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2 years ago

Which of the following would likely weigh about 8 pounds?

Mathematics

1 answer:

LenKa [72]2 years ago

4 0

1.A 2.A 3.D 4. 2 8/15 I’m not sure about the the question 3

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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

Write 20 as a product of prime factors.

Aliun [14]

Answer:

1, 2, 4, 5, 10

Step-by-step explanation:

4 0

2 years ago

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Thom needs 3/4 yard of brown fabric, 2/4 yard of blue fabric, and 3/4 yard of green fabric to make some costumes for a play.

kherson [118]

Answer:

Step-by-step explanation:

Hey there!

I think that some of the content in your question is missing so I will be solving for how much yards of fabric is needed in total

Since all of the fractions have common denominators, we can comfortably add them together

3/4+3/4+2/4 is 8/4

8/4 can be simplied to 2

So the total amount of yards of fabric Thom needs in total is 2 yards

5 0

1 year ago

Which equation is in standard form?

evablogger [386]

The answer is C. 2x+3y=12

3 0

2 years ago

Is it just me or is this confusing???

user100 [1]

Yup it is definently confsing

6 0

2 years ago

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