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3 years ago

Ladder

1 answer:

5 0

Sin(theta) = O/H = 5/16 (this us the ratio)
If we go further for the problem:
sin(theta) = 5/16 becomes sin-1 (5/16) = 18.2°

Good luck!

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Prove the formula for (d/dx)(cos−1(x)) by the same method as for (d/dx)(sin−1(x)). Let y = cos−1(x). Then cos(y) = and 0 ≤ y ≤ π

gtnhenbr [62]

Answer:

$\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

$y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\$

$\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}$

Therefore;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }$

Since x = cos y from the above substitute;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }$

Hence, $\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$ gives the required proof

5 0

4 years ago

Which of the following expressions is a factor of the polynomial x2+3/2x-1?

mafiozo [28]

Answer:

the answer is x-1/2

3 0

3 years ago

Read 2 more answers

Evaluate 31 + 2x when x = 4.

Korolek [52]

X=4 so
2x=8
2x4=8
8+31 =39

3 0

3 years ago

Read 2 more answers

5. Which equation does not represent a line

Dimas [21]

D because the x-intercept would be 1/3, not 3

7 0

3 years ago

Slope=2/3;y-intercept=-1 write the linear equation in slope -intercept form

Mnenie [13.5K]

Answer:

$\large\boxed{y=\dfrac{2}{3}x-1}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

We have the slope $\bold{m=\dfrac{2}{3}}$ , and the y-intercept b = -1.

Substitute:

$y=\dfrac{2}{3}x-1$

6 0

3 years ago