If the radius of a circle is cut in half, what is the scale factor needed to adjust the area of the original circle to the smaller circle?
Answers
When the radius is halved, your area will be divided by 4. If you think about it, radius is already half of the diameter so your area is already divided by 2, so if you cut the radius is half again, your area will be divided by 4.
Final answer:
When the radius of a circle is cut in half, the area of the circle is reduced to one-fourth (0.25) of the original. Thus, the scale factor needed to adjust the original area to the smaller one is 0.25 or 1/4.
Explanation:
The question pertains to the relationship between the radius and area of a circle. The area of a circle is given by the formula A = πr², where r is the radius. If the radius of the circle is cut in half, the new radius becomes r/2. Substituting this into the formula for the area, we get A = π(r/2)² = πr²/4.
In other words, the area of the smaller circle is one-fourth (/4), or 0.25, that of the original circle. Therefore, the scale factor needed to adjust the area of the original circle to the smaller circle is 0.25 or 1/4.
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Related Questions
Can someone help me solve 5(t+2) please
Indicate whether the following statements are True (T) or False (F). 1. The difference of two integers is always a natural number. 2. The difference of two integers is always an integer. 3. The sum of two integers is always an integer. 4. The quotient of two integers is always an integer (provided the denominator is non-zero). 5. The ratio of two integers is always positive 6. The product of two integers is always an integer. 7. The quotient of two integers is always a rational number (provided the denominator is non-zero).
I NEED HELP ON THIS MAKE SURE IT RIGHT PLEASE ASAP
At 10:57 A.M. A submarine was at a depth of feet. Its depth then changed at a rate of -8 feet per minute. What was its depth at 11:03 A.M.? Group of answer choices
Answers
Answer:
To find the dimensions of the flower bed, we can set up an equation based on the given information. Let’s assume the length of the shortest side is x. According to the problem, one side is twice the length of the shortest side, which means it is 2x, and the third side is 15 feet more than the length of the shortest side, which means it is x + 151.
The perimeter of a triangle is the sum of all its sides. In this case, we have:
x + 2x + (x + 15) = 143.
Simplifying the equation, we get:
4x + 15 = 143.
Subtracting 15 from both sides of the equation, we have:
4x = 128.
Dividing both sides of the equation by 4, we find:
x = 32.
Now that we know the value of x, we can find the lengths of all three sides:
Shortest side: x = 32 feet.
Side twice the length of the shortest side: 2x = 64 feet.
Third side: x + 15 = 47 feet.
Therefore, the dimensions of the flower bed are approximately 32 feet, 64 feet, and 47 feet.
Answers
(25 * x^2) / (5 * x) + (8 * x^2) / x = 5 * x + 8 * x = 13 * x
The correct result would be 13 * x.
Answers
Final answer:
The price of one piece of bubble gum is $0.15. This can be determined by setting up algebraic equations based on the given information, allowing the fudge and bubble gum prices to be calculated.
Explanation:
The subject of this question is algebra and it uses a system of simultaneous equations to find the price of each piece of candy.
- Let's say 'f' is the cost of fudge and 'g' is the cost of gum.
- We can write two equations based on the information given: 5f + 3g = 5.70 and 2f + 10g = 3.60.
- To find the cost of the bubble gum first, we can eliminate 'f' by multiplying the first equation by 2 and the second one by 5 which will give us: 10f + 6g = 11.40 and 10f + 50g = 18.00
- Then we subtract the second equation from the first equation. This gives us: 44g = 6.60.
- Finally, we divide by 44 to get the price of gum, 'g' = 6.60 / 44 = $0.15.
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Overhead rate = 95%
Retail price of parts = $134.75
Total cost of job = $241.98
Hourly rate? $
Answers
overhead rate = 95% - mostly dependent on labor
retail price of parts = 134.75
total cost of job = 241.98
241.98 - 134.75 = 107.23
107.25 / (4.5 x 1.95) = 107.25 / 8.78 = 12.22 hourly rate
labor : 12.22 x 4.5 = 54.99
overhead: 54.99 x 95% = 52.24
retail price of parts = 134.75
total cost of job: 241.98
Answer:
$12.22
Step-by-step explanation:
Answers
Final answer:
After 0.003 seconds, we would have 1.25g of the initial 10g Po-214 left. The decay process can be modeled with the exponential function: N = 10 * , where N is the final amount, N0 is the initial amount, t is time, and T is the half-life.
Explanation:
The subject matter pertains to the concept of half-life in physics which interprets the decay of a radioactive material. In radioactive decay, the number of atoms in a radioactive sample decreases exponentially over time. This time is taken into consideration in the form of their half-lives. In the case of Po-214, the half-life is given as 0.001 seconds.
Before finding how much of Po-214 is left after 0.003 seconds, let's first understand the calculation. After one half-life (0.001 second), half of the sample will be left, i.e., 10g/2 = 5g. After another half-life (another 0.001 second), half of this 5g will be left, i.e.,5g/2 = 2.5g. After the third half-life (the remaining 0.001 second), we will have 2.5g/2 = 1.25g left. So, after 0.003 seconds, we would have 1.25g of Po-214 remaining from the initial 10g.
The decay process can be modeled with an exponential function N = N0 * , where N is the final amount, N0 is the initial amount, t is time, and T is the half-life. For this problem, the equation would be: N = 10 * (1/2)^(0.003/0.001).
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Answers
(x,y) format
if x=0, y=4 soo
y=x+4 is one equation