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Oksanka [162]
3 years ago
9

20. Which set of parametric equations over the interval 0 ≤ t ≤ 1 defines a line segment with initial point (–5, 3) and terminal

point (1, –6)?
x(t) = –5 + t; y(t) = 3 – 6t
x(t) = –5 + 3t; y(t) = 1 – 6t
x(t) = –5 + 6t; y(t) = 3 – 9t
x(t) = –5 + 8t; y(t) = 1 – 7t
Mathematics
1 answer:
lesya [120]3 years ago
7 0

Given:

Initial point = (–5, 3)

Terminal point = (1, –6)

To find:

The set of parametric equations over the interval 0 ≤ t ≤ 1.

Solution:

The interval is 0 ≤ t ≤ 1, initial point is (–5, 3) and terminal point is (1, –6). It means,

x(0)=-5,y(0)=3

x(1)=1,y(1)=-6

Put t=1 in each parametric equation.

In option A,

x(1)=-5+1=-4\neq 1

In option B,

x(1)=-5+3(1)=-5+3=-2\neq 1

In option D,

x(1)=-5+8(1)=-5+8=3\neq 1

Therefore, options A, B and D are incorrect.

In option C,

x(1)=-5+6(1)=-5+6=1

y(1)=3-9(1)=3-9=-6

Put t=0 in x(t) and y(t).

x(0)=-5+6(0)=-5

y(0)=3-9(0)=3

Since, only in option C x(0)=-5,y(0)=3,x(1)=1,y(1)=-6, therefore, the correct option is C.

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Nat2105 [25]

1. Geometric Sequence

2. a_n = a_{n-1} * 3

3. a_n = 6 * (3)^{n-1}

Step-by-step explanation:

Given sequence is:

6, 18, 54, 162,....

Here

a_1 =6\\a_2 = 18\\a_3 = 54

(a) Is this an arithmetic or geometric sequence?

We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.

We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r

r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3

As the common ratio is same, the given sequence is a geometric sequence.

(b) How can you find the next number in the sequence?

Recursive formulas are used to find the next number in sequence using previous term

Recursive formula for a geometric sequence is given by:

a_n = a_{n-1} * r

In case of given sequence,

a_n = a_{n-1} * 3

So to find the 5th term

a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486

(c) Give the rule you would use to find the 20th week.

In order to find the pushups for 20th week, explicit formul for sequence will be used.

The general form of explicit formula is given by:

a_n = a_1 * r^{n-1}

Putting the values of a_1 and r

a_n = 6 * (3)^{n-1}

Hence,

1. Geometric Sequence

2. a_n = a_{n-1} * 3

3. a_n = 6 * (3)^{n-1}

Keywords: Geometric sequence, common ratio

Learn more about geometric sequence at:

  • brainly.com/question/10666510
  • brainly.com/question/10699220

#LearnwithBrainly

4 0
3 years ago
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