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3 years ago

14

3. Convert this rate (80km/hr) to a rate measured in m/s

1 answer:

scoray [572]3 years ago

8 0

22,24 meters per second

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baherus [9]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = $\frac{\sqrt3}{2}$

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

$\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}$

Proof LHS → RHS:

LHS cos 165

Double-Angle: cos (2 · 165) = 2 cos² 165 - 1

⇒ cos 330 = 2 cos² 165 - 1

⇒ 2 cos² 165 = cos 330 + 1

Given: $2 \cos^2 165 = \dfrac{\sqrt3}{2} + 1$

$\rightarrow 2 \cos^2 165 = \dfrac{\sqrt3}{2} + \dfrac{2}{2}$

Divide by 2: $\cos^2 165 = \dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \dfrac{2\sqrt3+4}{8}$

Square root: $\sqrt{\cos^2 165} = \sqrt{\dfrac{4+2\sqrt3}{8}}$

Scratchwork: $\cos^2 165 = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2$

$\rightarrow \cos 165 = \pm \dfrac{\sqrt3+1}{2\sqrt2}$

Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

$\rightarrow \cos 165 = - \dfrac{\sqrt3+1}{2\sqrt2}$

LHS = RHS $\checkmark$

4 0

3 years ago

What percentage of U.S. states have names that start with the letter W

Eduardwww [97]

50 states, 4 start with W (Washington, West Virgina, Wisconsin, Wyoming)
So its 8%

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3 years ago

Y=2x+b in y=MX+b form

Fynjy0 [20]

It would appear your original equation is in Y=MX+b form, where M=2

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3 years ago

Find the inverse function of f informally. f(x) = 6x

yaroslaw [1]

$f^-^1(x) = \frac{x}{6}$

8 0

3 years ago

HELP ASAP pleaseeee

AlekseyPX

$\\ \sf\longmapsto 3y=z-2x$

Take z to left

$\\ \sf\longmapsto -2x=3y-z$

Take out -

$\\ \sf\longmapsto 2x=-3y+z$

$\\ \sf\longmapsto 2x=z-3y$

$\\ \sf\longmapsto x=\dfrac{z-3y}{2}$

5 0

3 years ago

Read 2 more answers