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3 years ago

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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What are the roots of the polynomial equation x^2+8x-48=0

____ [38]

Given polynomial x^2+8x-48 = 0

x^2+12x-4x-48 = 0

x(x+12)-4(x+12) = 0

(x+12)(x-4) = 0

x+12 = 0

Subtract 12 from each side.

x+12-12 = 0-12

x = -12

and x-4 = 0

Add 4 to each side.

x-4+4 = 0+4

x = 4

Roots are -12,4.

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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

Step-by-step explanation:

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) <= (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