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3 years ago

Verify: sin(Θ/3)cos(Θ/3) = 1/2sin(2Θ/3)

Mathematics

1 answer:

gregori [183]3 years ago

8 0

Answer:

is this even real math ?

Step-by-step explanation:

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URGENT PLEASE HELP!!!!!

telo118 [61]

(1)

we are given

$\frac{y}{6} =x$

we can find for y

multiply both sides by 6

$\frac{y}{6}*6 =6*x$

$y=6x$

we can see that y is directly proportional to x

so, option-D........Answer

(2)

y varies inversely with x

so, we can write it as

$y=k\frac{1}{x}$

now, we are given

y=5 when x=2.5

so, we can plug it here

$5=k\frac{1}{2.5}$

and then we can solve for k

$5*2.5=2.5*k\frac{1}{2.5}$

$k=12.5$

now, we can plug back

$y=\frac{12.5}{x}$

we can plug x=20

$y=\frac{12.5}{20}$

$y=0.625$ .............Answer

(3)

we are given

The current, I, in a circuit varies inversely with the resistance, R

so, we can write it as

$I=\frac{k}{R}$

we have R=12 when I=3

so, we can plug it

$3=\frac{k}{12}$

now, we can solve for k

$3*12=12*\frac{k}{12}$

$k=36$

now, we can plug back

$I=\frac{36}{R}$

we can plug R=6

$I=\frac{36}{6}$

$I=6$ ................Answer

6 0

3 years ago

Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Darina [25.2K]

Answer:

Given definite integral as a limit of Riemann sums is:

$\lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

Step-by-step explanation:

Given definite integral is:

$\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}$

Substituting (2) in above

$f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$