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3 years ago

Describe the interval shown using an inequality, set notation, and interval notation. (Picture attached!) Thank you!

Mathematics

1 answer:

marta [7]3 years ago

5 0

Answer:

inequality: x > -3

Set notation: {x: x> -3}

Interval notation: [-3, ∞)

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Which line has a slope 3/4

horsena [70]

Answer:

Line C

Step-by-step explanation:

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3 years ago

Read 2 more answers

Jacklynn wondered how much of the moon covers if half of the moon is shaded. She learned in Science Class that the moon has radi

Lesechka [4]

Answer:

6.3 × 10⁶ square miles

Step-by-step explanation:

We are given,

The radius of the moon is approximately 1000 miles.

We know that the moon resembles a sphere and also,

Area of sphere = $4\pi r^{2}$ , where r is the radius.

Now, the area of the moon = $4\pi 1000^{2}$ = 1.26 × 10⁷ square miles

Since, only the half of the area is clear to view.

So, the area left to view = $\frac{1.26\times 10^7}{2}$ = 6.3 × 10⁶ square miles.

Hence, the area of the moon in view is 6.3 × 10⁶ square miles.

8 0

4 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

4 years ago

How do I answer this please help homework due tomorrow x

ryzh [129]

Answer:

63.6 m^2

Step-by-step explanation:

A = (pi)r^2

r = d/2 = 9 m / 2 = 4.5 m

A = (3.142)(4.5 m)^2

A = 63.6 m^2

8 0

3 years ago

Please help me out! I have only 1 hour left! I will give brainlist to correct answers. 5 stars and thanks for ALL answers, even

IrinaK [193]

Answer:

The small tire would make about 127 rotations.

The large tire would make about 38 rotations.

b. Would you rather ride a bicycle made with two large wheels or two small wheels? Explain.

Two large wheels. Because the larger wheel makes a smoother ride and you spend less energy in order to move, compared to smaller wheels. Also, the larger the diameter, the further it can travel over one revolution.

A bicycle with would allow you to travel farther with each rotation of the pedal.

The larger one. Because in one rotation the larger wheel moves 188.49 inches and the smaller one 56.55 inches.

$C= 188.49\text{inches}$