Find the distance between the pair of points: (-3,-6) and (1,2).

Mathematics

1 answer:

Butoxors [25]1 year ago

8 0

d² = (y2 - y1)² + (x2 - x1)²

..............

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Х Y

Montano1993 [528]

Answer:

y = 0.5x + 3

Step-by-step explanation:

7 0

1 year ago

The limit as h approaches 0 of (e^(2+h)-e^2)/h is ?

Whitepunk [10]

If you plug in 0, you get the indeterminate form 0/0. You can, therefore, apply L'Hopital's Rule to get the limit as h approaches 0 of e^(2+h),
which is just e^2.
[e^(2+h) − e^2]/h = [e^2(e^h−1)]/h

so in the limit, as h goes to 0, you'll notice that the numerator and denominator each go to zero (e^h goes to 1, and so e^h-1 goes to zero). This means the form is 'indeterminate' (here, 0/0), so we may use L'Hoptial's rule:

=e^2

3 0

2 years ago

Brock is a plumber. He charges a flat rate of $40 to visit a house to inspect its plumbing. He charges an additional $20 for eve

GalinKa [24]

Let x = hours of service.
Let y = total charges for x hours
The fixed charge is $20.
The charge per hour is $20.

Brock's charges for x hours is
y = 40 + 20x

This is a straight line with slope = 20 and y-intercept = 40.
The correct graph is W.

Answer: W

8 0

2 years ago

3^x= 3*2^x solve this equation

kompoz [17]

In the equation

$3^x = 3\cdot 2^x$

divide both sides by $2^x$ to get

$\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3$

Take the base-3/2 logarithm of both sides:

$\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}$

Alternatively, you can divide both sides by $3^x$ :

$\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13$

Then take the base-2/3 logarith of both sides to get

$\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}$