The answer is 5.13 in²
Step 1. Calculate the diameter of the circle (d).
Step 2. Calculate the radius of the circle (r).
Step 3. Calculate the area of the circle (A1).
Step 4. Calculate the area of the square (A2).
Step 5. Calculate the difference between two areas (A1 - A2) and divide it by 4 (because there are total 4 segments) to get <span>the area of one segment formed by a square with sides of 6" inscribed in a circle.
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Step 1:
The diameter (d) of the circle is actually the diagonal (D) of the square inscribed in the circle. The diagonal (D) of the square with side a is:
D = a√2 (ratio of 1:1:√2 means side a : side a : diagonal D = 1 : 1 : √2)
If a = 6 in, then D = 6√2 in.
d = D = 6√2 in
Step 2.
The radius (r) of the circle is half of its diameter (d):
r = d/2 = 6√2 / 2 = 3√2 in
Step 3.
The area of the circle (A1) is:
A = π * r²
A = 3.14 * (3√2)² = 3.14 * 3² * (√2)² = 3.14 * 9 * 2 = 56.52 in²
Step 4.
The area of the square (A2) is:
A2 = a²
A2 = 6² = 36 in²
Step 5:
(A1 - A2)/4 = (56.52 - 36)/4 = 20.52/4 = 5.13 in²
Answer:
9 ft
Step-by-step explanation:
Let's begin with the formula for the volume of a square pyramid. If s is the base length, then the area of the base is s^2. The volume of the pyramid is then V = (1/3)(base area)(height). We know the volume and the base length (s), and want to find the height. Solving V = (1/3)(base area)(height)
for height, we get:
3V = (base area)(height), or
3V
---------------- = height
base area
Substituting 75 ft^3 for V and (5 ft)^2 for base area, we get:
3(75 ft^3) 9 ft
height = ------------------ = ----------------- = 9 ft
25 ft^2 1
Answer:
Step-by-step explanation:
A person invested $2,500 in an account growing at a rate allowing the money to double every 11 years. How long, to the nearest tenth of a year would it take for the
value of the account to reach $3,800?
The formula for exponential growth given as:
A(t) = Ao (1/2)^t/t½
A(t) = Amount after time t = $3,800
Ao = Initial amount invested = $2500
t = Time in years
t½ = Time it takes to double = 11 years
Hence,
3800 = 2500(1/2)^t/11
Divide both sides by 2500
3800/2500 = 2500(1/2)^t/11/2500
Some of the answers are going to be negative fractions, and some are going to be positive. I can't show the work on here right now but I hope that this helped a little bit. If you have any further questions then let me know and I can try to help you!
If the satellite moves at a speed of 27,000 km p/h, your answer depends on the question.
This could be written in an algebraic expression, such as:
27,000x = S [for S stands for the ultimate speed of the satellite]
Of course, if this is a 3rd grade level question, I highly doubt they have even gotten started to including the alphabet into math.
So, I would suggest plugging 4 into X.
To explain this to her, just say that the speed needs to be multiplied by the amount of hours it has traveled. (I got 4 because there is a '4' in the question instead of 'for').
Meaning,
27,000 x 4 = 108,000 km per 4 hours
If her teacher decides to ask why that number, have her explain the question did not make sense so she plugged in a 4 to find an answer to a certain amount of hours.
Hope that helps a bit with the confusion!
