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matrenka [14]
3 years ago
12

(a) Find the Riemann sum for f(x) = 4 sin(x), 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Rou

nd your answers to six decimal places.)

Mathematics
1 answer:
miskamm [114]3 years ago
5 0

Split up the integration interval into 6 subintervals:

\left[0,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac\pi2\right],\ldots,\left[\dfrac{5\pi}4,\dfrac{3\pi}2\right]

where the right endpoints are given by

r_i=i\dfrac{\frac{3\pi}2-0}6=\dfrac{i\pi}4

for 1\le i\le6. Then we approximate the integral

\displaystyle\int_0^{3\pi/2}4\sin x\,\mathrm dx

by the Riemann sum,

\displaystyle\sum_{i=1}^6f(r_i)\frac{\frac{3\pi}2-0}6=\pi\sum_{i=1}^6\sin\frac{i\pi}4

=\pi\left(\dfrac1{\sqrt2}+1+\dfrac1{\sqrt2}+0-\dfrac1{\sqrt2}-1\right)=\dfrac\pi{\sqrt2}\approx\boxed{2.221441}

Compare to the actual value of the integral, which is exactly 4.

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Which expression is equivalent to StartFraction c squared minus 4 Over c + 3 EndFraction divided by StartFraction c + 2 Over 3 (
Firdavs [7]

Answer:

C

Step-by-step explanation:

Given:

\dfrac{c^2-4}{c+3}\div  \dfrac{c+2}{3(c^2-9)}

Changing the division to multiplication by taking the reciprocal of the second fraction.

\dfrac{c^2-4}{c+3}X  \dfrac{3(c^2-9)}{c+2}

<u>The correct option is C</u>

3 0
2 years ago
Read 2 more answers
One number is 9 more than twice another. If their difference is 22, what is the larger number?
mafiozo [28]
Let, the numbers are: x, y
So, Equations will be: x - y = 22
x = 2y + 9

Substitute the value of x in first equation, 
2y + 9 - y = 22
y = 22 - 9
y = 13

x - 13 = 22
x = 22 + 13 = 35

In short, Larger number would be 35

Hope this helps!
4 0
3 years ago
I need answer not links ​
tatuchka [14]
It’s a positive correlation I’m pretty sure.
7 0
3 years ago
Could someone please explain/help me to do this using Pythagoras theorem?
alex41 [277]

Answer:

\boxed{478.02}

Step-by-step explanation:

→ First understand what Pythagoras theorem is

Pythagoras is a theorem used to find the hypotenuse (the side opposite to the right-angle) of a triangle. We would need the base lengths as well the height in order to use Pythagoras.

→ State the formula and identify the letters

a² + b² = c² ⇒ where 'a' is 380cm, 'b' is 290cm and 'c' is what we are trying to work out

→ Substitute in the values into the formula

380² + 290² = c²

⇒ Simplify

144400 + 84100 = c²

⇒ Collect the numbers together

228500 = c²

⇒ Square root both sides to find 'c'

478.0167361 = c

→ The length of the diagonal is 478.02

8 0
3 years ago
Let g(x) = – x^2 + 4x + 3. Find and simplify g(-3).​
Evgen [1.6K]

Steps to solve:

g(x) = – x^2 + 4x + 3 when g(-3).

~Substitute x with -3.

g(-3) = -(-3)^2 + 4(-3) + 3

~Simplify

g(-3) = -9 - 12 + 3

~Simplify using PEMDAS

g(-3) = -18

Best of Luck!

7 0
3 years ago
Read 2 more answers
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