A square based prism and a cylinder both have the same height of 4cm and the same base area. If the volume of the square based prism is 452cm cubed based on the concepts of Cavalieri's principle, what is the approximate circumference of the base of the cylinder?

Answer:

y = 2x -4

Step-by-step explanation:

2y = 4x - 8

Divide each side by 2

2y/2 = 4x/2 - 8/2

y = 2x -4

Answer:

The answer is "25 ml".

Step-by-step explanation:

Dose[tex]= 500 \ mg\\\\[/tex]

Solution [tex]= 100\ \frac{mg}{teaspoonful}\\\\[/tex]

Calculating the Conversions:

Teaspoonful [tex]= 5 \ ml \ \text{(Ounce = 30 ml = 6 Tablespoonsful)}[/tex]

[tex]\therefore\\\\Solution = \frac{100\ mg}{ 5\ ml} = 20\ \frac{mg}{ml}\\\\Dose \ volume = \frac{500\ mg}{ 20\ \frac{mg}{ml}} = 25\ ml[/tex]

Answer:

SA=2πrh+2πr2=2·π·12·3+2·π·122≈282.7cm2

Answer: l,j,k

Step-by-step explanation:

Answer:

Jackie: 11

Paula: 19

Step-by-step explanation:

11+19 = 30

Answer:

"97" is the appropriate answer.

Step-by-step explanation:

Given:

Number of trees,

= 485

Orchards of trees,

= 5

The number of trees in each orchard will be:

= [tex]\frac{Number \ of \ trees}{Orchards \ of \ trees}[/tex]

= [tex]\frac{485}{5}[/tex]

= [tex]97[/tex]

Answer:

17.y=-x+12

18.y=-1/4x+7

Step-by-step explanation:

17.a Solve for y (y=-5+x)

17. b Reciprocal (y=-1x-5)

17. c Subsitute equation into (8,-1) (-1=-13=y=x+12)

18.a Subtract y values and x values= (6-4)/(4-12)=2/-8=-1/4, this will be your slope

18. b Plug in -1/4 into either of the two ordered pairs to find y value=(12,4)=(4=-3)=y value=7.

18. c=y=-1/4x+7

Answer:

6.75x + 5.50y = 186.75

Step-by-step explanation:

The stuffed mushrooms cost 6.75 dollars and the tomato bread costs 5.50 dollars.

Answer:

186.75

Step-by-step explanation:

6.75x+5.50y=186.75

Answer:

66%

Step-by-step explanation:

[tex]-10x\:+\:\left(20\cdot \left(1-x\right)\right)=\:0[/tex]

x = [tex]\frac{2}{3}[/tex] = .666 = 66%

Given:

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]              ...(i)

Surface area of a sphere:

[tex]A=4\pi r^2[/tex]                      ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is [tex]\dfrac{28}{3}[/tex] times the surface area.

[tex]V=\dfrac{28}{3}\times A[/tex]

[tex]\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2[/tex]

Multiply both sides by 3.

[tex]4\pi r^3=112\pi r^2[/tex]

[tex]\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}[/tex]

[tex]r=28[/tex]

Using (i), the volume of the sphere is:

[tex]V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3[/tex]

[tex]V\approx 91989[/tex]

Using (ii), the surface area of the sphere is:

[tex]A=4\times \dfrac{22}{7}\times (28)^2[/tex]

[tex]A=9856[/tex]

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.

Explanation

a sanwich which is most commonly a square, has the side lengths of 5 and 5.

cuting this in half will give you a 45-45-90 triangle

the legs will be measure of x, and the hypotonuse will be x[tex]\sqrt{2}[/tex]

so the hypotonuse is  5[tex]\sqrt{2}[/tex]

The diagonal length of the sandwich after it is cut in half is approximately 6.106 inches.

Using the Pythagorean theorem, we can calculate the diagonal length as follows:

diagonal² = length² + height²

diagonal² = (5 inches)² + (3.5 inches)²

diagonal² = 37.25 inches²

Taking the square root of both sides, we find:

diagonal = √37.25 inches

Calculating the square root of 37.25, we get:

diagonal ≈ 6.106 inches

Therefore, the diagonal length of the sandwich after it is cut in half is approximately 6.106 inches.

Learn more about length

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Answer:

Option D, 52

Answered by GAUTHMATH

Answer:

15x^9

Step-by-step explanation:

A=l x w

5x^4 times 3x^5 is basically 3*5*x^4*x^5

when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9

Answer:

Step-by-step explanation:

The angle bisector of a triangle divides the opposite side in 2 segments that are proportional to the other 2 sides of the triangle. Namely:

[tex]\frac{15}{18}=\frac{w}{30}[/tex] and cross multiply.

18w = 450 so

w = 25

Answer:

C. Kiometers per hour. I think

Answer:

C is correct

Step-by-step explanation:

a is wrong because: 1*-1*-1*-1 =1

b) 1*1*1*1 =1

d) 1*-1*1*1 =1

only c 1*-1*-1*1 =-1 at the end of polynomial

Answer:

-60

Step-by-step explanation:

Answer:

The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.

Answer:

try 14n

Step-by-step explanation:

Answer:

[tex]r \: = 2sin2 \theta \\ = > r = 2.2sin\theta.cos\theta \\ = > r = 4sin\theta.cos\theta \: \\ \\ \sf \: we \: know \: that \: \\ x = r \: cos\theta \: \therefore \: cos\theta = \frac{x}{r} \\ \\ y = r \: sin\theta \: \therefore \: sin\theta = \frac{y}{r} \\ \\ \sf \: now \\ \\ r = 4 \times \frac{y}{r} \times \frac{x}{r} \\ = > {r}^{3 } = 4xy \\ \\ \sf \: again \: \: r = \sqrt{ {x}^{2} + {y}^{2} } \\ \\ = > {( \sqrt{ {x}^{2} + {y}^{2} } })^{3} = 4xy \\ = > {( {x}^{2} + {y}^{2} })^{ \frac{3}{2} } = 4xy \\ = > {( {x}^{2} + {y}^{2} })^{3} = 16 {x}^{2} {y}^{2} [/tex]

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Answer:

[tex]\sqrt[2]{8}[/tex]

Step-by-step explanation:

Remember the basic format of a fraction raised to a fractional exponent:

[tex]a^\frac{b}{c}=\sqrt[b]{a^c}[/tex]

Some terms to keep in mind are the following:

(a) is the base

(c) is the exponent

(b) is the index

Apply this information to the given problem:

[tex]2^\frac{3}{2}[/tex]

In this case, (2) is the base, and the index; (3) is the exponent. Apply the general format of the fraction exponent to change the expression from an exponent to a radical.

[tex]2^\frac{3}{2}=\sqrt[2]{2^3}[/tex]

Simplify the term under the radical:

[tex]\sqrt[2]{2^3}=\sqrt[2]{8}[/tex]

9514 1404 393

Answer:

  5/3 meters

Step-by-step explanation:

The area is the square of the side length, so the side length is the square root of the area.

  s = √(225/81) = 15/9 = 5/3 . . . meters

The length of a side of the table is 5/3 meters.

Answer:

V = 276.32 ft^3

Step-by-step explanation:

Volume of a cylinder is

V = pi r^2 h

The diameter is 4 so the radius is d/2 = 4/2 = 2

V = (3.14) ( 2)^2 * 22

V = 276.32 ft^3

Answer:

Total number of students in the college = 200 student

Step-by-step explanation:

Given:

Number of student make dean's list = 67 student

Percentage of student make dean's list = 33.5% of all student

Find:

Total number of students in the college

Computation:

Total number of students in the college = Number of student make dean's list / Percentage of student make dean's list

Total number of students in the college = 67 / 33.5%

Total number of students in the college = 67 / 0.335

Total number of students in the college = 200 student

Answer:100

Step-by-step explanation:

Given

Last year 160 new candidates submitted to work for agency

It is expected to increase by 25% that is , increase in one year should be

[tex]\Rightarrow 160+160\times 25\%\\\Rightarrow 160(1+0.25)\\\Rightarrow 160\times 1.25\\\Rightarrow 200[/tex]

200 application in the upcoming year. So, in 6 months, agency must have accepted 100 applications.

Answer: 56

Step-by-step explanation:

Let x be the number that is supposed to be subtracted from 61.

Given

61 - x = 5

Add both sides by x

61 - x + x = 5 + x

61 = 5 + x

Subtract 5 on both sides

61 - 5 = 5 + x - 5

x = 56

Hope this helps!! :)

Please let me know if you have any questions

Answer:

The volume of the cube is 21952.

Step-by-step explanation:

V = L x W x H

because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:

V= S^3

(S standing for side)

we know the height is 28 and as all sides measure the same we use the equation:

V= 28^3

28^3 = 21952

So, V= 21952

Answer:

The equation is true.

Step-by-step explanation:

In order to solve this problem, one must envision a right triangle. A diagram used to represent the imagined right triangle is included at the bottom of this explanation.  Please note that each side is named with respect to the angle is it across from.

Right angle trigonometry is composed of a sequence of ratios that relate the sides and angles of a right triangle. These ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

One is given the following equation,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

As per the attached reference image, one can state the following, using the right angle trigonometric ratios,

[tex]sin(A)=\frac{a}{c}\\\\sin(B)=\frac{b}{c}\\\\cos(A)=\frac{b}{c}\\\\cos(B)=\frac{a}{c}[/tex]

Substitute these values into the given equation. Then simplify the equation to prove the idenity,

[tex]\frac{sin(A)+sin(B)}{cos(A) +cos(B)}+\frac{cos(A)-cos(B)}{sin(A)-sin(B)}=0[/tex]

[tex]\frac{\frac{a}{c}+\frac{b}{c}}{\frac{b}{c}+\frac{a}{c}}+\frac{\frac{b}{c}-\frac{a}{c}}{\frac{a}{c}-\frac{b}{c}}=0[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

Remember, any number over itself equals one, this holds true even for fractions with fractions in the numerator (value on top of the fraction bar) and denominator (value under the fraction bar).

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{b-a}{c}}{\frac{a-b}{c}}[/tex]

[tex]\frac{\frac{a+b}{c}}{\frac{a+b}{c}}+\frac{\frac{-(a-b)}{c}}{\frac{a-b}{c}}[/tex]

[tex]1+(-1)=0[/tex]

[tex]1-1=0[/tex]

[tex]0=0[/tex]

Answer:

you can plug it back into the original equation to see if it fits the solution. if not then you have another solution you need to solve for.

Answer:

if we're talking on linear equations, then the two equations would intersect at one point. or when you solve it, it'll be only 1 number that can fit that equation.

p.s.: sub to #gauthmath# sub reddit if ya can ^^

Answer:

sorry I don't know

sorry I Don't know

Answer:

DE=27

EF=13

DG=13

GF=27

Step-by-step explanation:

12x+3=5x+17

12x-5x=17-3

u'll get 14 then simply it by the numbe of X u'll get 2 then replace the X with the number