What is the range of ƒ(x) = |x|? (–∞, ∞) [0, ∞) (

Help pleaseeeee it’s urgent!!!

Ad libitum [116K]

Answer:

(2,-7)

Step-by-step explanation:

Use the midpoint formula! (Attached is a picture of it!)

1) Plug in the values:

(5-1)/2,(-6+-8)/2

2) Simplify:

4/2,-14/2

3) Solve:

(2,-7)

6 0

3 years ago

Help me g + 3 + 4(9 + 2) =

GrogVix [38]

Answer:

g+3 +36+8=

g+39+8=

g+47

You can't find an answer but this is how you would simplify it :)

Step-by-step explanation:

4 0

3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

3 years ago

The numbers of pencils in joes backpack is 5 more than the number of pencils in sara's backpack.if joe has 8 pencils in his back

Basile [38]

The answer would be 3 more

7 0

3 years ago

Blank - 5.27 = 2.99 literally forgot how decimals work

bulgar [2K]

Answer:

8.26

Step-by-step explanation:

you can solve this by putting x for blank

x-5.27=2.99

solve for x

x-5.27+5.27=2.99+5.27

x=8.26

3 0

2 years ago

Read 2 more answers

What is the range of ƒ(x) = |x|? (–∞, ∞) [0, ∞) (–∞, 0) (0, ∞)