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BARSIC [14]
3 years ago
13

Consider the spiral given by c(t) = (e2t cos(2t), e2t sin(2t)). Show that the angle between c and c' is constant. c'(t) = _____L

et θ be the angle between c and c'. Using the dot product rule we have the following. c(t) · c'(t) = c(t) · c'(t) cos(θ) 2e4t =________ cos(θ)

Mathematics
1 answer:
Tcecarenko [31]3 years ago
8 0

Answer:

angle is 45° which is constant

Step-by-step explanation:

We use formula for two vectors <u>a </u>and <u>b</u>    to calculate angle θ between them by formula

cos θ =  <u>a .</u> <u>b</u>  / magnitude of <u>a </u>  ×  magnitude of <u>b</u>

<u>Please see the attached file</u>

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PLEASE help Write an allgebraic expression for 67 more than the product of 126 and b
m_a_m_a [10]
126b + 67

Product is multiplication, so multiply 126 and b. Then 67 more, aka add
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3 years ago
Inverse Function In Exercise,analytically show that the functions are inverse functions.Then use the graphing utility to show th
DanielleElmas [232]

Answer:

g^{-1}(x)=f(x)=e^{\frac{x}{3}}

Step-by-step explanation:

We have been given two functions as g(x)=\text{ln}(x^3) and f(x)=e^{\frac{x}{3}}. We are asked to show that both functions are inverse of each other algebraically and graphically.

Let us find inverse function of g(x)=\text{ln}(x^3) as:

y=\text{ln}(x^3)

Interchange x and y values:

x=\text{ln}(y^3)

Using log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

x=3\cdot \text{ln}(y)

\frac{x}{3}=\frac{3\cdot \text{ln}(y)}{3}

\frac{x}{3}=\text{ln}(y)

Using log definition; If \text{log}_a(b)=c, then b=a^c, we will get:

y=e^{\frac{x}{3}}

g^{-1}(x)=e^{\frac{x}{3}}

Therefore, we can see that function f(x)=e^{\frac{x}{3}} is inverse of function g(x)=\text{ln}(x^3).

We can see that both functions are symmetric about line y=x, therefore, both functions are inverse of each other.  

8 0
4 years ago
Find the x−and y−intercepts. 3x + 12y = −48
Yanka [14]

Answer:

y-intercept: (0,-4)

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Step-by-step explanation:

To solve for X, Substitute 0 for Y and continue.

To solve for Y, Substitute 0 for X and continue.

3 0
3 years ago
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ohaa [14]

Step-by-step explanation:

use the midpoint formula

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3 0
3 years ago
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konstantin123 [22]

<span>Let each side perpendicular to the river be "x".
Then the side parallel to the river is "2400-2x".</span>

 

The function would be:

<span>A(x) = x(2400-2x)

</span>

And it would be: A(x) = 2400x - 2x^2

 

To solve the equation:

<span>
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Maximum Area happens where:

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To find the length it will be:

 

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6 0
3 years ago
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