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2 years ago

Is this function linear or nonlinear?

Mathematics

1 answer:

Sergio039 [100]2 years ago

7 0

The answer is nonlinear. It goes in a sharp downward curve, whereas a linear function is a straight line.

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The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correc

masya89 [10]

Answer:

Therefore the angle of intersection is $\theta =79.48^\circ$

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

$r_1(t)=(2t,t^2,t^4)$

and $r_2(t)=(sin t , sin5t, 2t)$

To find the tangent of a carve , we have to differentiate the carve.

$r'_1(t)=(2,2t,4t^3)$

The tangent at (0,0,0) is [ since the intersection point is (0,0,0)]

$r'_1(0)=(2,0,0)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{2^2+0^2+0^2} =2$

Again,

$r'_2(t)=(cos t ,5 cos5t, 2)$

The tangent at (0,0,0) is

$r'_2(0)=(1 ,5, 2)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{1^2+5^2+2^2} =\sqrt{30}$

If θ is angle between tangent, then

$cos \theta =\frac{r'_1(0).r'_2(0)}{|r'_1(0)|.|r'_2(0)|}$

$\Rightarrow cos \theta =\frac{(2,0,0).(1,5,2)}{2.\sqrt{30} }$

$\Rightarrow cos \theta =\frac{2}{2\sqrt{30} }$

$\Rightarrow cos \theta =\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =cos^{-1}\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =79.48^\circ$

Therefore the angle of intersection is $\theta =79.48^\circ$ .

8 0

2 years ago

3+x) 5<br> Solve it for me, and tell me how to do it EXPLANATION NEEDED

grigory [225]

I’m not too sure of what the equation is but I made a guess let me know if this was the right equation please I can redo it.

But, when solving this equation you are trying to find the value of x. To do that you have to get rid of the 3.

You would either add or subtract the 3 on both sides.

When the three is gone you should have somthing like

x = 5
- 3

Which you would move on to subtract the 5-3 and get 2.

x= 2

Here’s a picture of how I solved it

3 0

2 years ago

A parabola can be drawn given a focus of (-4, 4) and a directrix of y = –6. Write

AlexFokin [52]

Answer:

6y+2x

Step-by-step explanation:

A parabola can be drawn given a focus of (-4, 4) and a directrix of y = –6. Write

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2 years ago

4 cm on a map are equal to 6 km in real life. if two points are 16 cm apart on the map, how far apart are they in real life

Maksim231197 [3]

Answer:

24km

Step-by-step explanation:

16/4 is 4 so you multiply that by 6 and you get 24. the equation is (16/4)*6

6 0

2 years ago

a bottle of hand lotion is on sale for 2.25. If this price represents a 50% discount from the original price, what is the origin

dolphi86 [110]

The original price is $4.50 because when you multiply it by 50% you get $2.25

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2 years ago