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zhuklara [117]
3 years ago
12

What is the expected price of a calculator in the year 2000 if it costs $13 in 2015

Mathematics
1 answer:
Mumz [18]3 years ago
7 0

Answer:

$10.90

Step-by-step explanation:

I don't know why but it wants me to talk when I dont need to

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If two angles of a triangle each measure 50 degrees, then what is the measure of the third angle of the triangle? Complete the s
xxTIMURxx [149]

Answer: 80

Step-by-step explanation:

Triangles equal 180 therefore 50+50=100 and 180-80=80

3 0
3 years ago
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Find the domain and range of the function
Karolina [17]
Domain- {-2, 1, 0, 1, 2}
Range- {-2, 0, 2}

My domain is right but I don’t think my range is. I did learn this 4 years ago though so
5 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
Sanrina has determined she needs a truck with 800 cubic feet of space to move her furniture
sergij07 [2.7K]

Answer:

= 7×7.5×14.5

= 761.25

800-761.25

= 38.75

so the answer is c

7 0
3 years ago
Break apart addenda to find the sum 33+49
VladimirAG [237]
The sum of 33+49 = 82
Thirty-three plus forty-nine equals eighty two.
30+3 + 40+9 =80 +2
5 0
3 years ago
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