{361}{4\pi}})^2}\approx 6.13.

Answer: the approximate values: r≈28.74 in, h≈6.13 in. and the exact values:  

 r=\sqrt[3]{\dfrac{361}{4\pi}} in,

 h=\dfrac{180.5}{\pi (\sqrt[3]{\dfrac{361}{4\pi}})^2} in.

ANSWERED AT 21/01/2020 - 10:32 AM


QUESTION POSTED AT 21/01/2020 - 10:32 AM

A team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. The team then measured the distance the wheel had rolled and found it to be 35 cm. To the nearest tenth, what is the area of the wheel?. . 97.5 cm2. 195.1 cm2. 27.5 cm2. 390.1 cm2.

Circumference of the wheel in question = 35 cm
As the wheel is a circle, so
Circumference of the wheel = 2 * (pi) * (radius)
35 = 2 * (pi) * (radius)
Then
Radius = 35/2(pi)
Area of the wheel = (pi) * (radius) ^2
                             = (pi) * [35/2(pi)]^2
                             = (35)^2/4(pi)
                             = 1225/(4 * 3.14159)
                             = 1225/12.56636
                             = 97.48 cm^2
                             = 97.5 cm^2
The correct option among all the options that are given in the question is the first option.

ANSWERED AT 21/01/2020 - 10:32 AM


QUESTION POSTED AT 21/01/2020 - 10:32 AM

Which of the following is not required when factoring a difference of perfect squares?. A.. the polynomial contains two terms. B.. the polynomial's terms are perfect squares. C.. the polynomial's terms are being subtracted. D.. the polynomial is a perfect square trinomial

D. The polynomial is a perfect square trinomial. This is not a requirement for a given polynomial in factoring a difference of perfect squares.

ANSWERED AT 21/01/2020 - 10:30 AM


QUESTION POSTED AT 21/01/2020 - 10:30 AM

In order to apply the law of cosines to find the measure of an interior angle, it is enough to know...?. . A. The lengths of all three sides of the triangle.. B. The area of the triangle. C. At least two of the angles of the triangle and the length of one of its sides.

The correct answer is option A. Law of cosines is expressed as a^2=b^2+c^2−2bccosA. To be able to use this expression to find the interior angle, we need to know the lengths of all three sides of the triangle.

ANSWERED AT 21/01/2020 - 10:28 AM


QUESTION POSTED AT 21/01/2020 - 10:28 AM

The diagonal of a TV is 30 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the TV?. A. 15 inches by 15/3 inches. B. 15/2 inches by 15/2 inches . C. 60 inches by 60/3 inches . D. 60/2 inches by 60/2 inches

Let

x-------> the length of the rectangle

y------> the width of the rectangle

d----> the diagonal of the rectangle

we know that

The diagonal forms a pair of 30-60-90 right triangles

Step 1

Find the value of y

sin(30)=\frac{y}{d}

Solve for y

y=sin(30)*d

we have

sin(30)=\frac{1}{2}\\\\d=30\ in

substitute

y=\frac{1}{2} *30=15\ in

Step 2

Find the value of x

cos(30)=\frac{x}{d}

Solve for x

x=cos(30)*d

we have

cos(30)=\frac{\sqrt{3}}{2}\\\\d=30\ in

substitute

x=\frac{\sqrt{3}}{2}*30=15\sqrt{3}\ in

therefore

the answer is

15\ inches by 15\sqrt{3}\ inches


ANSWERED AT 21/01/2020 - 10:28 AM


QUESTION POSTED AT 21/01/2020 - 10:28 AM

A rectangle has an area of 96 sq ft if the width of the yard is 4 ft less than the length, what is the perimeter in ft of the yard?

The area of a rectangle is obtained through the equation,
  
                                  A = L x W 

The width of the yard is 4 ft less than the length and may be expressed as L - 4. Length may be solved through the following steps,
   
                               A = (L)(L-4)   ; 96 = L(L - 4)    ; L = 12 ft

The length and width are 12 ft and 8 ft, respectively. Perimeter may be solved through the equation,
 
                                           P = 2 x (L + W)

Substituting the values of L and W
 
                                           P = 2 x ( 12 ft + 8 ft) = 40 ft

Therefore, the perimeter of the yard is 40 ft. 




ANSWERED AT 21/01/2020 - 10:28 AM


QUESTION POSTED AT 21/01/2020 - 10:28 AM

Find cot θ if csc θ = square root of seventeen divided by four and tan θ > 0

We know that cosecant theta is hypotenus over opposite of a triangle. We are given that this value is equal to (√17)/4 so 4 is the opposite side of theta. Cotangent theta is the adjacent over opposite. We use the pythagorean theorem to find for the adjacent side.
a = √17 - 4^2
a = 1

Therefore, cotangent of theta is equal to 1/4.

ANSWERED AT 21/01/2020 - 10:26 AM


QUESTION POSTED AT 21/01/2020 - 10:26 AM

How many 2-inch segments are there in 12 ft.? a. 10 b. 24 c. 6 d. 72

Every foot is composed of 12 inches. Below is the way to solve the number of inches (n) in 12 ft.
 
                                     n = (12 ft) x (12 inches / 1 ft) = 144 inches

To determine the number of 2-inch segments, divide 144 inches by 2. The division gives an answer of 72. Thus, there are 72 2-inch segment in 12 ft. 
                                          

ANSWERED AT 21/01/2020 - 10:23 AM


QUESTION POSTED AT 21/01/2020 - 10:23 AM

Ruby red paint costs $0.50 per square inch. A ball is painted ruby red and costs $100.00 to paint. What is the diameter of the ball? Round to the nearest tenth of an inch.. A.4.0 in.. B.5.6 in.. C.8.0 in.. D.16.0 in.

Answer:

Option C is the answer.

Step-by-step explanation:

A ball is painted ruby red and costs $100.00 to paint and Ruby red paint costs $0.50 per square inch.

This means for an area of 4\pi r^{2}, $100 were used. 4\pi r^{2} because the ball is a sphere.

where r is the radius.

We know that , Area of ball * cost of paint per square inch = total cost of paint.

4\pi r^{2} \times0.5=100

2\pi r^{2}=100

r^{2}= \frac{100}{2\pi }

r^{2}=15.923 ; r=3.99 inch

Radius is 3.99 inches. or we can round this to 4 inches.

Hence, the diameter will be = 2\times4=8 inches.

Therefore, option C: 8 inches is the answer.

ANSWERED AT 21/01/2020 - 10:16 AM


QUESTION POSTED AT 21/01/2020 - 10:16 AM

Susan wrote the following statements:. . Statement 1: If two angles form a linear pair, then they are supplementary angles.. . Statement 2: If two lines intersect in one point, then exactly one plane contains both lines.. . Which geometry term does each statement represent?. . Statement 1: theorem; Statement 2: postulate. . Statement 1: definition; Statement 2: postulate. . Statement 1: theorem; Statement 2: definition.. . Statement 1: postulate; Statement 2: theorem

A theorem is considered to be a statement that is demonstrated to be correct by approved mathematical arguments and operations. Postulates or axioms as it is sometimes called, is considered to be true even without proof. Given these information, statement 1 is a theorem and statement 2 is a postulate. 

ANSWERED AT 21/01/2020 - 10:15 AM


QUESTION POSTED AT 21/01/2020 - 10:15 AM

Renee can sew a 25-square-foot quilt in 16 hours. Genera can sew the same size quilt in 12 hours. How long would it take them to sew the quilt working together?

First let us say that if a 25-square-foot quilt is done that is counted as 1 job. So the rate of Renee is 1 job/16 hours. The rate of Genera is 1/12. To solve the time to finish one job when both are working, we represent it with an algebraic expression as follows: 

 \frac{1}{16} + \frac{1}{12} = \frac{1}{x}

Then x = 6 6/7 hours. 

ANSWERED AT 21/01/2020 - 10:14 AM


QUESTION POSTED AT 21/01/2020 - 10:14 AM

A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches and a height of 5 inches. Are the volumes the same?. A.. Yes, because the heights are equal and the cross-sectional areas at every level parallel to the bases are also equal.. B.. Yes, because the figures are congruent.. C.. No, because the cross-sectional areas are not the same.. D.. No, because only the bases have the same area, not every cross section at every level parallel to the bases.. .

Given the values of the dimensions of the two prisms, the volumes are the same. Among the choices, the correct answer is A. "Yes, because the heights are equal and the cross-sectional areas at every level parallel to the bases are also equal." The volumes of both prisms can be solved by multiplying the cross-sectional area and the height. Solving both volumes would equate to a volume of 180 in^3.

ANSWERED AT 21/01/2020 - 10:13 AM


QUESTION POSTED AT 21/01/2020 - 10:13 AM

What is the greatest possible integer value of x for which square root of √x-5 is an imaginary number

The correct answer for this question is 4.

We have to bear in mind that any number  should be less than 5 to make the square root be an imaginary number.
Starting with 4
= square root (4 - 5)
= square root (-1)
= imaginary 

ANSWERED AT 21/01/2020 - 10:12 AM


QUESTION POSTED AT 21/01/2020 - 10:12 AM

A cone has a volume of 5 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?. . a. 15 in3. b. 20 in3. c. 25 in3. d. 30 in3

Volume of a cone: (1/3)*(PI)*(r^2)*h
5=(1/3)*(PI)*(r^2)*h
(r^2)*h=4.774648
Volume of the cylinder outside the cone: (PI)*(r^2)*h
V=(PI)*4.774648
V=15 in3

The answer is A. 15 in3

ANSWERED AT 21/01/2020 - 10:10 AM


QUESTION POSTED AT 21/01/2020 - 10:10 AM

Find the domain of f(x) = the square root of square of the quantity x plus 2.

What are the answer choices?

ANSWERED AT 21/01/2020 - 09:48 AM


QUESTION POSTED AT 21/01/2020 - 09:48 AM

Show and explain the theoretical probability of a player WINNING your probability game. for a spinner that has 8 sides (1-8) rules for the game so u know how to answer my question : Using a spinner and a coin. 2 players can play this game. So, the first person can spin the spinner and see where it lands on. The second person can start flipping the coin while the spinner is spinning, also see what sides it could land on ( HEADS or TAILS ). If the coin lands on heads, player 1 has a chance to gain or lose points in the round. If the coin lands on tails, player 2 has a chance. The player in focus then has 2 choices; they can flip the coin a second time or spin the spinner a second time. If they choose to flip a coin, they have to predict whether they think the coin will land on heads or tails. If they are correct, they gain the number of points showing on the spinner. If they are wrong, they lose that number of points. If they choose to re-spin the spinner, their goal is to beat the score of the first spin. If they do, they gain the difference in the points (for example: spin 1 lands on 2, spin 2 lands on 5; 5-2 = 3 points). If they spin a lower number, they lose the difference in points (example: spin 1 gets a 3, spin 2 gets a 1; 3-1 = 2 points lost) *If the spinner happens to land on the exact same number, the opponent gets 5 points. The first player to earn 40-points wins! BEST OF LUCK and have FUN !!! ^_~ !!!

You have a 1/2 chance of winning points on the flipping of the coin and a 36/64 chance of winning on the spinner. I got the coin because there's a half chance of guessing the side right and I got the spinner by drawing a two-way diagram.

ANSWERED AT 21/01/2020 - 09:39 AM


QUESTION POSTED AT 21/01/2020 - 09:39 AM

The base of a triangle is decreasing at the rate of 1 ft/sec, while the height is increasing at the rate of 2 ft/sec. At what rate is the area of the triangle changing when the base is 10 ft and the height is 70 ft? Remember to use the product rule when you find the expression for dA, dt.

We are given with the rate of change of the base, db/dt equal to 1 ft/ sec and the rate of change of the height of the triangle, dh/dt equal to 2 ft/sec. b is 10 ft and h is 70 ft. Area of triangle is equal to A= 0.5 bh The rate of change of the area is equal to dA/dt = 0.5 b dh/dt + 0.5 h db/dt. Substituting, dA= 0.5*10*2 + 0.5*70 * 1 equal to 45 ft2 / sec.

ANSWERED AT 21/01/2020 - 09:37 AM


QUESTION POSTED AT 21/01/2020 - 09:37 AM

Which best describes the dimensions of a plane a.A plane has zero dimensions because it represents a location on the coordinate plane. b.A plane has one dimension because it is made up of an infinite number of points. c.A plane has two dimensions because it is a flat surface that has length and width but no depth. d.A plane has three dimensions because it is made up of exactly three noncollinear points.

Wellll, hold up there for just a second. 

"A plane" is infinite.  Whatever direction you pick in "a plane",
the plane keeps going in that direction forever and never ends.
So "a plane" has NO dimensions.

Any PART of "a plane" has TWO dimensions, because any PART
of it that you pick occupies some length and some width.

A better way to say it is like this:

If you stick a nail into the plane at one point, THEN, to describe ANY
OTHER point in the plane relative to the nail, you need TWO NUMBERS.

THAT's why a line has one dimension, a plane has two, and a solid has
three dimensions ... it's how many numbers you need if you want to
send somebody to another point from where you're sitting.

ANSWERED AT 21/01/2020 - 09:37 AM


QUESTION POSTED AT 21/01/2020 - 09:37 AM

Two boys are throwing baseball back and forth the ball is 4 ft above ground when it leaves one child's hand with an upward velocity of 36 ft/s. If acceleration due to gravity is -16 ft/s squared how high above ground is the ball 2 seconds after it is thrown

If the ball is launched from 4 ft above the ground with an upward velocity
of 36 ft/s, and the acceleration due to gravity is -16 ft/s², then at any time
't' seconds after launch, its height above the ground is

                                   H  =  -8 t²  +  36 t  +  4 .

After 2 seconds,           H  =  -8(2)² + 36(2) + 4

                                       =  -32     + (72)   + 4

                                       =         44 feet above the ground .
_____________________________________________

Now, if the boys were to move their game to the Earth, where
the acceleration due to gravity is  32 ft/s²  instead of  16 ft/s² ,
the ball's behavior would be noticeably different.  Two seconds
after the same launch on Earth, the height of the ball would be    

                              H  =  -16 t²  +  36 t  +  4 .

                                  =  -16(2)² + 36(2) + 4

                                  =     -64   +   72    + 4

                                  =            12 feet above the ground

ANSWERED AT 21/01/2020 - 09:23 AM


QUESTION POSTED AT 21/01/2020 - 09:23 AM