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2 years ago

What do you prove in the base case of an inductive proof of a statement P(n) for all positive integers n?

Mathematics

1 answer:

umka21 [38]2 years ago

4 0

Negative Integers the positive cancels the negative so it’s a proof of statement

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Please help me on this one!

notka56 [123]

Answer:

1.97

Step-by-step explanation:

4.82 - 2.85 = 1.97

Pls mark brainliest. It will be my first. thanks

3 0

3 years ago

Read 2 more answers

James is studying different kinds of weather.

expeople1 [14]

What ?

Step by step step by step equations

7 0

3 years ago

PLZ SHOW ALL WORK

lara31 [8.8K]

Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width: w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x

Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6

Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224

And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.

3 0

3 years ago

6. What is the Greatest Common Factor of 45<br> and 60?<br> 14560

bazaltina [42]

Answer:

15 15 goes into 45 5 times and 60 5 times. highest number that goes into both numbers evenly

5 0

3 years ago

Read 2 more answers

An athletic field is a 48 yd-by-96 yd rectangle, with a semicircle at each of the short sides. A running track 20 yd wide surr

MA_775_DIABLO [31]

The distance would be equal to 2 times the longest side of the rectangle plus twice the shortest side multiplied by pi / 2 for the semicircle, that is:

longest side 96 and shortest 48

D = 2 * (96) + 2 * (1/2) * pi * 48

D = 192 + pi * 48

This shorter side, which starts at 48, will expand each time by two more in proportion to 20 of the running track between 8 than the number of divisions, that is, 2 * (20/8) = 5

In other words, there are 8 distances, like this:

D1 = 192 + 3.14 * 48 = 342.72 yd

D2 = 192 + 3.14 * (48 + 5) = 358.42 yd

D3 = 192 + 3.14 * (48 + 10) = 374.12 yd

D4 = 192 + 3.14 * (48 + 15) = 389.82 yd

D5 = 192 + 3.14 * (48 + 20) = 405.52 yd

D6 = 192 + 3.14 * (48 + 25) = 421.22 yd

D7 = 192 + 3.14 * (48 + 30) = 436.92 yd

D8 = 192 + 3.14 * (48 + 35) = 452.62 yd

6 0

3 years ago