Find the height in centimeters of a square pyramid with a volume of 72cm^ 3 and a base edge length equal to the height

Answers

Answer 1

Answer:

The height of the pyramid is 6 cm.

Step-by-step explanation:

The volume of a square pyramid is given by:

[tex] V = \frac{1}{3}A_{b}h = 72 cm^{3} [/tex]

Where:

[tex]A_{b}[/tex]: is the area of the base

h: is the height

Since the base edge length is equal to the height, the area of the base is:

[tex]A_{b} = l^{2} = h^{2} [/tex]

Hence, the height is:

[tex] 72 cm^{3} = \frac{1}{3}A_{b}h = \frac{1}{3}h^{2}h [/tex]

[tex] h = (3*72 cm^{3})^{1/3} = 6 cm [/tex]

Therefore, the height of the pyramid is 6 cm.

I hope it helps you!          


Related Questions

A company rents water tanks shaped like cylinders. Each tank has a radius of 6 feet and a height of 2 feet. The cost is $30 per cubic foot. How much does it cost to rent one water tank

Answers

Plug the numbers into the formula of pi x the radius^2 times the height. This will give you pi x 36 x 2 or 72 pi. Multiply 72 by 3.14 and then multiply it by 30. This gives a cost of $6,782.40 to rent one water tank

Step-by-step explanation:

Volume of tank = (pi)×(radius squared)×(height)

= 3.14×(6×6)×2

= 3.14×36×2

= 226.08 cu.ft

Each cu.ft is rented for $30

So, for 226.08 cu.ft is,

=226.08×$30

=$6782.3

What is the simplified form of the complex fraction? 2x2+7x+6x2+x−64x2−9x2−5x+6

Answers

Answer:

3x - 124

Step-by-step explanation:

kindly find solutions in the picture above

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is

-65x² + 2x + 6

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6

Combine all like terms.

(2x² + 6x² - 64x² - 9x²) + (7x - 5x) + 6

(8x² - 73x²) + 2x + 6

-65x² + 2x + 6

There are no common factors or like-terms to simplify.

So,

The simplified form is -65x² + 2x + 6

Thus,

The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is

-65x² + 2x + 6

Learn more about expressions here:

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Căn 84 bình phương trừ 37 bình phương chia 47

Answers

Answer:

[tex]\sqrt{84^{2} } -37^{2} /47[/tex]=257 9/47

Step-by-step explanation:

Sue has 3 cats. Each cat eats 1 4 of a tin of cat food each day. Sue buys 4 tins of cat food. Has Sue bought enough cat food to feed her cats for 5 days? You must show how you get your answer

Answers

Answer:

3 3/4 tins of food

Step-by-step explanation:

Number of cats = 3

Quantity of food for each cat per day = 1/4 of a tin

Total tins of cat food sue bought = 4 tins

Has Sue bought enough cat food to feed her cats for 5 days?

Quantity of food 3 cats eat per day = Quantity of food for each cat per day × Number of cats

= 1/4 × 3

= 3/4 of a tin

Total Quantity of food 3 cats eat for 5 days = Quantity of food 3 cats eat per day × 5 days

= 3/4 × 5

= (3 * 5) / 4

= 15/4

= 3 3/4 tins of food

Total Quantity of food 3 cats eat for 5 days = 3 3/4 tins of food

Recall,

Total tins of cat food sue bought = 4 tins

Therefore, Sue bought enough cat food to feed her cats for 5 days

The length of a rectangular playing field is 5m longer than its width. If the perimeter of the field is 150m,find it's width​

Answers

Answer:

35

Step-by-step explanation:

Make equations, l = w+5 and 2l + 2w = 150

Substitute w+5 into 2l + 2w = 150

Simplify to get 4w + 10 = 150

Subtract 10 from both sides to get 4w = 140

Divide both sides by 4 and you get 35 as width

Answer:

The width of the field is 35 meters.

Step-by-step explanation:

Recall that the perimeter of a rectangle is given by:

[tex]\displaystyle P = 2(w+\ell)[/tex]

Where w is the width and l is the length of the rectangle.

We know that the perimeter is 150 meters. Thus:

[tex]150=2(w+\ell)[/tex]

Divide both sides by two:

[tex]75=w+\ell[/tex]

We are given that the length is five meters longer than the width. So:

[tex]\ell = w+5[/tex]

Substitute:

[tex]75=w+(w+5)[/tex]

Combine like terms:

[tex]75=2w+5[/tex]

Subtract five from both sides:

[tex]70=2w[/tex]

And divide both sides by two. Hence:

[tex]w=35[/tex]

Thus, the width of the rectangular field is 35 meters.

Using long division, what is the quotient of this expression?
X^4+4x^3-5x^2+x-3/x^2+x-3

Answers

Answer:

Using long division method the answer is B

Step-by-step explanation:

x²+3x-5+(15x-18)/x²+x-3

The histogram below represents a data distribution with uniform class
widths. Which of the following is the median of the data distribution?
6
5
4
3
2
1
9 10
A. 4
B. 6
C. 5
c
D. 7

Answers

Answer:

C. 5

Step-by-step explanation:

The given data can be presented as follows;

[tex]\begin{array}{ccc}x&&y\\2&\leftrightarrow &1\\3&\leftrightarrow &4\\4&\leftrightarrow &6\\5&\leftrightarrow &7\\6&\leftrightarrow &6\\7&\leftrightarrow &3\\8&\leftrightarrow &2\\9&\leftrightarrow &1\\10&\leftrightarrow &1\end{array}[/tex]

We find the sum of the data points as follows;

n = 1 + 4 + 6 + 7 + 6 + 3 + 2 + 1 + 1 = 31

The median will be located in the (n + 1)/2 th data point

Therefore the median is the (31 + 1)/2 = 16th data point

The sum of the first three bars on the histogram = 11

The sum of the first four bars on the histogram = 18

Therefore, the 16th data point is located in the fourth bar which has x value of 5

The median is therefore, C. 5

Instructions: Find the measure of the indicated angle to the nearest degree.
50
?
25

Answers

Answer:

theta = 30 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp side/ hypotenuse

sin theta = 25/50

sin theta = 1/2

Taking the inverse sin of each side

sin ^-1 (sin theta) = sin ^-1 (1/2)

theta =  sin ^-1 (1/2)

theta = 30 degrees

Help,anyone can help me do quetion,I will mark brainlest.​

Answers

5.

1m = 0.001 km

So, 1m² = 10^-6

Area = 5027 m² = 5027 × 10 ^-6 km²

6.

1mm = 0.1 cm

1mm² = 10^-2

Area = 210× 297 mm² =62370 mm² = 62370 ×10^-2 cm²

What is the distance between (4, -10) and (4,-4)?

Answers

Answer:

For x there is no distance since they are both for. For y, they are -6 apart.

Step-by-step explanation:

Answer:

Fox x Diya is no distance since they are both for they are six apart

Step-by-step explanation:

(4-10)

and= just opposite size (10- 4) .

10 -4 = 6 answer 6

and (4-4)

answer is

0

the answer is six apart

understand

Find the surface area of this cylinder.
Round to the nearest tenth.

r = 3 cm
3 cm
SA = [ ? ] cm2


PLEASE HELP

Answers

Formula for the surface area of a cylinder: 2 x pi x r^2 + 2 x pi x r x h

Radius (r) = 3

Height (h) = 3

2 x pi x 3^2 + 2 x pi x 3 x 3

2 x pi x 9 + 2 x pi x 9

18pi + 18pi

36pi = 113.1 cm^2

Hope this helps!

The surface area of the cylinder is 113.0973 square centimeter.

What is surface area of a geometric shape ?

The surface area of a solid object is a measure of the total area that the surface of the object occupies. The surface area can only be present in any three dimensional geometric shape.

How to find the surface area of the cylinder ?

The surface area of the cylinder is given by - 2*π*r*h + 2*π*r*r

where r is the radius of the cylinder and h is the height of the cylinder from its base.

In the given problem, r = 3cm and h = 3cm .

⇒ Surface area = 2*π*3*3 + 2*π*3*3 square centimeters.

= 36π = 113.0973 square centimeters.

∴ Surface area = 113.0973 square centimeters.

Thus the surface area of the cylinder is 113.0973 square centimeter.

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Express 3.023 in P form where p and q are integers and q= 0 D​

Answers

Given:

The number is 3.023.

To find:

The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].

Solution:

The given number is 3.023. It can be written as:

[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]

[tex]3.023=\dfrac{3023}{1000}[/tex]

It cannot be simplified further because 3023 and 1000  have no common factors.

Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].

When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. = StartRoot (x minus x) squared + (y minus (negative p)) squared EndRoot = StartRoot (x minus 0) squared + (y minus p) squared EndRoot The distance between the directrix and is set equal to the distance between the and the same point on the parabola.

Answers

Answer:

The answer is "A point on the parabola  and Focus".

Step-by-step explanation:

[tex]= \sqrt{(x - x)^2 + (y- (-p))^2} = \sqrt{(x-0)^2+ (y-p)^2} \\\\= \sqrt{(0)^2 + (y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= \sqrt{(y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= (y+p) = (x)+ (y-p) \\\\= y+p = x+ y-p \\\\=2p=x\\\\=x=2p[/tex]

Whenever the focus and also the guideline are utilized in determining the parabolic formula, two distances have indeed been equal.

The distance from the direction, as well as a parabolic point, was equal to the distance from the center to a parabolic point.

Answer:

The distance between the directrix and a point on the parabola is set equal to the distance between the focus and the same point on the parabola.

Step-by-step explanation:

Hope this helps! :)

SOMEONE HELP ME PLEASE

Answers

9514 1404 393

Answer:

  1/12

Step-by-step explanation:

The probability of any given outcome is the ratio of the number of ways that outcome can happen to the total number of outcomes.

  P(4) = 1/6 . . . . . roll = 4 is one of 6 possible outcomes

  P(odd) = 3/6 = 1/2 . . . . . of the 6 possible outcomes, 3 are odd

__

The two rolls of the die are presumed to be independent, so the probability of the two outcomes is the product of their individual probabilities.

  P(4 & odd) = (1/6)(1/2) = 1/12

HELP ASAPPP !
select the correct answer from each drop-down menu.​

Answers

Answer:

3.8; 4

Step-by-step explanation:

In this exercise, you're are required to find the missing values by performing some arithmetic calculations.

For the first part;

Let the missing value be X

Translating the word problem into an algebraic expression, we have;

[tex] X = 2000 * 1.9 * 10^{-6} [/tex]

[tex] X = 3.8 * 10^{-3} [/tex]

For the second part;

Let the missing value be Y.

[tex] 3.8 * 10^{-3} = Y * 9.5 * 10^{-4} [/tex]

[tex] X = \frac {3.8 * 10^{-3}}{9.5 * 10^{-4}} [/tex]

[tex] X = 4 [/tex]

Therefore, the complete sentence would be written as follows;

[tex] 3.8 * 10^{-3} [/tex] is 2000 times greater than [tex] 1.9 * 10^{-6} [/tex]. It is also 4 times greater than [tex] 9.5 * 10^{-4} [/tex]

find the value of x.
2+3
12
5
1.2
6.6
07
12

Answers

Answer:

x = 7

Step-by-step explanation:

The triangles are similar

12/8 = (x+3+5)/(x+3) cross multiply expressions

12x + 36 = 8x + 64

12x - 8x = 64 - 36

4x = 28 divide both sides by 4

x = 7

if 3x-4=2(y-2)
find x_y​

Answers

Answer:

x = 2y/3

y = 3x/2

Answer:

Step-by-step explanation:

Can you answer this math homework? Please!

Answers

Answer:

10 T Shirts to have 105 dollars

Step-by-step explanation:

[tex]10.5x = 7.5x + 30[/tex]

[tex]3x = 30[/tex]

[tex]x = 10[/tex]

mary has 17 m of rope. She wishes to cut it in three pieces so that she has 3 m more than amanda, and amanda has 2 m less than Sarah.

Answers

Answer:

Length of Sarah rope    = 6 m

Length of Amanda's rope  = 4 m

Length of Mary's rope  = 7 m

Step-by-step explanation:

Let the length of Sarah rope = x

Length of Amanda's rope= x - 2

Length of Mary's rope = (x - 2 ) + 3 = x - 2 + 3 = x + 1

Length of rope = 17 m

x + x - 2 + x + 1 = 17

Combine like terms

x + x + x - 2 + 1 = 17

       3x  - 1 = 17

Add 1 to both sides

3x = 17 + 1

3x = 18

Divide both sides by 3

x = 18/3

x = 6

Length of Sarah rope = x  = 6 m

Length of Amanda's rope= x - 2 = 6 - 2 = 4 m

Length of Mary's rope =   x + 1 = 6 + 1 = 7 m

Enter the coordinates of the point
on the unit circle at the given angle. 0°

Answers

The points are ( 1,0) (0,1) .

The coordinates of the point on the unit circle -The coordinates for the points lying on the unit circle and also on the axes are (1,0), (–1,0), (0,1), and (0,–1). These four points (called intercepts) are shown here. When you square each coordinate and add those values together, you get 1. They're the sine and cosine values of the most common acute-angle measures.

a.) We seek the coordinates on the unit circle that represent an angle of 0 degrees.

The points on the unit circle are often provided by,

( cosθ, sinθ )

In order to do so,

θ= 0

to acquire,

(cos(0),sin(0))

(1,0)

b. With regard to the location on the unit circle where the angle is 90 degrees,

We swap out

θ = 90

to acquire,

(cos(90),sin(90))

This is condensed to, (0,1)

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Answer: 1,0

is the actual answer

What is the area of this triangle

Answers

Answer:

17.5 units

Step-by-step explanation:

im not good at explaining sorry

Which of the following angles is coterminal with - 2pi/3

Answers

Answer:

[tex]\frac{2\pi }{3} +x=2\pi[/tex]

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

[tex]=\frac{4\pi }{3}[/tex]

[tex]OAmalOHopeO[/tex]

Mrs.Click has a strawberry patch in her garden. It's border is 4/5 meters wide and 3/2 meters long. What is the area of Mrs.Clicks Garden?

Answers

Answer

Mrs. Click's Garden is 6/5 or 1 1/5 square meters.

Explanation

Mrs. Click's has a rectangular garden. To find the area of a rectangle, you multiply the width by the length. To find the area of Mrs. Click's Garden, you multiply 4/5 by 3/2.

To multiply fractions, you multiply the numerator by the denominator.

4×3 is 12 and 5×2 is 10. You get the fraction 12/10, which can be simplified to 6/5, or 1 1/5.

Find sin R.
a. sin R= 29/21
b. sin R= 21/20
c. sin R= 20/29
d. sin R= 21/29

Answers

Answer:

sin R = 20 / 29

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin R = opp / hyp

sin R = 20 / 29

Guided Practice


Use the vertical motion formula h = –16t2 + vt + c.


A child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft. Substitute the values into the vertical motion formula and let h = 0. Use the quadratic formula to solve for t. How long is the ball in the air?


A.
0.8 s


B.
0.8 s or –0.2 s


C.
0.2 s

Answers

Answer:

t = -0.22secs and 0.85secs

Step-by-step explanation:

Given the expression

h = –16t² + vt + c.

If a child tosses a ball upward with a starting velocity of 10 ft/s from a height of 3 ft, then;

v = 10, c = 3

Since we are to let h = 0, then the equation becomes:

0 = –16t² + 10t + 3

Multiply through by a minus sign

16t² - 10t - 3 = 0

Factorize the reulting expression:

t = -(-10)±√(-10)²-4(16)(-3)/2(16)

t = 10±√100+192/32

t = 10±√292/32

t = 10±17.09/32

t = 10-17.09/32 and 10+17.09/32

t = -7.09/32 and 27.09/32

t = -0.22secs and 0.85secs

Answer:

0.8 s

Step-by-step explanation:

I got it right in grandpoint.

Pleasee help me with this!!

Answers

Answer:

#1 is f.

#2 is d.

#3 is a.

#4 is b.

#5 is c.

#6 is g.

#7 is e.

Step-by-step explanation:

The digit "9" is in the ten's place because it is two numbers/spaces left from the decimal. If you make all the other digits "0", you'll be left with a value of 90.

The digit "1" is in the one's place because it is one number/space left from the decimal. Applying the same concept of making all the other digits "0", you'll be left with a value of 1.

The type of digits to the right of the decimal, starting from left to right, are the tenths place, hundredths place, thousandths place, ten-thousandths place, and millionths. Remember and know those digit types based on their position away from the decimal. The value will be there for you to see afterward.

help me please to solve this 2 questions pleasee faster.. i will mark you as brainliest​

Answers

Answer:

1. x=72, y=, 108

2.x=30, y=72

Step-by-step explanation:

Brainliest please~

calculate the value of 120 is increased by 120%​

Answers

Answer:

144

Step-by-step explanation:

currect answer for simple question

Answer:

264

Step-by-step explanation:

First find the amount of increase

120 * 120%

120 * 1.2

144

Add this to 120

120 +144

264

20 POINTS AND BRAIN LIESTJ ulia s urveyed the pl ayers on her so ccer team to see how many hou rs each mem ber prac ticed during the week. Her data is shown in the histo gram.

A histogram titled Prac tice Time has number of hours on the x -axis and number of players on the y-axis. 0.1 to 0.5 hours is 5 players, 0.6 to 1: 6, 1.1 to 1.5: 5, 1.6 to 2: 2, 2.1 to 2.5: 1, 2.6 to 3: 2, 3.1 to 3.5: 2, 3.6 to 4: 1, 4.1 to 4.5: 1.

Which of the following best describes the histogram?
The histogram is evenly distributed.
The histogram is symmetrical.
The left side of the histogram has a cluster.
The left side of the histogram is the mirror image of the right side.

Answers

Answer:

the left side of the histogram is the mirror image of the right side.

1/x^-2 x=7 yeet yeet

Answers

Answer:

49

Step-by-step explanation:

x = 7

1 / x^-2

= x^2

= 7^2

= 49

Answer: 49

Step-by-step explanation: yeet

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