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Ad libitum [116K]
3 years ago
12

An object has a mass of 440 kg and a volume of 11 m3. Find the density of the object in kg/m3.

Mathematics
2 answers:
Usimov [2.4K]2 years ago
7 0

Answer:

40 Kg/m cube

Step-by-step explanation:

FrozenT [24]3 years ago
5 0

Answer:

40 kg/m³

Step-by-step explanation:

To find the density divide the mass by the volume

440kg / 11 m³ = 40 kg/m³

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<span> Given polynomial x^2+8x-48 = 0</span>

<span>x^2+12x-4x-48 = 0</span>

<span>x(x+12)-4(x+12) = 0</span>

<span>(x+12)(x-4) = 0</span>

<span>x+12 = 0</span>

Subtract 12 from each side.

<span>x+12-12 = 0-12</span>

<span>x = -12</span>

<span>and x-4 = 0</span>

Add 4 to each side.

<span>x-4+4 = 0+4</span>

<span>x = 4</span>

<span>Roots are -12,4.</span>

4 0
3 years ago
1. Write the equation of the line best fit
Pavel [41]

Answer:

y=3/4x+2

Step-by-step explanation:

I found this by using desmos graphing calculator

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2 years ago
Howard is designing a chair swing ride. The swing ropes are 55 meters long, and in full swing they tilt in an angle of 29? . How
Allushta [10]

Answer: 50.85 meters

<u>Step-by-step explanation:</u>

cos 29 = \frac{55}{h}

55 cos 29 = h

48.10 = h

Pole  = h + 2.75

        = 48.10 + 2.75

         = 50.85

3 0
3 years ago
Read 2 more answers
Prove or disprove (from i=0 to n) sum([2i]^4) &lt;= (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
Geometry help please!
Gekata [30.6K]

given the following sets.

A = {0, 1, 2, 3}
B = {a, b, c, d}
C = {0, a, 2, b}

Find B  C.

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3 years ago
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