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Pepsi [2]
3 years ago
9

The probability density function f(x) for a uniform random variable x defined over the interval [2, 10] is

Mathematics
1 answer:
stellarik [79]3 years ago
3 0
F(x) = {1/8, 2 ≤ x ≤ 10}
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The 3rd one. (where the round part of the graph is at 0, 0) because that is where the y axis meets
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Find the slope of the curve r=cos(2theta) at theta=pi/6.. . Must this be solved parametrically? If so, why?
lara31 [8.8K]

By converting into parametric equations,

<span><span>x(θ)=r(θ)cosθ=cos2θ<span>cosθ
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By Product Rule,

<span>x'(θ)=−sin2θcosθ−cos2θsinθ</span>

<span>x'<span>(π/2)</span>=−<span>sin(π)</span><span>cos<span>(π/2)</span></span>−<span>cos(π)</span><span>sin<span>(π/2)</span></span>=1</span>

<span>y'(θ)=−sin2θsinθ+cos2θcosθ</span>

<span>y'<span>(π/2)</span>=−<span>sin(π)</span><span>sin<span>(π/2)</span></span>+<span>cos(π)</span><span>cos<span>(π/2)</span></span>=0</span>

So, the slope m of the curve can be found by

<span>m=<span>dy/dx</span><span>∣<span>θ=<span>π2
</span></span></span>= <span><span>y'<span>(π/2)/</span></span><span>x'<span>(π/2)
</span></span></span></span>=0/1

=0

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

6 0
3 years ago
What is the derivative of the following function? f(x) = 4x^6/cos^5(x)
KIM [24]

Answer:

f'(x) = \frac{24x^{5} \cos x + 20x^{6}\sin x}{\cos^{6}x }

Step-by-step explanation:

We have to find the derivative of the following function:

f(x) = \frac{4x^{6} }{\cos^{5} x }

Now, differentiating both sides with respect to x we get,

f'(x) = \frac{\cos^{5}x (24x^{5}) - 4x^{6}(5\cos^{4}x )(- \sin x)}{(\cos^{5}x )^{2}}

⇒ f'(x) = \frac{ 24x^{5} \cos x + 20 x^{6}\sin x}{\cos^{6}x } (Answer)

{Since, we know that, \frac{d(mx^{n} )}{dx} = m \times n x^{(n - 1)} and \frac{d(\cos^{n} x)}{dx} = n \cos^{(n - 1)} x(- \sin x) }

5 0
3 years ago
What is the commom difference in the following arithmetic sequence??
aalyn [17]
Each increases by a certain amount called the common difference

4.4-2.8=1.6
6-4.4=1.6
7.7-6=1.7
hmm, some error
maybe you meant 7.6

common difference is 1.6

answer is C
5 0
3 years ago
The body of a 154-pound person contains approximately 2×10^2 milligrams of gold and 6×10^3 milligrams of aluminum. Based on this
hram777 [196]

Answer:

2x10^2 and 6x 10^

Step-by-step explanation:

Hope I helped UwU

3 0
2 years ago
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