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3 years ago

Consider the region bounded by

1 answer:

Montano1993 [528]3 years ago

4 0

The equation is a circle centered at the origin with radius 8 (sqrt(64))
Therefore, the bounded region is just a quarter circle in the first quadrant.

Riemann Sum: ∑⁸ₓ₋₋₀(y²)Δx=∑⁸ₓ₋₋₀(64-x²)Δx

Definite Integral: ∫₀⁸(y²)dx=∫₀⁸(64-x²)dx

You might be interested in

Find the slope and y-intrcept of y=5/3x -4

natima [27]

Answer:

Slope: 5/3

y-intercept: (0, -4)

Step-by-step explanation:

Slope-Intercept Formula: y = mx + b

y is your output.

m is your slope.

b is your y-intercept.

7 0

3 years ago

Which expressions are equivalent to -3(2+7) A: -6+21 or B:-21+6

Neporo4naja [7]

Answer:

None

Explanation:

-3(2+7) = -3×9 = -27

-6+21 = 15

-21+6 = -15

Hence there is no equivalence

3 0

3 years ago

Negative one-sixth of a number is less than -9. write an inequality.

sladkih [1.3K]

Answer:

-1/6 n < -9

Step-by-step explanation:

Negative one-sixth of a number

-1/6 n

is less than -9

-1/6 n < -9

3 0

2 years ago

A minor league baseball team plays 128 games a seanson. If the tam won 16 more than three times as many games as they lost how m

tiny-mole [99]

Answer: The team won 100 games and losses 28 games

Step-by-step explanation:

Let the number of games won denoted by x and the games lost is denoted by y .

Given : A minor league baseball team plays 128 games in a season.

Team won 16 more than three times as many games as they lost.

Then, the system of equations, we have

$x+y=128-------(1)\\\\x=3y+16------------(2)$

We can rewrite equation (2) as $x-3y=16----------------(3)$

Now, Eliminate equation (3) from (1), we get

$y-(-3y)=128-16\\\\\Rightarrow\ 4y=112\\\\\Rightarrow\ y=\dfrac{112}{4}=28$

Substitute the value of y in (2), we get

$x=3(28)+16=84+16=100$

Hence, the team won 100 games and losses 28 games.

7 0

3 years ago

Ex 7) Imagine a mile-long bar of metal such as the rail along railroad tracks. Suppose that the rail is anchored on both ends an

Fantom [35]

9514 1404 393

Answer:

about 44.5 feet

Step-by-step explanation:

We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.

Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...

h = c·tan(α) . . . . . . where c = half the initial rail length

Then the length of the expanded rail is ...

s = r(2α) = (c/sin(2α)(2α) . . . . . . where s = half the expanded rail length

Rearranging this last equation, we have ...

sin(2α)/(2α) = c/s

It is this equation that must be solved iteratively. We find the solution to be ...

α ≈ 0.0168538794049 radians

So, the height of the circular arc is ...

h = 2640.5·tan(0.0168538794049) ≈ 44.4984550191 . . . feet

The rail will bow upward by about 44.5 feet.

_____

Additional comments

Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.

We don't know the precise shape the arc will take, but we suspect is is not a circular arc. It seems likely to be a catenary, or something similar.

We used Newton's method iteration to refine the estimate of the angle from that shown on the graph. The iterator used is x' = x -f(x)/f'(x), where x' is the next guess based on the previous guess of x. Only a few iterations are required obtain an angle value to full calculator precision.

3 0

3 years ago