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ollegr [7]
3 years ago
12

What is the side length of the largest square that can fit into a circle with a radius of 5 units?

Mathematics
1 answer:
Mariana [72]3 years ago
5 0
So 1st consider that it's a square! That's very important. So for a square, all 4 sides are equal.

And now considering that the given information is the diameter. So any angle made at the circle extended from the 2 points of diameter gives an angle of 90°

Now consider one triangle. So we already know that 2 sides of the triangle are equal (because they are 2 sides of a square) , has a side of 10 (diameter) and and angle of 90°. So remaining 2 angles are 45°

Now solve it by applying

\sin(45) \: \: \: \: = x \div 10 \\ (1 \div \sqrt{2} ) = (x \div 10) \\ 10 \div \sqrt{2} \: = x
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Let b be a number such that (2b+5)(b-1)=6b. What is the largest possible value of b? Express your answer as a common fraction.
Oksi-84 [34.3K]

Answer:

Foil the expression and solve the derivative with respect to b at f'(x)=02b^2+3b+5=6b\\d/dx(2b^2+9b+5=0)\\4b+9=0\\b=-9/4

Step-by-step explanation:

4 0
2 years ago
PLEASE HELP ASAP
lesya [120]

Answer:

conditions h, j, and k will form an integer

Step-by-step explanation:

any 2 integers added together will form an integer, it doesn't matter if the integers are odd or even

f and g can't be always true, since we don't know if the other number is has decimals

8 0
3 years ago
Read 2 more answers
An element with mass 780 grams decays by 16.3% per minute. How much of the element is remaining after 16 minutes, to the nearest
vitfil [10]
Exponential decay is a very common process especially when we are talking about radioactive materials. So, there is already a common formula for this type of behavior which is written below:

A = Pe^-rt
where
A is the amount left after time t
P is the initial amount at t=0
r is the rate

Substituting the values,
A = (780 g)(e^-0.163*16)
A = 57.5 g
8 0
3 years ago
Brainliest and points for best answer.
jeka57 [31]

Answer:

A

Step-by-step explanation:

3 0
3 years ago
For f(x) = x3 – x2, which gives an output of 48?<br> O f(-8)<br> O fl-4)<br> O f(4)<br> O f(8)
Misha Larkins [42]

Answer:

f(4)

Step-by-step explanation:

The output is the value of f(x) for a given value of x ( the input )

Substitute the given values of x into f(x) to determine the output, that is

f(- 8) = (- 8)³ - (- 8)² = - 512 - 64 = - 576 ≠ 48

f(- 4) = (- 4)³ - (- 4)² = - 64 - 16 = - 80 ≠ 48

f(4) = 4³ - 4² = 64 - 16 = 48

Thus f(4) gives an output of 48

4 0
2 years ago
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