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Elenna [48]
3 years ago
6

Aleksandra started studying how the number of branches in her tree grows over time. Every 1.5 years, the number of branches incr

eases by an addition of 2/7 of the total number of branches. The number of branches be modeled by a function, N, which depends on the amount of time, t (in years).
when aleksandra began the study, her tree had 52 branches.

Write a function that models the number of branches t years since aleksandra began studying her tree.
Mathematics
1 answer:
vova2212 [387]3 years ago
7 0

Answer:

N = 52 * (9/7)^(t/1.5)

Step-by-step explanation:

This problem can be modelated as an exponencial problem, using the formula:

N = Po * (1+r)^(t/1.5)

Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.

In our case, we have that N is the final number of branches after t years, Po = 52 branches, r = 2/7 and t is the number of years since the beginning (in the formula we divide by 1.5 because the rate is defined for 1.5 years)

Then, we have that:

N = 52 * (1 + 2/7)^(t/1.5)

N = 52 * (9/7)^(t/1.5)

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In an arithmetic sequence, a17 = -40 and
Viktor [21]

Answer:

Tn = 2Tn-1 - Tn-2

Step-by-step explanation:

Before we can generate the recursive sequence, we need to find the nth term of the given sequence.

nth term of an AP is given as:

Tn = a+(n-1)d

If a17 = -40

T17 = a+(17-1)d = -40

a+16d = -40 ...(1)

If a28 = -73

T28 = a+(28-1)d = -73

a+27d = -73 ...(2)

Solving both equations simultaneously using elimination method.

Subtracting 1 from 2 we have:

27d - 16d = -73-(-40)

11d = -73+40

11d = -33

d = -3

Substituting d = -3 into 1

a+16(-3) = -40

a - 48 = -40

a = -40+48

a = 8

Given a = 8, d = -3, the nth term of the sequence will be

Tn = 8+(n-1) (-3)

Tn = 8+(-3n+3)

Tn = 8-3n+3

Tn = 11-3n

Given Tn = 11-3n and d = -3

Tn-1 = Tn - d... (3)

Tn-1 = 11-3n +3

Tn-1 = 14-3n

Tn-2 = Tn-2d...(4)

Tn-2 = 11-3n-2(-3)

Tn-2 = 11-3n+6

Tn-2 = 17-3n

From 3, d = Tn - Tn-1

From 4, d = (Tn - Tn-2)/2

Equating both common difference

(Tn - Tn-2)/2 = Tn - Tn-1

Tn - Tn-2 = 2(Tn - Tn-1)

Tn - Tn-2 = 2Tn-2Tn-1

2Tn-Tn = 2Tn-1 - Tn-2

Tn = 2Tn-1 - Tn-2

The recursive formula will be

Tn = 2Tn-1 - Tn-2

5 0
3 years ago
Read 2 more answers
The length of a vegetable garden is 4 feet longer than its width. If the area of the garden is 140 square feet, find its dimensi
Lena [83]
Length is 14 and the width is 10
4 0
3 years ago
The figure shown is a rectangle. The green shape in the figure is a square. The blue and white shapes are rectangles, and the ar
VikaD [51]

Answer:

A. (2 × 6) + (3 × 8) + 6²

72 sq. inches.

B. 9 in. by 8 in.

Step-by-step explanation:

The white shape has dimensions of 2 in. by 6 in. and the green shape is a square.

So, the dimension of the green shape is 6 in. by 6 in.

Therefore, the length of the blue shape is (6 + 2) = 8 in.

Now, given that the area of the blue shape is 24 sq. in.

So, the width of the blue shape is \frac{24}{8} = 3 in.

Now, if we consider the total figure, then area of the entire figure = area of the  white shape + area of the green shape + area of the blue shape.

= (2 × 6) + (3 × 8) + 6² (Answer)

= 12 + 24 + 36  

= 72 sq, inches. (Answer)

Now, the length of the entire figure is (6 + 3) = 9 in. and width of the entire figure is (2 + 6) = 8 in.

Therefore, the dimensions of the entire figure will be 9 in. by 8 in. (Answer)

5 0
3 years ago
Please find the circumference, will give brainliest!
stich3 [128]

Answer:

43.96

Step-by-step explanation:

7 0
2 years ago
13*52 using the distributive property
pantera1 [17]

Hello!

13*52=676

Explanation: <em>This question is super easy. This question it just like a order of operations. First you had to multiply by 52, 13*52= 676 is the right answer. Hope this helps! And thank you for posting at here on Brainly. And have a great day! -Charlie</em>

6 0
3 years ago
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