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Dmitry [639]
3 years ago
9

Which value of a would make the following expression completely factored

Mathematics
2 answers:
solmaris [256]3 years ago
6 0

Answer:

A)

Step-by-step explanation:

We know that the expression (x^2 - a^2) can be written as (x-a)(x+a). So an expression of this type: (x^2 - a^2) wouldn't be completely factored because it could be factorized even more.

So we know that 36 = 6^2, 49= 7^2 and 81 = 9^2. So if we choose any of these options (Option B, C and D) it wouldn't be completely factored.

The correct is the option A, given that if a=12, it wouldn't be a perfect square, so it would be completely factored.

Bogdan [553]3 years ago
6 0

So I just did the problem and im pretty sure the answer is A

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Given the following table, what is the average rate of change from 2 ≤ x ≤ 5 ?
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What is the sum? <br> Thank you!
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2 years ago
There are 9 pies cut into 1/8 pieces, how many pieces would you get ?
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6 0
3 years ago
Find dy/dx when r=2 2cos(theta) , then find slope of tengent line at point(4, 2pi)
Korolek [52]

The slope of tangent line at point(4, 2pi) is undefined.

For given question,

We have been given a polar equation r = 2 + 2cos(θ)

We need find dy/dx as well as the slope of tangent line at point(4, 2π).

We know that, for polar equation we use,

x = r cos(θ)   and  y = r sin(θ)

plug the given value of r into these equations we get:

⇒ x = r cos(θ)

⇒ x = (2 + 2cos(θ) ) ×  cos(θ)

⇒ x = 2(cos(θ) + cos²(θ))

⇒ x = 2cos(θ) + 2cos²(θ)

Similarly,

⇒ y = r sin(θ)

⇒ y = (2 + 2cos(θ) ) ×  sin(θ)

⇒ y =  2(sin(θ) + sin(θ)cos(θ))

⇒ y =  2sin(θ) + 2sin(θ)cos(θ)

Now we find derivative of x and y with respect to theta.

\Rightarrow \frac{dx}{d\theta} =-2sin(\theta)+2(-2cos(\theta)sin(\theta))\\\\\Rightarrow  \frac{dx}{d\theta} =-2sin(\theta)-2sin(2\theta)          .............(1)

Similarly,

\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos^2(\theta)-sin^2(\theta))\\\\\Rightarrow \frac{dy}{d\theta}=2cos(\theta)+2(cos(2\theta))          ..............(2)

Now we find dy/dx

⇒ dy/dx = (dy/dθ) / (dx/dθ)

From (1) and (2),

\Rightarrow \frac{dy}{dx} =\frac{2cos(\theta)+2cos(2\theta)}{-2sin(\theta)-2sin(2\theta)} \\\\\Rightarrow \frac{dy}{dx} =\frac{2(cos(\theta)+cos(2\theta))}{-2(sin(\theta)+sin(2\theta))}\\\\\Rightarrow \frac{dy}{dx} =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}

We know that The slope of tangent line is given by dy/dx.

So, the slope is: m =-\frac{cos(\theta)+cos(2\theta)}{sin(\theta)+sin(2\theta)}

Now we need to find the slope of tangent line at point(4, 2pi)

Substitute θ = 2π in above slope formula.

\Rightarrow m =-\frac{cos(2\pi)+cos(2\times 2\pi)}{sin(2\pi)+sin(2\times 2\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{0+sin(4\pi)}\\\\\Rightarrow m=-\frac{1+cos(4\pi)}{sin(4\pi)}

⇒ m = ∞

The slope of tangent line at point(4, 2pi) is not defined.

This means, the tangent line must be parallel to Y-axis.

Therefore, the slope of tangent line at point(4, 2pi) is undefined.

Learn more about the slope here:

brainly.com/question/10785137

#SPJ4

8 0
2 years ago
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