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3 years ago

9

Tanya has several different ways she likes to walk home. One route takes 20 minutes, two of the routes take 30 minutes, and two

take 40 minutes.
Tanya randomly chooses a route to walk home.

What is the probability, to the nearest percent, that it will take her 30 min to walk home?

2 answers:

stira [4]3 years ago

8 0

50% because there are 4 routes and 2 take 30 minutes, 2/4 = 50/100 = 50%

Dimas [21]3 years ago

8 0

About 50% in all of the 30min

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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 $\theta =79.48^\circ$ .

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3 years ago

Write the number in scientific notation.<br> 1,920,000

LUCKY_DIMON [66]

The answer is 1.92 x 10^6

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3 years ago

Evaluate i^31 please help

Nadya [2.5K]

ANSWER

${i}^{31} = - i$

EXPLANATION

We want to evaluate

${i}^{31}$

Use indices to rewrite the expression as:

$= {i}^{30} \times i$

We know that

${i}^{2} = - 1$

So we rewrite the expression to obtain;

$= ({ {i}^{2}) }^{15} \times i$

This gives us;

$= {( - 1) }^{15} \times i$

This simplifies to

$= - 1 \times i$

$= - i$

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3 years ago

A car travelled 100 km with half the distance at 40 km/h and the other half at 80 km/h. Find the average speed of the car for th

Nana76 [90]

We must look at this question in steps
The first half of the journey is travelled at 40 km/h
Half of 100km is 50 km
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Distance = Speed x Time
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We can work out the time:

50km / 40km/h = 1.25 hours

Next we look at the second half of the journey
50km at 80km/h
50km / 80km/h = 0.625 hours

Add together both times to work out how long the entire journey took
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Using the Speed formula from before
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3 years ago

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timurjin [86]

20 and 0 are your answers

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2 years ago