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inessss [21]
3 years ago
13

What is the simple rational expression for 10b + 100 ________ b + 10

Mathematics
2 answers:
PtichkaEL [24]3 years ago
4 0

Answer:

10 ( b+10)

Step-by-step explanation:

10 b + 100

Factor out a 10

10 * b + 10 * 10

10 ( b+ 10)

hope it helps !!!!

Alexandra [31]3 years ago
3 0

Answer:

10b + 100 _= 10(b + 10)

Step-by-step explanation:

find common factor for 10b and 100 and put it in front of ( )

divide each term by 10 and put answer inside ( )

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A) 2 cm

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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

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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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3 years ago
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