What is the slope of the line graphed on the coordinate plane?

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

6 0

Answer:

-1/12

Step-by-step explanation:

slope=(-2-(-1))/(6-(-6))

-1/12

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I need help in this!

In-s [12.5K]

For a function to begin to qualify as differentiable, it would need to be continuous, and to that end you would require that $a$ is such that

$\displaystyle\lim_{x\to0^-}g(x)=\lim_{x\to0^+}g(x)\iff\lim_{x\to0}ax=\lim_{x\to0}x^2-3x$

Obviously, both limits are 0, so $g$ is indeed continuous at $x=0$ .

Now, for $g$ to be differentiable everywhere, its derivative $g'$ must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:

$g'(x)=\begin{cases}a&\text{for }x0\end{cases}$

and at this time, we don't know what's going on at $x=0$ , so we omit that case. We want $g'$ to be continuous, so we require that

$\displaystyle\lim_{x\to0^-}g'(x)=\lim_{x\to0^+}g'(x)\iff\lim_{x\to0}a=\lim_{x\to0}2x-3$

from which it follows that $a=-3$ .

3 0

3 years ago

Kerry and her brother and noticed there is 3/4 of a pint of ice cream in the freezer. After they eat some ice cream there is 1/3

7nadin3 [17]

Answer:

$\frac{5}{12} \ of\ a \ pint$ .

Step-by-step explanation:

Given:

Kerry and her brother and noticed there is 3/4 of a pint of ice cream in the freezer.

After they eat some ice cream there is 1/3 of a pint left.

Question asked:

How much ice cream did Kerry and her brother eat ?

Solution:

Total ice cream in the freezer = $\frac{3}{4} \ of\ a\ pint$

Ice cream left = $\frac{1}{3}\ of\ a \ pint$

<h3>They ate = Total ice cream in the freezer - Ice cream left after they ate</h3>

$=\frac{3}{4} -\frac{1}{3} \\ \\\\Taking \ LCM \ of 4 \ and\ 3, we \ got ,12\\ \\=\frac{3\times3-4\times1}{12} \\\\ =\frac{9-4}{12} \\ \\ =\frac{5}{12}$