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3 years ago

Really don’t understand this

Mathematics

2 answers:

podryga [215]3 years ago

6 0

Answer:

Step-by-step explanation:

First you need to identify whether you need to you sin cos or tan. From there you will be able to use the angle and one of these to work out x and y.

vodomira [7]3 years ago

5 0

The answer is 7
tan(45) = 7/x
x = 7 / tan(45)
x=7

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Please help me with this final math question asap. I will mark brainliest Thank you so much! Question 5/5

V125BC [204]

Answer:

MP is approximately equal to ON because one side of a rectangle is always the same as another side of a rectangle.

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

Simplify the expression:<br><br> q+5(3+6q)

xenn [34]

Answer:

31q+15

Step-by-step explanation:

7 0

3 years ago

Rachel's free throw average for basketball is 60%. She wants to predict how many times in the next 50 tries she will make a free

Gnoma [55]

If she shot her average she would make 30 out of 50 shots (AKA 60%)
She could use the index cards to record each shot, recording 5 results on each one of the 10 cards

I understand this answer is really late for you but I hope you can still use it or someone else can use it if they have the same assignment

5 0

3 years ago

Read 2 more answers

a bag contains 20 pink marbles and 12 yellow marbles. you choose a marble at random. what is the probability of selecting a pink

Sati [7]

So the total amount of marbles is: 20+12=32
there are 20 pink marbles
20/32 = 10/16 = 5/8 (simplified)

4 0

3 years ago