What is the position of C on the number line below write your answer as a fraction or mixed number

Determine if the lines r1(t) = <3, 0, 2> + t <1, 2, −2> and r2(s) = <0, 1, −1> + s <4, 1, 1> intersect,

Temka [501]

Answer:

Yes lines are intersecting, point of intersection is <4,2,0>.

Step-by-step explanation:

Given parametric equations of line are:

$r_{1}(t) = + t \\ r_{1}(t) = \\ r_{1}(t) = ---(1)$

$r_{2}(s) = + s \\ r_{2}(s) = \\ r_{2}(s) = ---(2)\\$

If lines are intersecting then parametric coordinates of (1) are equal to (2)

$3+t=4s---(A)\\2t=1+s---(B)\\2-2t=s-1---(C)\\$

Considering A and B to find values of t and s

From A

t=4s-3---(D)

Putting in (B)

2(4s-3)=1+s

8s-6=1+s

7s=7

s=1

Then

t=4-3

t=1

If lines are intersecting then these values of s and t must satisfy (C)

2-2(1)=1-1

0=0

This shows lines are intersecting.

At this value of t, (1) becomes

$r_{1}(1) = \\=$

Putting s=1 in (2)

$r_{2}(1)=4, 1+1,-1+1>\\=$

Point of intersection is <4,2,0>.

4 0

3 years ago

An orange is shot up into the air with a catapult. The function given by h(t)+20+60t-16t² models the oranges height in feet, t s

Ganezh [65]

Answer:

C, E

Step-by-step explanation:

As a rule, these ballistic motion equations are only applicable for heights above the final resting place. Usually, that is the ground (h=0). Time is always measured as a non-negative quantity beginning at the time of launch.

The function is meaningless after the time the object comes to rest on the ground, so the domain of the function extends from 0 until that time.

These considerations allow us to evaluate the offered statements.

A. The domain never includes negative values. (A is not a true statement)

B. The heights are the same at times that are symmetrical around the time of the maximum height. Here, that time is about 1.9 seconds, not 1.5 seconds, so the heights will be different at 1 and 2 seconds after launch. (B is not a true statement)

C. The graph of the function shows the height reaches 0 at about 4.06 seconds, a little after 4 seconds. (C is true)

D. Based on our answer to C, we know t=10 is outside the domain of the function. (D is not a true statement)

E. The value of the function is 20 when t=0, so the function tells us the orange is 20 feet above the ground when it is launched. (E is true)

The true statements are C and E.