Find the supplementary angle of 116 degrees.

(c). It is well known that the rate of flow can be found by measuring the volume of blood that flows past a point in a given tim

aleksklad [387]

(i) Given that

$V(R) = \displaystyle \int_0^R 2\pi K(R^2r-r^3) \, dr$

when R = 0.30 cm and v = (0.30 - 3.33r²) cm/s (which additionally tells us to take K = 1), then

$V(0.30) = \displaystyle \int_0^{0.30} 2\pi \left(0.30-3.33r^2\right)r \, dr \approx \boxed{0.0425}$

and this is a volume so it must be reported with units of cm³.

In Mathematica, you can first define the velocity function with

v[r_] := 0.30 - 3.33r^2

and additionally define the volume function with

V[R_] := Integrate[2 Pi v[r] r, {r, 0, R}]

Then get the desired volume by running V[0.30].

(ii) In full, the volume function is

$\displaystyle \int_0^R 2\pi K(R^2-r^2)r \, dr$

Compute the integral:

$V(R) = \displaystyle \int_0^R 2\pi K(R^2-r^2)r \, dr$

$V(R) = \displaystyle 2\pi K \int_0^R (R^2r-r^3) \, dr$

$V(R) = \displaystyle 2\pi K \left(\frac12 R^2r^2 - \frac14 r^4\right)\bigg_0^R$

$V(R) = \displaystyle 2\pi K \left(\frac{R^4}2- \frac{R^4}4\right)$

$V(R) = \displaystyle \boxed{\frac{\pi KR^4}2}$

In M, redefine the velocity function as

v[r_] := k*(R^2 - r^2)

(you can't use capital K because it's reserved for a built-in function)

Then run

Integrate[2 Pi v[r] r, {r, 0, R}]

This may take a little longer to compute than expected because M tries to generate a result to cover all cases (it doesn't automatically know that R is a real number, for instance). You can make it run faster by including the Assumptions option, as with

Integrate[2 Pi v[r] r, {r, 0, R}, Assumptions -> R > 0]

which ensures that R is positive, and moreover a real number.

5 0

2 years ago

Gene ran 90 meters in 16.3 seconds. alma ran 90 meters in 17.2 seconds. who had the fastest time

maria [59]

Answer:

Gene ran faster

Step-by-step explanation:

The fastest time is the smallest time since they ran the same distance

gene ran 90 meters in 16.3 seconds.

alma ran 90 meters in 17.2 seconds

16.3 < 17.2

Gene ran faster

7 0

1 year ago

WILL GIVE BRAINLIEST IMMEDIATELY!!!!!!! GIVE EXPLANATION + ANSWER FOR BRAINLIEST

Monica [59]

The correct answer is:

D. ∠FGE≅∠NMP

Explanation:

The symmetric property states that if two quantities are equal (or congruent), you can "flip" them around the equals sign (or congruence sign).

This means since EFG is congruent to HJK, then HJK is congruent to EFG.

5 0

3 years ago

Read 2 more answers

A book sold 31,700 copies in its first month of release. Suppose this represents 8.8% of the number of copies sold to date. How

elena-14-01-66 [18.8K]

For this case we propose a rule of three:

31700 ------------> 8.8%

x ----------------------> 100%

Where "x" represents the number of copies sold to date.

$x = \frac {100 * 31700} {8.8}\\x = \frac {3170000} {8.8}\\x = 360,227.273$

Thus, to date 360,227 copies of the book have been sold.

ANswer:

To date, 360,227 copies of the book have been sold.

8 0

3 years ago

Find the equivalent fraction of 2/3 having denominator 6 and 6 and numerator 10.

4vir4ik [10]

Step-by-step explanation:

having denominator 6,

X/6= 2/3

X= 4

so, 4/6= 2/3

having numerator 10,

10/X= 2/3

X= 15

so, 10/15= 2/3

7 0

2 years ago