MATHEMATICS COLLEGE

If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions for t 0. Do the particles collide? If they collide find t. If not enter NONE.r1(t)=r2(t)=<9t-14,t^2,13t-42>t=

Answers

Answer 1

Answer:

Answer:

The particles collide when t = 7 at the point (49, 49, 49).

Step-by-step explanation:

We know the trajectories of the two particles,

$r_1(t)=\langle t^2,16t-63,t^2\rangle\nr_2(t)=\langle 9t-14,t^2,13t-42\rangle$

To find if the tow particles collide you must:

Equate the x-components for each particle and solve for t

$t^2=9t-14\nt^2-9t+14=0\n\left(t^2-2t\right)+\left(-7t+14\right)=0\nt\left(t-2\right)-7\left(t-2\right)=0\n\left(t-2\right)\left(t-7\right)=0$

The solutions to the quadratic equation are:

$t=2,\:t=7$

Equate the y-components for each particle and solve for t

$16t-63=t^2\n^2-16t+63=0\n\left(t^2-7t\right)+\left(-9t+63\right)=0\nt\left(t-7\right)-9\left(t-7\right)=0\n\left(t-7\right)\left(t-9\right)=0$

The solutions to the quadratic equation are:

$t=7,\:t=9$

Equate the z-components for each particle and solve for t

$t^2=13t-42\nt^2-13t+42=0\n\left(t^2-6t\right)+\left(-7t+42\right)=0\nt\left(t-6\right)-7\left(t-6\right)=0\n\left(t-6\right)\left(t-7\right)=0$

The solutions to the quadratic equation are:

$t=6,\:t=7$

Evaluate the position vectors at the common time. The common solution is when t = 7.

$r_1(7)=\langle 7^2,16(7)-63,7^2\rangle=\langle 49,49,49\rangle\n\nr_2(7)=\langle 9(7)-14,7^2,13(7)-42\rangle=\langle 49,49,49\rangle$

For two particles to collide, they must be at exactly the same coordinates at exactly the same time.

The particles collide when t = 7 at the point (49, 49, 49).

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1 is 25% of what number?

Answers

Answer:

25% of 4 is 1.

Step-by-step explanation:

100% of 4 is 4, therefore 25 percent of 4 equals 1.

Explain how to write 2 dividid 5 as a fraction

Answers

Answer:

2/5

Step-by-step explanation:

Two divided by 5 is simply written as 2/5.

Hope I helped!

2/5 is how it’s written as a fraction, 2 is over 5, 2 goes inside and 5 outside when you write the division expression

8) Which equations below would be parallel by just looking at theequations

1. y=2x + 10 and y= 3x -12
2. y= 4x -2 and y= 4x + 3
3. y=10 and y= 15x
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Answers

Answer: y=4x-2 and y=4x+3

Mary sells to her father, robert, her shares in a corp for $55,000. the shares cost mary $80,000. how much loss may mary claim from the sale

Answers

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Mary Sells shares = $55,000

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Solve this equation using the inverse operation: x + 8 = -5

Answers

Hey there!

x + 8 = -5

SUBTRACT 8 to BOTH SIDES

x + 8 - 8 = -5 - 8

CANCEL out: 8 - 8 because it give you 0

KEEP: -5 - 8 because it help solve for the x-value

NEW EQUATION: x = -5 - 8

SIMPLIFY IT!

x = -13

Therefore, your answer is: x =-13

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

$x=-13$

Step-by-step explanation:

We can subtract 8 from both sides.

$x+8=-5\n(x+8)-8=(-5)-8\nx=-13$

Calculate the rent of a decreasing annuity at 8% interest compounded quarterly with payments made every quarter-year for 7 years and present value $78,000.

Answers

The general Formula for a decreasing Annuity is:
$P = ( ((1+i)^n -1)/(i (1+i)^n)) R$
For this example we have:
P = 78,000
n = 7*4 = 28
i = 8%/4 = 2% = 0.02

After substituting you can find value for R, rent.

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