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PolarNik [594]
2 years ago
13

Find the solution to each of these recurrence relations and initial conditions. use an iterative approach such as that used in e

xample 10.
a.an = 3an−1, a0 = 2
b.an = an−1 + 2, a0 = 3
c.an = an−1 + n, a0 = 1
d.an = an−1 + 2n + 3, a0 = 4
e.an = 2an−1 − 1, a0 = 1 f ) an = 3an−1 + 1, a0 = 1 g) an = nan−1, a0 = 5 h) an = 2nan−1, a0 = 1
Mathematics
1 answer:
Kamila [148]2 years ago
8 0
Ok he anawee is d I’m pretty sure
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a squirrel is 24 feet up in a tree and tosses a nut out of the tree with an initial velocity of 8 feet per second. the nuts heig
marin [14]

The nut lands first on gorund

<em><u>Solution:</u></em>

The squirrel climbs down the tree in 2 seconds

Given that,

A squirrel is 24 feet up in a tree and tosses a nut out of the tree with an initial velocity of 8 feet per second

<em><u>The nuts height, h, at time t seconds can be represented by the equation:</u></em>

h(t) = -16t^2 + 8t+24

-16t^2 + 8t+24 = 0\\\\-2t^2 + t + 3 = 0\\\\2t^2 - t-3=0\\\\Split\ the\ middle\ term\\\\2t^2 + 2t-3t -  3 = 0\\\\Break\ the\ expression\ into\ groups\\\\(2t^2 + 2t) -(3t+3) = 0\\\\2t(t+1) -3(t+1) = 0\\\\(t+1)(2t-3) = 0\\\\Therefore,\\\\t + 1 = 0\\\\t = -1\\\\2t-3=0\\\\2t = 3\\\\t = \frac{3}{2} = 1.5

time cannot be negative, so ignore t = -1

Thus the nut takes 1.5 seconds to reach ground

From given,

The squirrel climbs down the tree in 2 seconds

Therefore, the nut lands first on gorund

5 0
2 years ago
What is the solution to this system of linear equations? 7x – 2y = –6 8x y = 3 (–6, 3) (0, 3) (1, –5) (15, –1)
erik [133]

Answer:

(0,3)

Step-by-step explanation:

we have

7x-2y=-6 ----> equation A

8x+y=3 ----> equation B

Multiply the equation B by 2 both sides

2(8x+y)=2*3

16x+2y=6 ------> equation C

Adds equation A and equation C

7x-2y=-6\\16x+2y=6\\--------\\7x+16x=-6+6\\23x=0\\x=0

Find the value of y

7(0)-2y=-6

-2y=-6

y=3

the solution is the point (0,3)

3 0
2 years ago
Read 2 more answers
kate would like to find the height of her favorite rollercoaster at the amusement park. She noticed that she casts a 2 foot shad
alex41 [277]

Set up a proportion with Katie’s height / Katie’s shadow = roller coasters height / its shadow. So it is 5 feet / 2 feet = x feet / 60 feet. To solve cross multiply so it becomes 2x = 300 and x = 150 feet

5 0
2 years ago
What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
Deffense [45]
So you have a right angle triangle. You need to use trig for this, as you have two values you can figure out a third.

You know that you have

90 deg. angle
19 deg. angle
Therefor you have 71 deg. angle

sin19 = x/15
15sin19 = x
x = 2.2

Now do Pythagoras c^2-b^2=a^2

a = 14.8

So the sides are 2.2 and 14.8 units long. (If these numbers are wrong tell me and I'll edit answer)

7 0
2 years ago
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Rich is driving from Philadelphia to Pittsburgh at 70 mph and Michelle is driving from Pittsburgh to Philadelphia at 65 mph. If
Margaret [11]
The distance from <span>Philadelphia to Pittsburgh is 305 miles.

Both are travelling towards each other. When they will meet the sum of distance traveled by both would be 305 miles, as together they have covered the entire distance between the two cities.

We know that:

Distance = Speed x Time

We know the distance. We know the speeds. Since they are travelling towards each other, the overall speed will be the sum of speeds of Rich and Michelle. So we can say with a speed of 135 mph they have to cover 305 miles.

305 = 135 x Time

Time = 305/135 = 2.25 hours = 2 hours and 15 minutes

So, they will meet after 2 hours and 15 minutes.

So, C option is the correct answer</span>
5 0
2 years ago
Read 2 more answers
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