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3 years ago

9

Write a variable expression to describe the rule for the sequence. Then find the 100th term in the sequence. –4, 1, 6, 11, 16, .

. .

1 answer:

SVETLANKA909090 [29]3 years ago

3 0

Answer:

a+(n-1)d

Step-by-step explanation:

491

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Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tab

natta225 [31]

Answer:

(a) at t=2, the particle is moving toward the origin

(b) a(t) = 70(8 -9t^2)/(3t^2 +8)^3; a(2) = -0.245

(c) the particle approaches x = 1/3 as t gets large

Step-by-step explanation:

(a) The function x(t) is negative for -3 < t < 3, so at t = 2, the particle is to the left of the origin.

The velocity of the particle is given by the derivative of the position function:

$x'(t)=\dfrac{(3t^2+8)(2t)-(t^2-9)(6t)}{(3t^2+8)^2}=\dfrac{70t}{(3t^2+8)^2}$

Then, at t=2, the expression is positive, indicating the particle is moving toward the origin.

__

(b) The acceleration is the derivative of the velocity, so is ...

$a(t)=\dfrac{70(3t^2+8)^2-(70t)(12t)(3t^2+8)}{(3t^2+8)^4}=\dfrac{70(3t^2+8-12t^2)}{(3t^2+8)^3}\\\\\boxed{a(t)=\dfrac{70(8-9t^2)}{(3t^2+8)^3}}$

Then at t=2, the acceleration is ...

a(2) = 70(8 -9·4)/(3·4+8)^3 = 70(-28)/8000

a(2) = -0.245

__

(c) As t gets large, the value of x(t) approaches t^2/(3t^2) = 1/3.

7 0

4 years ago

The negative sign in 15t-2t belongs to the term____?

alexdok [17]

The expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.

Solution:

Given expressions are 15t – 2t and 2t – 15t.

To determine 15t – 2t is equivalent to 2t – 15t or not.

Substitute t = 2 in above two expressions.

15t – 2t = 15(2) – 2(2)

= 30 – 4

= 26

2t – 15t = 2(2) – 15(2)

= 4 – 30

= –26

The values of the expressions are different when t = 2.

So, 15t – 2t is not equivalent to 2t – 15t.

Hence the expression 15t – 2t not equivalent to 2t – 15t because the negative sign in 15t – 2t belongs to the term 2t.

7 0

3 years ago

Linear Transformations<br><br> To reflect a linear function about the y-axis, the slope is what

baherus [9]

Answer: Multiplied by -1

Example:

Let's say we had the linear function y = 2x+5

Reflecting this over the y axis means we replace every x with -x and simplify

y = 2x+5 becomes y = 2(-x)+5 and that simplifies to y = -2x+5

The y intercept stays the same the whole time. This is because the y intercept is on the mirror line of the y axis. Stuff on the mirror line does not move.

Notice the jump from the old slope (2) to the new slope (-2) has us multiply by -1.

4 0

3 years ago

lisa is painting a fence that is 26 feet long and 7 feet tall. A gallon of paint will cover 350 square feet. Write and slove a p

swat32

2<span>6 x 7 = 182 now divide that by 16 and your answer is 11.375 round that up to 12.</span>

5 0

4 years ago

Which expression is equivalent to 24 + 30 A) 6(4+5) B 6(4+6) C 8(3+4) D 8(3+12)

lorasvet [3.4K]

A=54. And 24+30=54. So the answer is A

3 0

3 years ago