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Yuri [45]
3 years ago
6

The curves r1(t) = 2t, t2, t3 and r2(t) = sin t, sin 5t, 3t intersect at the origin. Find their angle of intersection, θ, correc

t to the nearest degree.
Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

The angle between the curves is 80.27°.

Step-by-step explanation:

Given that

r₁(t) = <2t, t²,t³>

Differentiating with respect to t

r'₁(t) = <2, 2t,3t²>

Since it is intersect at origin.

Then r'₁(0)= <2,0,0>      [ putting t=0]

The tangent vector at origin of r₁(t) is

r'₁(0)= <2,0,0>

Again,

r₂(t)= <sin t, sin 5t, 3t>

Differentiating with respect to t

r'₂(t)= <cost, 5 cos 5t, 3>

Since it is intersect at origin.

Then r'₂(0)= <1,5,3>      [ putting t=0]

The tangent vector at origin of r₂(t) is

r'₂(0)= <1,5,3>      

The angle between the carves is equal to the angle between their tangent.

We know that

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

Putting the all values

Cos \theta = \frac{.}{\sqrt{2^2+0^2+0^2}\sqrt{1^2+5^2+3^2}}

 \Rightarrow \theta =cos^{-1}(\frac{2}{2\sqrt{35}})

 ⇒θ= 80.27°

The angle between the curves are 80.27°.

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Sarah saved $12.75 every week for a number of weeks, w. She received an additional $25 during the last week in which she saved m
Umnica [9.8K]

Answer:

12.75w + 25 = 114.25

w = 7

Step-by-step explanation:

since sarah is receiving 12.75 each week for a number of weeks, w (we don't know its value yet)  we know that first part of the equation: that 12.75 is the coefficient next to w. Then we have the extra 25, so we know that adding 12.75w and 25 would give us sarah's total amount, which is 114.25.

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12.75w = 89.25

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3 0
3 years ago
Am i correct?? thanks for checking my answer :)
UNO [17]

Answer:

no

Step-by-step explanation:

since the y=mx+b format is used here, your b is -5. for this to be correct, your y-int needs to be on -5, not -2 as you have it. Other than that, i believe you are correct


3 0
3 years ago
Read 2 more answers
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