A large planetarium in the shape of a dome is being built. When it is complete, the base of the dome will have a circumference of 87 kilometers. What area of land was required for this planetarium?

Answers

Answer 1

Area = pi * r^2, circumference = 2*pi*r, u need to get 'r' the radius:

r = 87 km / 2 / pi = 13.846 km,

Now the areas is:

A = pi * 13.486^2 = 602.32188213127836 km^2 = 602.32 km^2

Huge

Answer 2

Answer:

602.32 km²

Step-by-step explanation:

First, find the radius of the circle using the circumference formula

C = 2π*r

87 = 2π*r

∴ r = 13.8465 km

Second, using the radius, calculate the area:

A = π * r²

A = π * 13.8465²

A = 602.32 km ²

Related Questions

Which of the following best describes the expression 6(y + 3)?

1.)The product of two constant factors six and three plus a variable
2.)The sum of two constant factors six and three plus a variable
3.)The product of a constant factor of six and a factor with the sum of two terms
4.)The sum of a constant factor of three and a factor with the product of two terms

Answers

6(y + 3)

The product of a constant factor of 6 and a factor with the sum of 2 terms

Answer: Hence, option '3' is correct.

Step-by-step explanation:

Since we have given that

[tex]6(y+3)[/tex]

This expression can be written in statement.

Here, we can see that there are two terms:

1) A constant factor of 6

2) Sum of two terms

So, according to options it can be written as :

The product of constant factor of 6 and a factor with the sum of two terms i.e. y and 3.

Hence, option '3' is correct.

HELPPPPPPPPPPPPPPPPPPPP

Answers

A.
the y intercept is where x=0
x represents the number of months
when the number of months is 0, that is the initial number of games won

that looks to be a little below y=2, so maybe y=1.8?
the y intercept is y≈1.8
it represents the number of games won with 0 months of practice

B.
we can use y=mx+b
m=slope
b=y intercept
we know the y intercept
find the slope
slope=rise/run
the I'm going from x=0 to x=10
the rise is about 18.95 (from 1.8 to 20.75)
the run is 10
so slope would be 18.95/10=1.895

the equation would be y=1.895x+1.8
the points were (0,1.8) and (10,20.75)

Please help me :) Thanks!

Answers

x^2+12x+5 = (x+6)^2 -31,

So the minimum value is y = -31. Dunno if -31 or you have to type =-31, I guess just '-31'?

With derivatives:

y' = 2x+12=0, x = -6, then y(-6) = 36-72+5 = -36+5 =-31

Just to be sure!!!! lol

The minimum value for y in the equation y = x² + 12x + 5 is (-6,-31). Here's how I figured it out:

Step 1: Figure out if the parabola is going up or down. If "a" is positive, the parabola will go up. If "a" is negative, the parabola will go down. In your case...

a = 1
Positive
Up
____________________________________________________________

Step 2: Find the Axis of Symmetry.

Formula: -b -12 -12
--------- = ------------ = ------------- = -6
2a 2(1) 2

The axis of symmetry is x = -6.
____________________________________________________________

Step 3: Plug in the value you found for the axis of symmetry for x into your original equation.

f(-6) = -6² + 12(-6) + 5
f(-6) = 36 - 72 + 5
f(-6) = -36 + 5
f(-6) = -31

The minimum gets written as an ordered pair: (-6,-31).
⊕ The axis of symmetry is the first number in the coordinate pair.
⊕ The answer that you get to step 3 is the second number in the pair.
____________________________________________________________

I hope that my answer helps you! This is the method that I use to solve these types of problems, but there are also other methods.

how to write unit form for (2 tens 1 one) x 10

Answers

Numbers are arranged by their place values. Place values give a quantity of value to a certain digit in a number. Given a number, the rightmost number is the ones place, followed by the tens place, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, as so on and so forth. The place value of a certain digit is 10 times bigger than its adjacent digit to the right.

So for this problem, all you have to do is multiply the number of units of each place value, then multiple them all by 10.

(2(10) + 1(1))×10
21 × 10 = 210

Therefore, the number is equivalent and written as 210.

A recipe for muffins calls for 3⁄5 of a cup of sugar and 4 cups of flour. If you want to make a bigger batch, using 5 cups of flour, how much sugar will you need?

Answers

(3/5) / 4 = x / 5
cross multiply
4x = 5(3/5)
4x = 3
x = 3/4....it would need 3/4 cups of sugar

A car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. What was the mean for the profits of the sales?

Answers

Mean or Average is all of the sums divided by how many of the choices are there, so all of 10,126+9,99+12,398+12,007+4567=49097 and divided by all the choices you have which is 5 is 9819.4

Answer:

$9819.4

Step-by-step explanation:

We have been given that a car dealer recently sold five cars for the following profits: $10,126, $9,999, $12,398, $12,007, and $4,567. We are asked to find the mean for the profits of the sales.

Since mean is the average of numbers. So let us add all the profits and divide the sum of profits by number of cars.

[tex]\text{Mean for the profits of the sales}=\frac{10126+9999+12398+12007+4567}{5}[/tex]

[tex]\text{Mean for the profits of the sales}=\frac{49097}{5}[/tex]

[tex]\text{Mean for the profits of the sales}=9819.4[/tex]

Therefore, the mean for the profits of sales is $9819.4.

Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as service charges. Company B charges $8 per hour and an additional $40 as service charges.

Part A: Write an equation to represent each company's total charges for renting a truck for a certain number of hours. For both equations (one for Company A and one for Company B), define the variable used. (4 points)

Part B: Which company would charge less for renting a truck for 8 hours? Justify your answer. (3 points)

Part C: How much money is saved by using the services of Company A instead of Company B to rent a truck for 2 hours? (3 points)

Answers

Part A:
Company A: $7 per hour +$30 service charge =money spent
Company B: $8 per hour +$40 service charge =money spent

Part B:
Company A: $7(8)+$30 = $86
Company B: $8(8)+$40 = $104

Part C:
Company A: $7(2)+$30 = $44
Company B: $8(2)+$40 = $56
You would save $12 if you use Company A instead of Company B's truck rental.

Express without negative exponents

Answers

1/5^-1 = 5

.4^-2 = 6.25

so it would be 5 x 6.25

Find the value of X in the problem below. Geometry

Answers

(3x+10) +14x = 180

17x +10 = 180

17x=170

x = 170/17 = 10

x = 10

An angle measures 20° more than the measure of a complementary angle. What is the measure of each angle?

Answers

complementary angles, sum = 90
so
x + x + 20 = 90
2x = 70
x = 35

35 + 20 = 55

answer
the measure of each angle: 55 and 35

A triangle has angles that measure 30, 60, 90. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle?

Answers

10cos60=5
10sin60=8.66
since you have the measure of the hypotenuse, add 10+5+8.66
=23.66

An architectural drawing lists the scale as 1/4 = 1. If a bedroom measures 3 1/2 by 5 1/4 on the drawing, how large is the bedroom

Answers

The bedroom is 14x21. I hope this helps :)

Answer:

The measure of the bedroom is 14 by 21

Step-by-step explanation:

This scale represents the every measure in the drawing is a 1/4 of the original measure, so to find the original measure you must multiply the measure you find in the drawing by 4.

So for the beadroom (3 1/2, 5 1/4), you multiply each one by 4

The real measures of the beadroom are:

(3 1/2 * 4, 5 1/4 * 4)

(14,21)

The measure of the bedroom is 14 by 21

Which planet is 10 times as far as earth is from the Sun

Answers

the answer to 15 is Saturn

Saturn is the answer

2. If you have budgeted 12% of your monthly income for groceries, how much can you spend on groceries if you earn $950 bi-weekly?

Answers

bi weekly means you get paid every 2 weeks ( 2 times a month)

950*2 = 1900 per month for pay

1900*0.12 = 228 a month for food

Answer:

if you earn $950 bi-weekly, you earn 2 x 950 = $1900 per month. If you have budgeted 12% of your monthly income for groceries you need to find 12% of $1900: (1900 / 100) x 12 = 228. Answer: you can spend $228 a month on groceries.

If p-1 is a factor of p^4+p^2+p-k the value of k is

Answers

p=1
p^4+p^2+p-k=0

1+1+1-k=0 k=3

The value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]

How to determine the value of k?

The expression is given as:

[tex]p^4+p^2+p-k[/tex]

The factor is given as:

p - 1

Set the factor to 0

p - 1 = 0

Add to both sides

p = 1

Substitute 1 for p in the expression and equate it to 0

[tex]1^4+1^2+1-k = 0[/tex]

Evaluate the exponents

1+1+1-k = 0

Evaluate the sum

3-k = 0

Add k to both sides

k = 3

Hence, the value of k is 3 if p - 1 is a factor of [tex]p^4+p^2+p-k[/tex]

Answers

Move k to the other side to isolate d.

So we will get 3d = 8c - 8d - k

Now divide both sides by 3 to isolate d.

So d = 8/3c - 8/3d - k/3

If n = 8 and 16 • 2m = 4n – 8, then m = ?

Answers

Hello there! Thank you for asking your question here at Brainly. I will be assisting you today with answering your question, and will teach you how to handle it on your own in the future.

First, let's examine the question, and proceed to evaluate once we understand what we're dealing with.

"If n = 8, and 16 • 2m = 4n - 8, then m = ?"
This question is requesting for us to input the value for n, and then solve for m.

Here is our equation:
16 • 2m = 4n - 8

Let's plug in 8 for n.
Our equation should look like this now:
16 • 2m = 4(8) -8
First, let's get 4(8) by itself; Add 8 to both sides.
16 + 8 = 24
-8 + 8 = 0

Our equation is now:
24 • 2m = 4(8)
Multiply 4 by 8 to simplify the right side of the equation.
4 • 8 = 32

Now we have:
24 • 2m = 32

To solve for m, we need to isolate 2m and then divide both sides by 2.
Subtract 24 from both sides to isolate 2m.
24 - 24 = 0
32 - 24 = 8

Our equation is now:
2m = 8
Divide both sides by 2 to solve for m.
2m / 2 = m
8 / 2 = 4

Our final equation and solution is:
m = 4.
The value for m is 4.
I hope this helps!

Final answer:

The value of m is 0.75 when n = 8 and the equation 16 • 2m = 4n – 8 is satisfied, by performing simple algebraic operations to isolate and solve for m.

Explanation:

To find the value of m when n = 8 and 16 • 2m = 4n – 8, we first replace n with 8 in the second equation:

16 • 2m = 4(8) – 8

16 • 2m = 32 – 8

16 • 2m = 24

Now we divide both sides of the equation by 16 to isolate 2m:

2m = 24 / 16

2m = 1.5

Finally, to find m, we divide both sides of the equation by 2:

m = 1.5 / 2

m = 0.75

So the value of m that satisfies the given conditions is 0.75.

What is the area of a triangle that has a height of 4 feet and a base length of 9 feet? 18 feet2 36 feet2 144 feet2 324 feet2

Answers

18 feet.

9 x 4 = 36

36/2 = 18

18 feet is the answer hope this helps!!

The restaurant bill you and your friend received was not itemized. You ordered 2 drink refills and the egg breakfast, for a total of $8.40. Your friend ordered 3 refills and the egg breakfast for $9.35.
(a) Write a system of equations for the situation. Use r for the amount charged for a refill and b for the amount charged for the egg breakfast.
(b) Graph the equations in the system.
(c) Use your graph to estimate how much each item cost.

Answers

Show work: Total=$17.75 R=$0.95×5 R=$4.75 $17.75-$4.75=$13.00 $13.00÷2=$6.50

Answer:
(1) Egg Breakfast $6.50
(2) Egg Breakfast $6.50
(3) Refill #1 $0.95
(4) Refill #2 $0.95
(5) Refill #3 $0.95
(6) Refill #4 $0.95
(7) Refill #5 $0.95

Check answer: $6.50+$6.50=$13.00
$0.95+$0.95=$1.90
$0.95+$0.95=$1.90
$1.90+$1.90=$3.80
$3.80+$0.95=$4.75
$13.00+$4.75=$17.75

Total: $17.75

Write an equation ten times the sum of half a number and 6 is 8.

Answers

10(1/2x+6)=8
Is the equation. Hope this helped!

10(x/2+6)=8
the x/2 means x over two

If the APY of a savings account is 2.4% and if the principal in the savings account is $2200 for an entire year, what will be the balance of the savings account after all the interest is paid for the year? A. $2200 B. $2252.80 C. $2300 D. $2205.28

Answers

To solve this problem, we must recall that the formula for money with compound interest is calculated as:

Total = Principal × ( 1 + Rate ) ^ n

Total = $2,200 × ( 1 + 0.024 ) ^ 1

Total = $2,252.80

Therefore the answer is letter B.

Two trains leave stations 252 miles apart at the same time and travel toward each other. One train travels at 80 miles per hour while the other travels at 100 miles per hour. How long will it take for the two trains to meet?

Answers

First things first, distance = speed x time
So let's have "t" represent the time by both trains.
The first train shall be Train A and the other becoming Train B, so now we have Train A going 80t miles and Train B going 100t miles.

If two trains head toward each other, they will have traveled a total of 252 miles. The faster train will have traveled further (Train B), so the meeting point will be closer to the slower train's starting point (Train A).

So now we do 80t + 100t = 252
Which becomes 180t = 252
And by diving 252 by 180, you'll get that t is 1.4
This would mean they would meet at one hour and 24 minutes.

Final answer:

The time it takes for two trains traveling towards each other at speeds of 80 mph and 100 mph, and starting 252 miles apart, is found by dividing the distance by their combined relative speed. It takes them 1.4 hours or 1 hour and 24 minutes to meet.

Explanation:

To solve the problem of calculating the time it takes for two trains to meet, we need to understand the concept of relative speed in motion problems. When two objects move towards each other, their relative speed is the sum of their individual speeds. In this case, one train travels at 80 miles per hour and the other at 100 miles per hour, giving us a combined relative speed of 80 mph + 100 mph = 180 mph.

The distance between the two trains is 252 miles, and to find the time taken for the trains to meet, we divide the total distance by the relative speed:

Time = Distance / Relative Speed

Time = 252 miles / 180 mph

Time = 1.4 hours or 1 hour and 24 minutes for the two trains to meet.

Which factor does the width of the peak of a normal curve depend on?

Answers

the answer would be standard deviation.

Answer: The width of the peak depends on the Standard Deviation. The standard deviation is a measure used to quantify the variation or dispersion in the data set. If the standard deviation is low, this means that the set of data tends to be closer to the mean, then the width of the peak in the normal curve is small, for other part if the standard deviation is big, this means that the variation is big and the data set is more spread, this causes that the width of peak to be larger.

11 POINTS GUYS PLZ
Answer 12 and 14

Answers

12) 10.77 + 2.09 + 0.75 = 13.61

13.61 x 1.07 = $14.56

total amount = $14.56

14) C shows the possible combinations

Which is a unit rate ? 4 dollars to 3 cans 5 students to 2 teachers 6 hours and 1 book 3 miles 2 days

Answers

6 hours to 1 book is a unit rate because the independent variable (books) is equal to 1.

Hope this helps!

Answer:

6 hours to 1 book

Step-by-step explanation:

Which is an obtuse angle?

∠CAB

∠BAC

∠BCA

∠ABC

Answers

BCA is an obtuse angle

Obtuse angle is an angle that is greater than 90° but less than 180°

∠BCA ← answer

Haley and Samuel can each make one gift box in two hours. Rachael takes three hours to make the gift box alone. If Haley, Samuel, and Rachael work together, how long will it take them to make one gift box?

Answers

It will take 40 minutes for them to make one gift box.

Combined rates

Given that Haley and Samuel can each make one gift box in two hours, while Rachael takes three hours to make the gift box alone, to determine, if Haley, Samuel, and Rachael work together, how long will it take them to make one gift box, the following calculation must be performed, using combined rates:

1/2 + 1/2 + 1/3 = X3/6 + 3/6 + 2/6 = X8/6 = X6/6 = 1 hour8/6 = 40 minutes

Therefore, it will take 40 minutes for them to make one gift box.

Learn more about combined rates in https://brainly.com/question/10729109

#SPJ1

Answer:It will take 40 minutes for them to make one gift box

Step-by-step explanation:

Solve the equation for the letter L: A=LW

L = AW
L equals W over A
L = A − W
none of the above

Answers

[tex] \frac{L}{A} =LW[/tex] ⇒ Multiply both sides by A
[tex] \frac{LA}{A}=LWA [/tex] ⇒ The terms 'A' on the LHS cancel each other
[tex]L=LWA[/tex] ⇒ Divide both sides by 'L'
[tex] \frac{L}{L}= \frac{LWA}{L} [/tex] ⇒ The terms 'L' on the LHS cancel each other to '1' and the terms 'L' on the RHS will also cancel each other
[tex]1= WA[/tex]

The correct answer is the last option = none of the above

Everett made 3/5 of the baskets he shot. Suppose he shot 60 baskets. How many did he make?

Answers

Everett made 36 shots

You have to multiply 5×12 to get 60. And whatever you do on the bottom you do on the top. So
you then multiply 3×12 and you
get 36. So he got 36 out of 60
shots.

3 (12) 36
-- = --
5 (12) 60

How to simplify the expression 60/(-4)

Answers

Hey!

We could rewrite the problem as: [tex]\frac{60}{-4}[/tex]
Since we have a negative number, we could rewrite the fraction like this.
[tex]=-\frac{60}{4}[/tex]
Let's simplify it...
[tex]-\frac{60}{4}=-15[/tex]
Our answer would be:
[tex]=-15[/tex]

Thanks!
-TetraFish

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