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3 years ago

What is an expression for the distance between the origin and a point P(x,y)

Mathematics

1 answer:

kirza4 [7]3 years ago

5 0

Answer:

$d = \sqrt{ {x}^{2} + {y}^{2} }$

Step-by-step explanation:

Distance between origin (0, 0) and point (x, y) is given as:

$d = \sqrt{ {(x - 0)}^{2} + {(y - 0)}^{2} } \\ \\ \red{ \bold{ d = \sqrt{ {x}^{2} + {y}^{2} } }}$

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The diameter of a bacteria colony that doubles every hour is represented by the graph below. What is the diameter of the bacteri

Nady [450]

Do you notice anything strange about those points ?

(0, 1),
(1, 2),
(2, 4),
(3, 8).

The y-coordinate of each point is (2) raised to the power of the x-coordinate.

First point:   x=0, y=2⁰ = 1
Second point: x=1, y=2¹ = 2
Third point:    x=2, y=2² = 4
Fourth point: x=3, y=2³ = 8

The equation of the curve appears to be

   y = 2 ^ x .

So, after 10 hours, x=10, and y = 2¹⁰ = 1,024 .

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3 years ago

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nydimaria [60]

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Step-by-step explanation:

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3 years ago

A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min

sesenic [268]

$A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})$
$\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$
$A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4$

We're given that $A(0)=30$ . Multiply both sides by the integrating factor $e^{t/100}$ , then

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C$
$A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}$

Given that $A(0)=30$ , we have

$30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02$

so the amount of salt in the tank at time $t$ is

$A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}$

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Ratio with two equivalent measurements would be 1

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