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2 years ago

What are factorials? And how do you do them in fractions like

Mathematics

1 answer:

Ket [755]2 years ago

4 0

I think that it is 54

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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

Which relation is not a function

3241004551 [841]

Answer:

Step-by-step explanation:

4 0

2 years ago

The teenagers of a school sold 430 tickets for their Christmas program. The girls sold 15% more tickets than the boys sold. How

Paul [167]

The girls sold 230
The boys sold 200

8 0

3 years ago

What is 3/2 x + 30 degrees

jekas [21]

Sum of internal angles of any triangle = 180∘

∴x + 2x + 3x = 180∘
∴6x = 180∘
∴ x = 30∘

So the angles are: 30∘, 60∘ and 90∘

3 0

2 years ago

13 14<br> x<br> 7 11<br> What is 13/7 times 14/11 equal

Ostrovityanka [42]

Answer:

(2 × 7 × 13) / (7 × 11) =

((2 × 7 × 13) ÷ 7) / ((7 × 11) ÷ 7) =

(2 × 7 ÷ 7 × 13)/(7 ÷ 7 × 11) =

(2 × 1 × 13)/(1 × 11) =

(2 × 13)/11 =

26/11;

Step-by-step explanation:

6 0

2 years ago

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