Order the following from greatest to least

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

I'm having trouble with this -9x + 4y = 55 -11x + 7y = 82

lubasha [3.4K]

Answer:

Step-by-step explanation:

99x - 44y = -605

-99x + 63y = 738

19y = 133

y = 7

-9x + 28 = 55

-9x = 27

x = -3

(-3, 7)

7 0

3 years ago

Read 2 more answers

What is the surface area of a coke bottle? how do you figure it out?

svetlana [45]

Can or bottle? A can will be the calculation for the surface area of a cylinder which is A= $2 \pi rh+2 \pi r^{2}$ if r is the radius of the circle on the top and bottom of the can and h is the height of the can. A can is basically two circles and a big rectangle. For a bottle I don't know there are too many components and no numbers to solve for that

6 0

3 years ago

Simplify completely*******

Elodia [21]

Answer:

$\displaystyle \frac{x - 12}{4}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Factoring

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{2x - 24}{8}$

Step 2: Simplify

[Fraction - Numerator] Factor: $\displaystyle \frac{2(x - 12)}{8}$
[Fraction] Reduce: $\displaystyle \frac{x - 12}{4}$

8 0

2 years ago

Read 2 more answers

Cameron is older than Hassan. Their ages are consecutive integers. Find Cameron's

Alexxandr [17]

Answer:

25

Step-by-step explanation:

So consecutive integers, just means they're separated by a value of 1. This can be generally expressed as "a, a+1" where these two values would be consecutive integers assuming "a" is an integer.

So let's express Hassan's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive integer, Cameron's can be expressed as "x+1"

So the equation we need to set up is Cameron's age + 5(Hassan's age) = 145

So we can substitute the variables we defined to express Cameron and Hassan's age: $(x+1) + 5(x) = 145$

Distribute the 5: $x+1+5x$

Add like terms: $6x+1 = 145$

Subtract 1 from both sides: $6x=144$

Divide both sides by 6: $x=24$

Since we used "x" to represent Hassan's age, Hassan's age is 24. Since we used "x+1" to represent Cameron's age, Cameron's age is "24+1" which is just 25

6 0

1 year ago