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jok3333 [9.3K]
3 years ago
7

Given that A = (9,9,2), B = (1,3,5) and C = (5,6,4), find the vector equation of the line through A and B

Mathematics
1 answer:
juin [17]3 years ago
6 0

Answer:

Equation = 9i + 9j + 2k - λ ( 8i + 6j - 3k)

Step-by-step explanation:

Vector equation of a line passing through two points A & B is : r = a + λ(b - a)

Given A = (9,9,2) ; B = (1,3,5)

Equation of line : r = 9i + 9j + 2k + λ [ (1-9) i + (3-9) j + (5-2) k ]

= 9i + 9j + 2k + λ ( -8i + -6j + 3k)

= 9i + 9j + 2k - λ ( 8i + 6j - 3k)

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jenyasd209 [6]

Answer:

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Step-by-step explanation:

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respond to the following in a minimum of 175 of your own words: how would you explain the differences between the trapezoidal ru
harkovskaia [24]

The differences between the trapezoidal rule and simpson's rule is -

The trapezoidal rule and Simpson's method, the latter a set of formulas of varying complexity, are both Newton-Cotes formulas, that are used to examine and model complex curves.

<h3>What is trapezoidal rule?</h3>

The trapezoidal rule is just an integration rule that divides a curve into small trapezoids to calculate the area under it. A area under the curve is calculated by adding the areas of all the small trapezoids.

Follow the steps below to use the trapezoidal rule to determine the area under given curve, y = f. (x).

  • Step 1: Write down the total number of sub-intervals, "n," as well as the intervals "a" and "b."
  • Step 2: Use the formula to determine the width of the sub-interval, h (or) x = (b - a)/n.
  • Step 3: Use the obtained values to calculate this same approximate area of a given curve, ba f(x)dx Tn = (x/2) [f(x0) + 2 f(x1) + 2 f(x2) +....+ 2 f(n-1) + f(n)], where xi = a + ix
<h3>What is Simpson's method?</h3>

Simpson's rule is used to approximate the area beneath the graph of the function f to determine the value of the a definite integral (such that, of the form  b∫ₐ f(x) dx.

Simpson's 1/3 rule provides a more precise approximation. Here are the steps for using Simpson's rule to approximate the integral ba f(x) dx.

  • Step 1: Figure out the values of 'a' & 'b' from interval [a, b], as well as the value of 'n,' which represents the number of subintervals.
  • Step 2: Determine the width of every subinterval using the formula h = (b - a)/n.
  • Step 3: Using the interval width 'h,' divide this same interval [a, b] [x₀, x₁], [x₁, x₂], [x₂, x₃], ..., [xn-2, xn-1], [xn-1, xn] into 'n' subintervals.
  • Step 4: In Simpson's rule formula, substitute all of these values and simplify. b∫ₐ f(x) dx ≈ (h/3) [f(x0)+4 f(x1)+2 f(x2)+ ... +2 f(xn-2)+4 f(xn-1)+f(xn)].

Thus, sometimes we cannot solve an integral using any integration technique, and other times we don't have a particular function to integrate. Simpson's rule aids in approximating the significance of the definite integral in such cases.

To know more about the Simpson's method and trapezoidal rule, here

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3 0
1 year ago
How am I supposed to do that??
marissa [1.9K]

Answer:

not a solution

Step-by-step explanation:

y = -3/4 x +3

Is (3,2) a solution?

Substitute the point into the equation and see if it  is true

2 = -3/4(3) +3

2 = -9/4 +3

2 = -9/4 +16/4

2 = 7/4

False

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3 years ago
Given: if you go to the water park then you will need to bring sunscreen
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Answer:

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Killer whales in the Pacific are about 2.6 m long at birth. They grow at a rate of about 0.38 m per year, up to the age of 10 or
Tpy6a [65]
5-2.6= 2.4
2.4/.38= 6.316
6.316

Answer is rounded, not 100% if this is correct but that is how I would solve.
4 0
3 years ago
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