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3 years ago

identifying equation in point slope form for the line perpendicular to y equals negative 1 / 3x - 6 that passes through -1,5

Mathematics

1 answer:

solmaris [256]3 years ago

3 0

Answer:

y = 3x +8

Step-by-step explanation:

The slope of the given line is -1/3. The slope of a perpendicular line is the opposite of the reciprocal of that: -1/(-1/3) = 3.

Then, in point-slope form, the equation of the line is ...

... y - k = m(x - h) . . . . . for slope m through point (h, k)

... y - 5 = 3(x -(-1)) . . . . . for line of slope 3 through (-1, 5)

... y = 3x +8 . . . . . . . . . simplify

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Samuel needs to estimate the product of 24 x 395.

First method

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2 years ago

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2 years ago

In 2000, the population of Massachusetts

Zepler [3.9K]

Answer:

The population reaches 7 million people in the year 2032.

Step-by-step explanation:

We have that

$f(x) = 6.3*(1.0032)^{x}$

Using this model, find the year when the population reaches 7 million people.

This is x years after 2000, in which x is found when f(x) = 7. So

$f(x) = 6.3*(1.0032)^{x}$

$7 = 6.3*(1.0032)^{x}$

$(1.0032)^{x} = \frac{7}{6.3}$

$(1.0032)^{x} = 1.11$

We have to following logarithm rule

$\log{a^{x}} = x\log{a}$

So we apply log to both sides of the equality

$\log{(1.0032)^{x}} = \log{1.11}$

$x\log{1.0032} = \log{1.11}$

$x = \frac{\log{1.11}}{\log{1.0032}}$

$x = 32.66$

2000 + 32.66 = 2032

The population reaches 7 million people in the year 2032.

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2 years ago