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aleksandr82 [10.1K]

2 years ago

9

What is the slope of a line that is perpendicular to 5 x – 2 y = 1 ?

1 answer:

lord [1]2 years ago

4 0

Answer:

The slope is 5/2

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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

An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of random

Serhud [2]

Answer:

The probability of choosing a blue or yellow highlighter when one yellow highlighter is picked is 17/25.

Step-by-step explanation:

Here, according to the question:

Total number of yellow highlighters = 12

Total number of blue highlighters = 6

Total number of green highlighters = 4

Total number of orange highlighters = 3

So, the total number of highlighters = 12 + 6 + 4 + 3 = 25

Let E1 : Event of selecting a yellow highlighter.

P(E1) = $\frac{\textrm{Total number of yellow highlighters}}{\textrm{Total Highlighters}}$ = $\frac{12}{25}$

Let E2 : Event of selecting blue or yellow highlighter ONCE yellow highlighter is selected.

So, the total yellow highlighters left after selecting one = 12 -1 = 11

Also, the number of blue highlighter = 6

So, the TOTAL FAVORABLE options to E2 = 6+ 11 = 17

P(E2) =

$\frac{\textrm{Total number of yellow + Blue highlighters}}{\textrm{Total Highlighters}}$ = $\frac{17}{25}$

Hence, the probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected is 17/25.

7 0

3 years ago

Which expression is equivalent to ( 4 1/3)^3 ?

shutvik [7]

(13/3)^3 or (13/3)•(13/3)•(13/3)

5 0

2 years ago

Simplify:<br> 3x+1b+10g-4x

Aneli [31]

Answer:

b+10g-x

Step-by-step explanation:

3x-4x=x

New equation becomes:

b+10g-x

4 0

2 years ago

Read 2 more answers

Write 10 1/2 as a decimal number

VikaD [51]

Answer:

10.5

Step-by-step explanation:

1/2 as a decimal is 0.5

so 10 is a whole number so i dont have to change it.

then answer is 10.5

7 0

3 years ago

Read 2 more answers