A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot.

Please explain how to solve this problem, not just the answer.

Answers

Answer 1

The area of the square pyramid building is the amount of space on it

The maximum base length of the building is 67.42 cm

How to determine the maximum side length?

The given parameters are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b^2

The total surface area is calculated using:

T = L + b^2

So, we have:

T = 10b^2 + b^2

Evaluate the sum

T = 11b^2

The maximum surface area is 50,000 square feet

So, we have:

11b^2 = 50000

Divide both sides by 11

b^2 = 50000/11

Take the square root of both sides

b = 67.42

Hence, the maximum base length of the building is 67.42 cm

Read more about square pyramids at:

https://brainly.com/question/27226486

Answer 2

Answer: 71 feet

Step-by-step explanation:

Let's assume that the side length of the base of the square pyramid is x. Then, the slant height of the pyramid would be 5x, as given in the problem.


The lateral surface area of a square pyramid can be calculated using the formula:


Lateral surface area = (perimeter of base) × (slant height) / 2

The perimeter of the square base is 4x. So, the lateral surface area of the square pyramid can be written as:

Lateral surface area = 4x × (5x) / 2 = 10x^2

We are told that the construction material used for the outside of the building is between 20,000 square feet and 50,000 square feet. So, we can set up the following inequality:

20,000 ≤ 10x^2 ≤ 50,000

Dividing both sides by 10, we get:

2000 ≤ x^2 ≤ 5000

Taking the square root of both sides, we get:

44.7 ≤ x ≤ 70.7

Since we are looking for the maximum possible value of x, we can round 70.7 up to the nearest foot, which is 71 feet.

Therefore, the maximum possible side length of the base of the building is 71 feet.


Related Questions

Consider the sum 7+(-11)+4

Answers

Answer:

0

Step-by-step explanation:

7-11=-4

-4+4=0

Which expression is equivalent to z+z+z+z+3?

A. 7z
B. 4z + 3
C. 3z +4
D. z3​

Answers

B (4z + 3) is the correct answer. This is because you collect like-terms (z in our case)

Answer:

4z+3

Step-by-step explanation:

multiply the z's giving four z's and we don't know the value of z so we can't add 3 to it

The sum of the three interior angles of a triangle is 180. Suppose one angle is 74 and the remaining two angles are the same measure. Reason numerically to find the measures of the remaining angles.

Answers

Answer:

53

Step-by-step explanation:

[tex]sum \: of \: angles = 180 \\ 180 = 74 + 2x \: where \: x \: is \: the \: measure \: of \: the \: other \: angles \\ 180 - 74 = 2x \\ 106 = 2x \\ x = \frac{106}{2} \\ x = 53[/tex]

Always welcome

please help with this problem!!

Answers

Answer:

12 cups

Step-by-step explanation:

The ratio he uses is

2 parts strong coffee

3 parts milk

Let's say he makes a recipe exactly like the amounts of the ratio.

2 cups strong coffee

3 cups milk

Total: 2 cups + 3 cups = 5 cups

He wants to make 30 cups, so 5 cups is not enough.

Let's double the amounts of the recipe keeping the same ratio of 2 to 3.

2 × 2 = 4 cups strong coffee

3 × 2 = 6 cups milk

Total: 4 cups + 6 cups = 10 cups

He wants to make 30 cups, so 10 cups is not enough.

We can keep on going up by multiplying the numbers in the ratio by larger numbers, but there is a quicker way.

We need to multiply both numbers in the ratio by a number, let's call it x, so that when both numbers in the ratio are multiplled by x, and the ingredients are added, we end up with 30 cups.

Multiply both numbers in the ratio by x.

2x cups of strong coffee

3x cups of milk

Now add: the total amount will be 5x cups

We want 30 cups, so

5x = 30

Solve for x.

x = 30/5 = 6

x, the multiplier we need is 6.

2x cups strong coffee = 2(6) cups = 12 cups

3x cups milk = 3(6) cups = 18 cups

Answer: 12 cups

compute the probability of tossing a six-sided die and getting a number less than 3

Answers

Answer:

We can think of our denominator as 6 in our probability, because there are 6 total sides to this die.

Out of those 6 sides, they want to find out if we can roll a number less than 3.

First, let's find how many numbers there are on this die that are less than 3.

1 and 2, so there are 2 sides that contain numbers less than 3 on this die.

So there is a 2 out of 6 chance(2/6) which can be simplified to 1/3, of selecting a number less than 3 when rolling a die.

1/3 probability.

Convert this into a percent if you'd want:-

1/3 · 100

= 33.333... which can be rounded to a 33% probability.

What is the smallest positive integer n such that n! ends in at least 2019 zeros?​

Answers

Answer:

I think there's 502

Step-by-step explanation:

if this is a olunomical question that should be it I believe, because you have to write in standered form then when it equals zero, then factor it

Determine the perimeter of the figure below:
6 cm
5 1/2


helpppp

Answers

Answer:

•SEE BELOW•

WHAT IS PERIMETER?

>> PERIMETER MEANS THE SUM OF ALL SIDES OF FIGURE

NOW,LET'S SEE YOUR GIVEN QUESTION.

THE FIGURES 2 SIDES DATA IS GIVEN

6CM

5.5CM

THEREFORE : 6 + 5.5

: 11.5 CM

THE PERIMETER OF FIGURE IS 11.5 CM

Pat can drive 36 kilometers for every 3 liters of gas they put in their car.
Complete the table using equivalent ratios.
Kilometers
Liters
36
3
48
132

Answers

Answer:

Step-by-step explanation:

This is a proportion question which is 2 ratios which are equal to one another. If 3 of the 4 parts are known, the 4th part can be calculated.

36 liters.

36 km/3 Liters = x / 36             multiply both sides by 36

36*36 / 3 =  x

1296/3 = x

x = 432 km

So on 36 L he can go 432 km

3 liters

Given as 36 km

48 liters

36km/3 liters = x / 48 liters         Multiply both sides by 48

48*36/3 = x

576 km = x

So on 48 liters, he can go 576 km

132 liters

36 km/ 3 liters = x/132

x = 1564 km

On 132 liters Pat can go 1564 km

The total mass of 8 cereal boxes is 4 kilograms. What is the mass of each box of cereal in grams?

Answers

Answer:

500 grams

Step-by-step explanation:

we can conclude that the mass of each box is 0.5 kg by dividing 4 by 8

0.5 kg is 500 grams

Find the surface area of the Cylinder, will mark BRAINLIEST if correct

Answers

Answer:

About 1885 sq. ft

Step-by-step explanation:

[tex]v = \pi \: (10)^{2} (6) [/tex]

Since the radius is 10ft and the height of the cylinder is 6 ft you substitute that into the formula and you receive 1884.96.

In which step was the subtraction property of equality applied?

Answers

Answer:

step 1 is the answer

if you like my answer please like comment and mark me as brilliant

Answer:

D - The subtraction property of equality was not applied to solve this equation

Step-by-step explanation:

I got it right on the test

Explanation - they added 7 to both sides, so there was no subtraction property used

ents
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard
model requires 4 hours to assemble and 2 hours for finishing touches. The artisan model requires 2
hours to assemble and 2 hours for finishing touches. Based on their current staffing, they can
manage a maximum number of assembly hours available is 48 per day, and the maximum number
of finishing hours available is 44 per day.
Let x = the number of standard model bookcases produced per day and y = the number of artisan
model bookcases produced per day.
Write the system of inequalities that represents the maximum number of bookcases that can be
produced in one day.

Answers

Answer:

48 ≥ 4x + 2y

44 ≥ 2x + 2y

    First, we will look at assembling hours.

"The standard model requires 4 hours to assemble [and] the artisan model requires 2 hours to assemble"

    We also know they have 48 hours per day for assembly, x is standard model and y is artisan model.

48 = 4x + 2y

    Lastly, they do not need to make that many, but they can so we will use greater than or equal to.

48 ≥ 4x + 2y

    Now let us look at finishing hours.

"The standard model requires ... 2 hours for finishing touches. The artisan model requires ... 2 hours for finishing touches."

    We also know they have 44 hours per day for assembly, x is standard model and y is artisan model.

44 = 2x + 2y

    Again, they do not need to make that many, but they can so we will use greater than or equal to.

44 ≥ 2x + 2y

Convert the function from vertex form to standard form.
-1/2(x + 2)^2 - 3

Answers

Answer:

[tex] -\frac{1}{2}x^2-2x-5 [\tex]

Step-by-step explanation:

To convert it to standard form, all you need to do is expand the square and simplify. This would get us to: [tex]-\frac{1}{2}(x^2 + 4x + 4) - 3[/tex] which simplifies further to [tex]-\frac{1}{2}x^2-2x-2-3[/tex] and combine the -2 and -3 to get [tex] -\frac{1}{2}x^2-2x-5 [\tex]

Hope this helps :)

10 men can do the work in 8 days. how many men should be reduced to finish the work in 10 days​

Answers

If Reducing 2 men will bbe enough too finish the work in 10 days

For rate of work use the formualar

rate of work = quantity of work / duration

10 men can do the work at a rate of  =  1 / 8

x men can do same work at a rate of = 1 / 10

x * ( 1 / 8 ) = 10 * ( 1 / 10 )

x = 1 * 8 = 8

therefore 8 men can do the work in 10 days

number of men reduced = 10 men - 8 men = 2 men

Hope it helped

Can someone help me plssss!!!
The dimensions of a right rectangular prism are shown below.

How many cubes with side lengths of 1 over 6 inch are needed to fill the prism without gaps or overlaps?
show the work pls.​

Answers

Answer:

a.

Step-by-step explanation:

open chormecanvis and draw little cubes on the side of the prisum, thats wahat i did

For which values of x is the expression undefined x-8/x-5

Answers

Answer:

x = 5

Step-by-step explanation:

Any number over 0 is undefined. Given that, the values of x that make this expression undefined make the denominator equal to 0

x - 5 = 0

x = 5

I hope this helps!

A line passes through the point (-4,9) and has a slope of -3/2. Write an equation in slope intercept form for this line

Answers

Answer:

y = -3/2x + 3

Step-by-step explanation:

slope-intercept form: y - y₁ = m (x - x₁)

y - 9 = -3/2 ( x + 4)

y = -3/2 x - 6 + 9

y = -3/2x + 3

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

find sine or cosine using identity

Answers

Answer:

sin(theta) = [tex]\frac{\sqrt{7}}{4}[/tex]

Step-by-step explanation:

cos(theta) = [tex]\frac{x}{r}[/tex]

cos(theta) = [tex]\frac{3}{4}[/tex]

so x = 3 , r = 4 , and y =?

Pythagorean Theorem: x^2 +y^2 = r^2 or a^2 +b^2 = c^2

x^2 +y^2 = r^2

(3)^2 +y^2 = (4)^2

9 + y^2 = 16

y^2 = 7

[tex]y=\sqrt{7},-\sqrt{7}[/tex]

In Quadrant 1, so its only [tex]y=\sqrt{7}[/tex].

sin(theta) = [tex]\frac{y}{r}[/tex]

sin(theta) = [tex]\frac{\sqrt{7}}{4}[/tex]

Suppose GDP is $12 trillion, taxes are $3.6 trillion, private saving is $1.5 trillion, and public saving is $0.8 trillion. Assuming the economy is closed, complete the following table by calculating consumption, government purchases, national saving, and investment. Component Amount (Trillions of dollars) Consumption Government Purchases National Saving Investment

Answers

Assuming this economy is closed: Consumption $6.9 trillion; Government Purchases $11.2 trillion; National Saving $2.3 trillion; Investment $2.3 trillion.

Gross domestic product

a. Consumption

Private S = ( Y – T – C )

C = Y - T - Private S

C = $12 - $3.6 - $1.5 =$6.9 trillion

b. Government purchases

Public S = ( T - G )          

G = T - Public S                                                        

G = $12 - $0.8

G = $11.2 trillion

c and d. National saving and investment

National savings = Public S + Private S

National savings = $0.8 + $1.5

National savings =$2.3 trillion

Investment=Savings=$2.3 trillion

Therefore, Consumption $6.9 trillion; Government Purchases $11.2 trillion; National Saving $2.3 trillion; Investment $2.3 trillion.

Learn more about GDP here:https://brainly.com/question/1383956

Compare the integers.
-14
-23
A)
B)
> Greater than
O
= Equal to
D
Neither

Answers

Answer:

-14 > -23

Step-by-step explanation:

-14 is greater than -23 since it is closer to 0 than -23.

hope this helps!! p.s. i really need brainliest :)

Find a bank account balance if the account starts with $100, has an annual rate of 4%, and the money is left in the account for 12 years.

Answers

100 x .4 = 40

40 x 12 = 480

The bank account would have $480 over 12 years. Hope this helps and please mark brainliest

Represent the sum of the complex numbers 2−3i and −1−i on the complex plane.

Use the Point and Segment tools to plot all required points and segments.

Answers

Answer: I took the test and this is the answer.

PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

I believe it is Dissolve.

the ratio of the number of boys and girls in a class is 10:7 if there are 35 girls find the number of boys


Answers

Answer:

The solution to the question is in the attached image

HELP. WORTH 1 POINT
GIVING 10

Answers

Answer:

117

Step-by-step explanation:

well, if they are supplementary, and they are on the same line and a line is equal to 180 degrees, then its as easy as 180-63=117

I don’t understand this question. Someone help pls

Answers

Answer:

49.67ft

Step-by-step explanation:

i used the internet, use it too

In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is three more then the sum of the other digits. Find the three digits if the sum of all three digits is 15. Then find the number.

Answers

Answer:

591

Step-by-step explanation:

Let's use algebra to solve this question:

Units digit = x

Hundreds digit = x+4

Tens digit = 3 + (x+4) + x = 2x +7

All 3 digits = 15

so x + (x+4) + 2x + 7 = 15

4x +11 =15

4x = 4

x = 1

Then you substitute:

Units = 1

Hundreds = 1+4 = 5

Tens = 2(1) + 7 = 2 + 7 = 9

The number is therefore 591.

Solve the system of equations.
5x−4y=−10
y=2x−5

Answers

Answer:

x = 10

y = 15

Step-by-step explanation:

5x − 4y = −10  ⇒  ( 1 )

y = 2x − 5     ⇒ ( 2 )

Let us find the value of x.

For that, we can replace y with ( 2x - 5 ).

Let us take equation 1.

5x − 4y = −10

5x - 4 (  2x − 5 ) = -10

5x - 8x + 20 = -10

-3x = -20 - 10

-3x = - 30

Divide both sides by ( -3 ).

x = 10

And now let us find the value of y.

Let us take equation 2.

y = 2x − 5

y = 2 × 10 - 5

y = 20 - 5

y = 15

Answer:

X=10

Step-by-step explanation:

5x-4y=-10.....1

y=2x-5......2

sub 2 into 1

5x-4(2x-5)=-10

5x-8x+20=-10

5x-8x=-10-20

-3x=-30

x=10

sub x=10 into 2

y=2(10)-5

y=20-5

y=15

f(X)= 4X+8 g(X)= X+3, find f(X) • g(X)

Answers

Answer:

[tex]4x + 20[/tex]

Step-by-step explanation:

[tex]4(x + 3) + 8 = 4x + 12 + 8 = 4x + 20[/tex]

A cube has total surface area 150 cm square, find the volume of cube. somebody help me to solve this.​

Answers

Solution :

We have been provided with the total surface area of cube that is 150cm².

So here we will first find out the value of a side of cube.

Total surface area of cube :-

T.S.A. = 6a²

Here,

a is side of cube

Putting the values,

6a² = 150cm²

a² = 150 / 6

a² = 50 / 2

a² = 25

a = √25

a = 5

Henceforth,

Side of a cube is of 5 cm.

Finding out volume of cube :-

As we know that volume of cube is calculated by the formula :

V = a³

Putting the values,

V = 5³

V = 5 × 5 × 5

V = 25 × 5

V = 125

Henceforth,

Volume of cube is of 125 cm³.
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