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3 years ago

Write the equation of the line that passes through (4,-3) and (8,-12)

Mathematics

1 answer:

german3 years ago

3 0

Answer:

Step-by-step explanation:

(4 , -3) ; (8 , -12)

$Slope =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-12-[-3]}{8-4}\\\\=\dfrac{-12+3}{4}\\\\=\dfrac{-9}{4}$

m = -9/4 ; (4 , -3)

$y - y_{1}= m(x -x_{1}\\\\y - [-3]= \dfrac{-9}{4}(x -4)\\\\\\y + 3 = \dfrac{-9}{4}x -4*\dfrac{-9}{4}\\\\\\y + 3 =\dfrac{-9}{4}x+9\\\\\\y = \dfrac{-9}{4}x+9-3\\\\y=\dfrac{-9}{4}x+6$

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The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

6 0

3 years ago

What two numbers multiply to 54 and add up to 7

k0ka [10]

Xy = 54
x + y = 7

$xy = 54$
$\frac{xy}{x} = \frac{54}{x}$
$y = \frac{54}{x}$

$x + y = 7$
$x + \frac{54}{x} = 7$
$\frac{x^{2}}{x} + \frac{54}{x} = 7$
$\frac{x^{2} + 54}{x} = 7$
$x^{2} + 54 = 7x$
$x^{2} - 7x + 54 = 0$
$x = \frac{-(-7) \± \sqrt{(-7)^{2} - 4(1)(54)}}{2(1)}$
$x = \frac{7 \± \sqrt{49 - 216}}{2}$
$x = \frac{7 \± \sqrt{-167}}{2}$
$x = \frac{7 \± i\sqrt{167}}{2}$
$x = \frac{7 \± 12.9i}{2}$
$x = 3.5 \± 6.45i$
$x = 3.5 + 6.45i$ $or$ $3.5 - 6.45i$

x + y = 7
3.5 + 6.45i + y = 7
- (3.5 + 6.45i) - (3.5 + 6.45i)
y = 3.5 - 6.45i
  (x, y) = (3.5 + 6.45i, (3.5 - 6.45i)

  or

  x + y = 7
3.5 - 6.45i + y = 7
- (3.5 - 6.45i)   - (3.5 - 6.45i)
y = 3.5 + 6.45i
(x, y) = (3.5 - 6.45i, 3.5 + 6.45i)

The two numbers that add up to 7 and can multiply to 54 is 3.5 ± 6.45i.

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4 years ago

What is the slope-intercept form of the function described by this table?

Andru [333]

Answer:

y = - 3x + 4

Step-by-step explanation:

m = $\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$