Answer:
≈ 62.8
Step-by-step explanation:
Using the equal ratios of
=
, that is
=
= 5, thus
5 × sector = 100π ( divide both sides by 5 )
sector = 20π = 20 × 3.14 = 62.8 units²
Answer:
4
Step-by-step explanation:
The x coordinate is the same so the distnce is only the difference in y
5 - 1 = 4
This is the concept of algebra, given that the area of a rectangular pool is (15x-9), the possible dimensions of the pool by factoring will be:
Area=length×width
Area=(15x-9)
factoring the above we get:
Area=3(5x-3)
therefore the possible dimension will be:
length=5x units
width=3 units
Answer:
Using either method, we obtain: 
Step-by-step explanation:
a) By evaluating the integral:
![\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%20%5Cint%5Climits%5Et_0%20%7B%5Csqrt%5B8%5D%7Bu%5E3%7D%20%7D%20%5C%2C%20du)
The integral itself can be evaluated by writing the root and exponent of the variable u as: ![\sqrt[8]{u^3} =u^{\frac{3}{8}](https://tex.z-dn.net/?f=%5Csqrt%5B8%5D%7Bu%5E3%7D%20%3Du%5E%7B%5Cfrac%7B3%7D%7B8%7D)
Then, an antiderivative of this is: 
which evaluated between the limits of integration gives:

and now the derivative of this expression with respect to "t" is:

b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then

is continuous on [a,b], differentiable on (a,b) and 
Since this this function
is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:

Answer:
R, in beats per minute, can be approximated by the formulas, where a represents the person's age.
where R= 143 - 0.65a for women.... (1)
and R= 165 - 0.75a for men,..... (2)
So by implementing these two equation we get a = 40
So the age will be 40 years old
know more about “Mathematical Equation” here: brainly.com/question/1214333
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