1. If you report to work at 18.00 on a Wednesday and you get off at 02.50 on a

Mathematics

1 answer:

Ivanshal [37]2 years ago

7 0

Sheeeeeeeeeeeeeeeeeeeeeeeeeeeeesh

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The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, corr

san4es73 [151]

First get the tangent vectors by differentiating r1 and r2
$r_1 '(t) = (4,2t,3t^2) \\ \\ r_2'(t) = (cos (t), 5 cos(5t), 2)$
Evaluate at t=0
$r_1' = (4,0,0) \\ \\ r_2' = (1,5,2)$

Use identity for angle between 2 vectors:
$u*v = |u| |v| cos \theta$

Evaluate dot product and unit vectors:
$u*v = (4,0,0)*(1,5,2) = 4 \\ \\ |u| = \sqrt{4^2 +0^2+0^2} = 4 \\ \\ |v| = \sqrt{1^2 + 5^2+2^2} = \sqrt{30}$

Sub into identity and solve for theta:
$4 = 4 \sqrt{30} cos \theta \\ \\ cos\theta = \frac{1}{\sqrt{30}} \\ \\ \theta = 79.48$

Answer:
Angle of intersection is about 79 degrees.

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3 years ago

First-person to answer correctly gets brainiest<br><br> Find an equation for each line.

seropon [69]

Green = -1x - 1
Black = -2x
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Alex787 [66]

12 1/10
A quick way to get this one is to recognize that .1 is a decimal in the tenth place. Because of this, we know to put it over 10. Because 1/10 cannot be simplified, it is in simplest form. Now, simply return the whole number to the fraction.

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If 120 marks is 60% what is full marks

AveGali [126]

Let's say is "x", so, then "x" is the 100%, and we know that the 60% is 120, what the dickens is "x" anyway?

$\bf \begin{array}{ccll}
marks&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
x&100\\
120&60
\end{array}\implies \cfrac{x}{120}=\cfrac{100}{60}\implies x=\cfrac{120\cdot 100}{60}$

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anyanavicka [17]

Answer:

Listed

Please mark me as the brainliest and thanks

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