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2 years ago

Given cos 0 = 1/6 and angle 0 is in Quadrant IV, what is the exact value of sin 0 in

Mathematics

1 answer:

Vinil7 [7]2 years ago

4 0

cos 0 = 1/6

1 - cos²0 = sin²0

sin²0 = 35/36

in quadrant IV (4) the cos is positive sin is negative.

sin0 = - √35/6

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Find the equation of the line , use exact numbers

MArishka [77]

y=1/2x-3

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3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%20%5Cinfty%20%20%5Cfrac%7B%20%5Csqrt%5B%20%20%5Cscriptsize%5Cphi%

Rasek [7]

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

$I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx$

Replace $x \to x^{\frac1\phi} = x^{\phi-1}$ :

$I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

Split the integral at x = 1. For the integral over [1, ∞), substitute $x \to \frac1x$ :

$\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx$

The integrals involving tan⁻¹ disappear, and we're left with

$I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}$

8 0

2 years ago

IF YOU ANSWER ALL OF THIS ILL MARK YOU BRAINLIST NO CAP!

Zielflug [23.3K]

1) 4 = 16 divided by n
k + 5 = 11
x - 2 = 7
7 times a = 42
6 = 1/3 times s
r times 13 = 17
b - 5 = 16
No. It should be 24 = 8 times x
217 - x = 36
p = 8180 - 6780

Step-by-step explanation: Cause it is

6 0

2 years ago

Use the calculator to find the product. (1. 466 × 10–8)(5. 02 × 105) What is the coefficient of the product? What is the exponen

mestny [16]

The product of the factors in the given expression comes to be $7.35932 *10^{-3}$ .

The given expression is:

$(1.466*10^{-8} )(5.02*10^5)$

We can rewrite the given expression as

$(1.466*5.02)(10^{-8} *10^5)$

<h3>What is the exponent addition rule? </h3>

If we have two numbers with the same base we can write the product of the numbers as a single base followed by the addition of exponents.

$a^m*a^n = a^{m+n}$

$1.466*5.02=7.35932$

$10^{-8} *10^5 = 10^{-3}$ ....from exponent addition rule

So, $(1.466*10^{-8} )(5.02*10^5)=7.35932 *10^{-3}$

Therefore, the product of the factors in the given expression comes to be $7.35932 *10^{-3}$ .

To get more about exponents visit:

brainly.com/question/819893

6 0

2 years ago

Read 2 more answers

Anna wants to factor the polynomial p(x)=5x^4+40x. She knows that the sum of cubes formula is a^3+b^3=(a+b)(a^2−ab+b^2).

Artemon [7]

Answer:

Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.

Part B: Option 3, B: 5x(x+2)(x^2−2x+4)

Step-by-step explanation:

p(x) = 5x^4 + 40x

p(x) = 5x(x^3 + 8)

p(x) = 5x(x + 2)(x^2 - 2x + 4)

Part A: Option 2, A: Anna’s answer is incorrect. She correctly factored out 5x, but incorrectly identified a and b, so her answer cannot be correct.

Part B: Option 3, B: 5x(x+2)(x^2−2x+4)

7 0

3 years ago