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3 years ago

Can 16/120 be simplified? If so, what is the simplest form of it.

Mathematics

1 answer:

tia_tia [17]3 years ago

5 0

Answer:

2/15

Step-by-step explanation:

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3 years ago

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A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Ei

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3 years ago

Which expression is equivalent to ? Assume.

nikdorinn [45]

Answer:

2. $-2x^{8}y^{18}$

Step-by-step explanation:

We have been given an expression $\frac{10x^{6}y^{12}}{-5x^{-2}y^{-6}}$ and we are asked to find equivalent expression to our given expression.

Using fraction rule $\frac{a}{-b} =-\frac{a}{b}$ we can write our expression as: $-\frac{10x^{6}y^{12}}{5x^{-2}y^{-6}}$ .

Upon dividing 10 by 5 we will get,

$-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}$

Upon using exponent property for quotient $(\frac{a^{m}}{a^{n}} =a^{(m-n)})$ we will get,

$-\frac{2x^{6}y^{12}}{x^{-2}y^{-6}}=-2x^{(6--2)}y^{(12--6)}$

$-2x^{(6+2)}y^{(12+6)}$

$-2x^{8}y^{18}$

Therefore, our expression simplifies as $-2x^{8}y^{18}$ and 2nd option is the correct choice.

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4 years ago

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Suppose r⃗ (t)=cos(πt)i+sin(πt)j+5tkr→(t)=cos(πt)i+sin(πt)j+5tk represents the position of a particle on a helix, where zz is th

gtnhenbr [62]

Answer:

a) t = 4

b) v = pi j + 5 k

c) rt = 1i + (pi t) j + (20 +5t )k

Step-by-step explanation:

You have the following vector equation for the position of a particle:

$r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}$ (1)

(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.

For a height of 20 you have:

$5t=20\\\\t=\frac{20}{5}=4$

(b) The velocity of the particle is the derivative, in time, of the vector position:

$v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}$ (2)

and for t=4 (height = 20):

$v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}$

(c) The vector parametric equation of the tangent line is given by:

$r_t(t)=r_o+vt$ (3)

ro: position of the particle for t=4

$r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}$

Then you replace ro and v in the equation (3):

$r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}$

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4 years ago