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3 years ago

Has vertices

Mathematics

1 answer:

Rama09 [41]3 years ago

7 0

9514 1404 393

Answer:

B'(24, 12)

Step-by-step explanation:

The transformation due to dilation by a factor of 6 is ...

(x, y) ⇒ (6x, 6y)

We want to identify the original point, so we can find (x, y) using ...

(24, 12) = (6x, 6y)

(4, 2) = (x, y) . . . . . . divide by 6

The point with coordinates (4, 2) is point B, so the point with coordinates (24, 12) is B'.

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Round the decimal to a place of the underlined digit 5.657

kipiarov [429]

Answer:

5.6

Step-by-step explanation:

7 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

What is the list price 45 off 1/4

Vlad1618 [11]

34 is your answer hope it helps

5 0

3 years ago

Es The measure of an interior angle of a regular polygon is 120°. What is the measurb of each exterior angle? The polygon has

Troyanec [42]

The measure of each exterior angle is 60° and the polygon has 6 sides ⇒ 4th answer

Step-by-step explanation:

In a regular n-side polygon:

All sides are equal in lengths
All angles are equal in measure
The measure of each interior angle = $\frac{(n-2)*180}{n}$
The measure of each exterior angle = $\frac{360}{n}$
The sum of interior angle and exterior angle at a vertex is 180°

∵ The measure of an interior angle of a regular polygon is 120°

∵ The sum of interior angle and exterior angle at a vertex = 180°

∴ The measure of each exterior angle = 180 - 120

∴ The measure of each exterior angle = 60°

∵ The measure of each exterior angle = $\frac{360}{n}$

- Substitute the measure of the exterior angle by 60

∴ $60=\frac{360}{n}$

- By using cross multiplication

∴ 60 n = 360

- Divide both sides by 60

∴ n = 6

∴ The polygon has 6 sides

The measure of each exterior angle is 60° and the polygon has 6 sides

Learn more:

You can learn more about polygons in brainly.com/question/6281564

#LearnwithBrainly

5 0

3 years ago

Eleanor and her little sister Joanna are responsible for two chores on their family’s farm, gathering eggs and collecting milk.

iris [78.8K]

Answer:

4 dozens

Step-by-step explanation:

Find Eleanor and Joanna's ratio of eggs to milk

Eleanor:

Dozen eggs : gallons of milk

9 : 3

3 : 1

Joanna:

Dozen eggs : gallons of milk

2 : 2

1 : 1

They gather one gallon of milk each which means Joanna has 1 dozen eggs and Eleanor has 3 dozens of eggs.

Total dozen of eggs = 3 + 1 = 4

Therefore, total dozen of eggs the family have per week is 4 dozens.

4 0

3 years ago