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3 years ago

K(x)= -3x - 3; find k(-2)

Mathematics

1 answer:

Anastaziya [24]3 years ago

6 0

Answer:

$\huge{k( - 2)} = 3$

Step-by-step explanation:

$K(x)= -3x - 3$

To find the value of k substitute the value of k that's -2 into the original expression and solve for the value of k.

That's

$k( - 2) = - 3( - 2) - 3 \\ = 6 - 3 = 3$

We have the final answer as

Hope this helps you

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Find the real or imaginary solutions of 125x^3 - 27 = 0

hichkok12 [17]

Answer:

1.2}3,2

Step-by-step explanation:

4 0

3 years ago

If a speedboat can travel 34 nautical miles in 2 hours, how far can it travel in 3 hours? Round your answer to the nearest tenth

defon

Answer:

(34 / 2) * 3 = 51 nautical miles

Step-by-step explanation:

(34/2) => Finds miles per hour

* 3 => Finds total miles traveled in 3 hours

5 0

2 years ago

Read 2 more answers

Can y’all help find the surface area please and thank you

solong [7]

To find the area of a complex shape:

⇒ must cut the whole shape into a simpler shape

square with side lengths of 4 in
2 triangles with a base of 4 in. and a height of 8 in.
2 triangles with a base of 4 in. and a height of 10 in.

Let's calculate:

Area of 2 triangles with a base of 4 in. and a height of 8 in.

$Area = \frac{1}{2}*4*8 + \frac{1}{2}*4*8=16+16=32\\$

2 triangles with a base of 4 in. and a height of 10 in.

$Area = \frac{1}{2}*4*10 + \frac{1}{2}*4*10=20+20=40$

square with side lengths of 4 in

$Area = 4 * 4=16$

Total Area: 32 + 40 + 16 = 88 in²

Answer: 88 in²

Hope that helps!

8 0

1 year 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.

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