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3 years ago

For each explicitly-defined sequence below, write the first few terms. Then use the terms to write a recursive equation.

Mathematics

1 answer:

julia-pushkina [17]3 years ago

6 0

Answer:

Step-by-step explanation:

Problem A

t(1) = 2(1) + 5

t(2) = 2*2 + 5 = 9

t(3) = 2*3 + 5 = 11

t(4) = 2*4 + 5 = 13

So this is the explicit result. Now try it recursively.

t_3 = t_2 + 2

t_3 = 9 + 2

t_3 = 11 which is just what it should do.

t_n = t_(n - 1) + 2

Problem B

t(1) = 3 * 1/2

t(1) = 3/2

t(2) = 3*(1/2)^2

t(2) = 3 * 1/4

t(2) = 3/4

t(3) = 3*(1/2)^3

t(3) = 3 * 1/8

t(3) = 3/8

t(4) = 3 (1/2)^4

t(4) = 3 (1/16)

t(4) = 3/16

So in general

t_n = t_n-1 * 1/2

For example t(5)

t_5 = t_4 * 1/2

t_5 = 3 /16 * 1/2 = 3/32

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kompoz [17]

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$\sqrt{x^2+y^2}=\dfrac3{1+y}$

You can stop there, or try to find something that looks somewhat nicer.

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3 years ago

Question 4

Elanso [62]

Answer:

a $A = 30 + 0.45 n$

b $A = 90.3$

c 0 customers

Step-by-step explanation:

Given

$Base\ Amount = 30$

$Rate = 0.45$ per customer

Solving (a): Amount (A) on n customers

This is calculated as:

$A = Base\ Amount + Rate * n$

$A = 30 + 0.45 * n$

$A = 30 + 0.45 n$

Solving (b): Amount on 134 customers

In this case: n = 134

So:

$A = 30 + 0.45 * 134$

$A = 30 + 60.3$

$A = 90.3$

Solving (c): Customers at noon.

At noon, the amount is 30.

So:

$A = 30 + 0.45 n$

$30 = 30 + 0.45n$

Collect like terms

$0.45n = 30 - 30$

$0.45n =0$

$n = 0$

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2 years ago

How many math books and English books did Nicole purchase?

Ksju [112]

Create a system if equations to solve this.

First equation:
25m + 24e = 220

Second equation:
m + e = 9

Then you must solve the second equation for a variable.

Change m + e = 9 to e = 9 - m.

Then substitute (9 - m) for e in the first equation.

So 25m +24e = 220 becomes 25m + 24(9 - m) = 220.

Now you can solve the first equation because the only variable in it is m.

25m + 24(9 - m) = 220 (Original equation)
25m + 216 - 24m = 220 (Distribute)
m + 216 = 220 (Combine like terms)
m = 4 (Simplify)

Now plug in 4 for m in the second equation.

m + e = 9 (Original equation)
(4) + e = 9 (Substitute)
e = 5 (Simplify)

m represents Math Books and e represents English Books, so Nicole purchased 4 Math Books and 5 English Books.

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2 years ago

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Cloud [144]

Nothing else is given, so for the two triangles to be congruent, the only possible proof is the ASA theorem.
first pairs of angles: 2x+7=x+21 => x=14
second pairs of angles: 8y-4=4y+28 =>y=8
The two triangles share the same side PR
Based on the Angle-Side-Angle Triangle Congruence theorem, these two triangles are congruent with x=14, y=8
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3 years ago

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IgorLugansk [536]

Answer:

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Step-by-step explanation:

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