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3 years ago

Please help me understand and solve this

Mathematics

1 answer:

ss7ja [257]3 years ago

7 0

Step-by-step explanation:

just multiple them and you'll get the results and the results you got add them together

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Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 2t, 1 + 6t, 1 + 14t . Find the points at which their p

GuDViN [60]

Answer:

A) points at which paths intersect : (1,1,1) ; (2,4,8)

B) DNE

Step-by-step explanation:

A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:

$t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2$

you replace t1 from the first equation in the second equation:

$(1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}$

Then, for t2 = 0 and t2=1/2 you obtain for t1:

$t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2$

Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.

The points at which the paths intersect are:

$r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)$

B) You have the following two trajectories of two independent particles:

$r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)$

To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:

$t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t$

From the first equation you have:

$t=1+2t\\\\t=-1$

This values does not have a physical meaning, then, the particle do not collide

answer: DNE

5 0

3 years ago

What is the value of x? A.39 B.41 C.26 D.17

mojhsa [17]

Answer:

The answer is B.

Step-by-step explanation:

You have to use Pythogorean Theorem, c² = a² + b² where c is the hypotenuse and a,b is the side lengths :

${c}^{2} = {a}^{2} + {b}^{2}$

Let a = 40,

Let b = 9,

${c}^{2} = {40}^{2} + {9}^{2}$

${c}^{2} = 1600 + 81$

${c}^{2} = 1681$

$c = \sqrt{1681}$

$c = 41 \: units$

*Take note, hypotenuse will always be the longest length among the 3 lengths.

*Pythogorean Theorem can only applied in a right-angle triangle.

3 0

3 years ago

I’m stuck on this which one is correct ?

stepan [7]

The answer is c. Bcs A + B = 90 [ 35 + 55 = 90]

3 0

3 years ago

Read 2 more answers

Help me 6 = 1/5 (4y + 10)

gregori [183]

Step-by-step explanation:

open the bracket

6={(1/5×4y) + 1/5×10}

6=4/5y+2

6-2=4/5y

4=4/5y

divide both sides by 4/5

y=1/5

4 0

3 years ago

Read 2 more answers

Approximate pi plus the square root of 70 to the nearest hundredth.

stich3 [128]

Answer:

11.51

Step-by-step explanation:

In general, a calculator is required to evaluate the irrational sum ...

π + √70

<h3>Calculator result</h3>

The result from a readily-available online calculator is shown in the attachment.

π + √70 ≈ 11.51

Additional comment

You have probably memorized pi to several digits: 3.1416. To obtain the required estimate means you need to approximate √70 to about the same level of precision.

For a number n = a² +b, the square root can be approximated by the continued fraction ...

√n ≈ a +b/(2a +b/(2a +...))

Effectively, the root (r) can be iterated from the recursive formula ...

r' = a +b/(a +r)

For √70, we have 70 = 8² +6 ⇒ a=8, b=6

If the initial approximation of the root is r0≈a=8, then a couple of iterations gives ...

r1 = 8 + 6/(8 +r0) = 8 + 6/(8 +8) = 8 3/8

r2 = 8 + 6/(8 +r1) = 8 +6/(8 +8 3/8) = 8 48/131

This has sufficient accuracy for the purpose. The decimal equivalent of the sum then becomes ...

3.1416 +8.3664 = 11.5080 ≈ 11.51

5 0

2 years ago

Please help me understand and solve this​

Please help me understand and solve this