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4 years ago

10

Help me out :O What is the volume of three cubes, each with a side length of fraction 1 over 3 foot? V = s3, where s is the side

length.

1 answer:

Readme [11.4K]4 years ago

4 0

Answer:

Step-by-step explanation:

$s = \frac{1}{3}ft\\$

Volume of a cube = s³ ft³

Volume of 3 cubes = 3 * s³

$= 3 * \frac{1}{3} * \frac{1}{3} *\frac{1}{3}\\\\= \frac{1}{3} *\frac{1}{3}\\\\=\frac{1}{3*3}\\\\=\frac{1}{9} ft^{3}$

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Which simplifications of the powers of i are correct?

OleMash [197]

The correct simplifications of powers of i are:

a. i^27=−i

d. i^8=1

e. i^5=i

Step-by-step explanation:

We know that

$i^2=-1\\i^3=-i\\i^4=1$

We can use the smaller powers of i to solve the larger powers.

a. i^27=−i

$i^{27}\\={i^{24}}.i^3\\={i^{4*6}}.-i\\=(i^4)^6.-i\ \ \ \ As\ we\ know\ i^4=1\\=(1)^6.-i\\=1*-i\\=-i$

b. i^28=i

$i^{28}\\=i^{4*7}\\=(i^4)^7\\=(1)^7\\=1$

c. i^14=1

$i^{14}\\=i^{12}.i^2\\=(i^{4*3}).i^2\\=> i^2=-1\\=(i^4)^3.-1\\=(1)^3*-1\\=-1$

d. i^8=1

$i^8\\=i^{4*2}\\=(i^4)^2\\=(1)^2\\=1$

e. i^5=i

$i^5\\=i^{2*2*1}\\=i^2*i^2*i\\=(-1)(-1)(i)\\=i$

Hence,

The correct simplifications of powers of i are:

a. i^27=−i

d. i^8=1

e. i^5=i

Keywords: Imaginary units, Iota

Learn more about imaginary units at:

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3 years ago

Twelve blocks are prepared, so 4 are red , 4 are white, and 4 are blue. What is the probability of picking a green block. What i

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There are no green blocks to the probability of picking a green block would be 0. The probability of not picking a red block would be 8/12 = 2/3

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Help Katherine has a new job and earns salary of $55,000. max has a new job and earns a salary of $64,000. Katherine will receiv

monitta

The equation that represent the same salary is 55,000x+2,500x=64,000+1500x

<h3>What is Algebra?</h3>

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

Given:

Katherine has a new job and earns salary of $55,000. Katherine will receive a salary increase of $2,500 per year .

max has a new job and earns a salary of $64,000. Max will receive a salary increase of $1,500 per year.

So, in the case they would have the same salary for some x years the expression can be

Katherine salary along with increment= 55000+ 2500x

Max salary along with increment= 64000+ 1500x

Hence, equation ca be used to find x, the number of years it will take Katherine to earn the same salary as Max is 55,000x+2,500x=64,000+1500x.

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1 year ago

Whats the y-intercept

svet-max [94.6K]

Answer:

2

Step-by-step explanation:

the y-intercept is where the line meets the y-axis

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3 years ago

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Solve the following differential equations using Laplace transforms. Assume zero initial conditions and that the forcing functio

Rom4ik [11]

Answer:

(A) $X(S)=\frac{1.25}{S^2+4}$

(B) $X(S)=\frac{0.2941}{S}$

Step-by-step explanation:

We have to find the Laplace transform

(a) x(t) + 7 x(t) = 5 cos2t

Taking Laplace of both side

$X(X)+7X(S)=5\times \frac{2}{S^2+4}$

$8X(S)=\frac{10}{S^2+4}$

$X(S)=\frac{1.25}{S^2+4}$

(B) $x(t)+8x(t)+25x(t)=10u(t)$

Taking Laplace transform of both side

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$34X(S)=\frac{10}{S}$

$X(S)=\frac{0.2941}{S}$

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3 years ago