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r-ruslan [8.4K]
2 years ago
13

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

t to the nearest degree.
Mathematics
1 answer:
masya89 [10]2 years ago
8 0

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.

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Answer:

(2,3)

Step-by-step explanation:

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To find the y-coordinate, proceed similarly.  Find the average of 2 and 4.  It is 3.

Thus, the midpoint is (2, 3).

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John is looking at the eagle on top of a building The height of the building is 120 ft Approximately how many feet is Jack away
bearhunter [10]

Answer:

The answer is below

Step-by-step explanation:

The question is not complete. A similar question is attached and is solved.

Solution:

A triangle is a polygon with three sides and three angles. Types of triangles are scalene, acute, obtuse, isosceles, equilateral and right angled triangle.

A right angled triangle is a triangle with one angle equal to 90 degrees. The longest side of a right angled triangle is known as the hypotenuse. Trigonometric identities is used to show the relationship between the angles and sides of a right angled triangle, i.e.:

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From the image:

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Q # 1 Graph the function<br>Y = |X + 2| - 3
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First of all we know the Absolute Value Function that is:

\left | x \right |= \left \{ {{x \ \ \ \ x \geq 0} \atop {-x \ \ \ \ x\ \textless \ 0}} \right.

This is called the Parent Function <em>of the Absolute Value Function.</em>

From the equation:

y=\left | x+2 \right |-3

The term:

\left | x+2 \right |

means that the the Parent Function is <em>shifted</em> two units <em>to the left</em>.

On the other hand, the term:

-3

means that the function \left | x+2 \right | is <em>shifted</em> three units <em>downward. </em>So the result is the graph shown below

4 0
3 years ago
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