Find the measurements

Mathematics

1 answer:

alexandr1967 [171]3 years ago

5 0

Answer:

X=75 y=90

Step-by-step explanation:

180-105=75

X=75

180-90=90

Y=90

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Please show me how to solve the initial value problem <br> y'=tanx y(pi/4)=3

AlexFokin [52]

The ODE is separable, i.e. you can write

$\dfrac{\mathrm dy}{\mathrm dx}=\tan x\iff\mathrm dy=\tan x\,\mathrm dx$

Integrating both sides gives the general solution.

$\displaystyle\int\mathrm dy=\int\tan x\,\mathrm dx$
$y=-\ln|\cos x|+C$

Given that $y\left(\dfrac\pi4\right)=3$ , we have

$3=-\ln\left|\cos\dfrac\pi4\right|+C$
$3=-\ln\dfrac1{\sqrt2}+C$
$3-\ln\sqrt2=C$

and so the particular solution to the IVP is

$y=-\ln|\cos x|+3-\ln\sqrt2$
$y=3-\ln|\sqrt2\cos x|$

4 0

3 years ago

Use a half-angle identity to find the exact value of sinPi/8

stellarik [79]

Answer:

sin(π/8) = (1/2)√(2-√2)

Step-by-step explanation:

Using the half-angle formula ...

$\sin{\dfrac{\theta}{2}}=\sqrt{\dfrac{1-\cos{\theta}}{2}}$

We can let θ = π/4 and simplify the result as follows:

$\sin{\dfrac{\pi}{8}}=\sqrt{\dfrac{1-\cos{(\pi/4)}}{2}}=\sqrt{\dfrac{1-\dfrac{\sqrt{2}}{2}}{2}}=\sqrt{\dfrac{2-\sqrt{2}}{4}}\\\\=\boxed{\dfrac{1}{2}\sqrt{2-\sqrt{2}}}}$