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3 years ago

Find the area of a circle given the radius is 8.

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

7 0

Answer:

Step-by-step explanation:

8² = 64

64 · π ≈ 201.06

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A.) 15<br> B.) 45<br> C.) 60<br> D.) 30

Cerrena [4.2K]

Look at the picture.
measure of ∠2 is equal 30°

3 0

3 years ago

AP Calculus redo! I know the answer but can't figure out exactly how to get there. Thank you! I want to work through the steps.

Monica [59]

You're approximating

$\displaystyle\int_1^5 x^2\,\mathrm dx$

with a Riemann sum, which comes in the form

$\displaystyle\int_a^b f(x)\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^nf(x_i)\Delta x_i$

where $x_i$ are sample points chosen according to some decided-upon rule, and $\Delta x_i$ is the distance between adjacent sample points in the interval.

The simplest way of approximating the definite integral is by partitioning the interval into equally-spaced subintervals, in which case $\Delta x=\dfrac{b-a}n$ , and since $[a,b]=[1,5]$ , we have

$\Delta x=\dfrac{5-1}n=\dfrac4n$

Using the right-endpoint method, we approximate the area under $f(x)$ with rectangles whose heights are determined by their right endpoints. These endpoints are chosen by successively adding the subinterval length to the starting point of the interval of integration.

So if we had $n=4$ subintervals, we'd split up the interval of integration as

$[1,5]=[1,2]\cup[2,3]\cup[3,4]\cup[4,5]$

Note that the right endpoints follow a precise pattern of

$2=1+\dfrac44$
$3=1+\dfrac84$
$4=1+\dfrac{12}4$
$5=1+\dfrac{16}4$

The height of each rectangle is then given by the values above getting squared (since $f(x)=x^2$ ). So continuing with the example of $n=4$ , the Riemann sum would be

$\displaystyle\sum_{i=1}^4\left(1+\dfrac{4i}4\right)^2\dfrac44$

For $n=5$ ,

$\displaystyle\sum_{i=1}^5\left(1+\dfrac{4i}5\right)^2\dfrac45$

and so on, so that the definite integral is given exactly by the infinite sum

$\displaystyle\lim_{n\to\infty}\sum_{i=1}^n\left(1+\dfrac{4i}n\right)^2\dfrac4n$

4 0

3 years ago

In triangle ABC angle C 105° B 45° BD median of triangle ABC find the angle bdc

antiseptic1488 [7]

Answer:

Step-by-step explanation:

$105 + 45 + bdc = 180$

bdc=30

8 0

1 year ago

Bob bought 3 packs of model cars he gave 4 cars to ann Bob has 11 cars left how many model cars were in each pack

Harrizon [31]

First add 11 and 4 because you need to know how many he had in total 11+4=15 then divide 15 by 3 and then you have you answer 15/3=5.
There are 5 model cars in each pack.

5 0

3 years ago

2. The equation of a circle is x^2 + 2x + y^2 + 6y = 0.

pentagon [3]

Answer:

a)
${x}^{2} + 2x + {y}^{2} + 6y = 0$
${x}^{2} + 2x + 1 + {y}^{2} + 6y + 9 = 10$
${(x + 1)}^{2} + {(y + 3)}^{2} = 10$
b)
center I(-1;-3)

$radius = \sqrt{10}$

8 0

4 years ago