What is the common ratio for this geometric sequence?

Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=5t−5 and y(t)=2t−k, and the position

Ipatiy [6.2K]

Answer:

Part A) Not collide

Part B) k = 4

Part C) Particle B is moving fast.

Step-by-step explanation:

Two particles move in the xy-plane. At time, t

Position of particle A:-

$x(t)=5t-5$

$y(t)=2t-k$

Position of particles B:-

$x(t)=4t$

$y(t)=t^2-2t+1$

Part A) For k = -6

Position particle A, (5t-5,2t+6)

Position of particle B, $(4t,t^2-2t-1)$

If both collides then x and y coordinate must be same

Therefore,

For x-coordinate:

5t - 5 = 4t

t = 5

For y-coordinate:

$2t+6=t^2-2t-1$

$t^2-4t-7=0$

$t=-1.3,5.3$

The value of t is not same. So, k = -6 A and B will not collide.

Part B) If both collides then x and y coordinate must be same

For x-coordinate:

5t - 5 = 4t

t = 5

For y-coordinate:

$2t-k=t^2-2t-1$

Put t = 5

$10-k=25-10-1$

$k=4$

Hence, if k = 4 then A and B collide.

Part C)

Speed of particle A, $\dfrac{dA}{dt}$

$\dfrac{dA}{dt}=\dfrac{dy}{dt}\cdot \dfrac{dt}{dx}$

$\dfrac{dA}{dt}=2\cdot \dfrac{1}{5}\approx 0.4$

Speed of particle B, $\dfrac{dB}{dt}$

$\dfrac{dB}{dt}=\dfrac{dy}{dt}\cdot \dfrac{dt}{dx}$

$\dfrac{dB}{dt}=2t-2\cdot \dfrac{1}{4}$

At t = 5

$\dfrac{dB}{dt}=10-2\cdot \dfrac{1}{4}=2$

Hence, Particle B moves faster than particle A

8 0

3 years ago

Point P on the number line shows Lara's score after the first round of a quiz: A number line is shown from negative 8 to 0 to po

Luda [366]

Answer:

The correct group of answer is D) 3 + (−4) = −1, because −1 is 4 units to the left of 3

Step-by-step explanation:

Consider the provided information.

Point P on the number line shows Lara's score after the first round of a quiz:

Point P is shown on 3.

That means after the first round her total was 3.

In round two, she lost 4 points.

Therefore, she score −4 points in 2nd round

To find the total points at the end of round 2, we need to add -4 to 3.

3+(−4)=−1

Here −1 is 4 units to the left of 3.

Hence, the correct group of answer is D) 3 + (−4) = −1, because −1 is 4 units to the left of 3

3 0

4 years ago

Read 2 more answers

Imamu pays $30 each month for his gym membership what is the change in the amount of money in his account after 2/3 of the year?

SSSSS [86.1K]

240/360 so that answer is 240

6 0

4 years ago

Find the slope of the line passing through each of the following pairs of points.

ArbitrLikvidat [17]

Answer:

0

Step-by-step explanation:

m= y2-y1/x2-x1

=0-0/-3-5

=0/-8

=0

7 0

3 years ago

Read 2 more answers

Is 12 ft equal to 4 yd?

levacccp [35]

Answer:

yes, 12 feet is equal to 4 yards.

if you want to know haw, let me know :)

hope this helped and gave a great day <3

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers