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3 years ago

1. Which equation is true when m = 12?

Mathematics

1 answer:

kobusy [5.1K]3 years ago

7 0

Answer:

are there any more details? cant solve anything from what you have provided

Step-by-step explanation:

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Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the derivative does not exist at

KIM [24]

Answer:

The derivative of the function does not exist.

Step-by-step explanation:

The alternative form of a derivative is given by:

$f'(c)= \lim_{x \to c} \dfrac{f(x)-f(c)}{x-c}$

Our function is defined as:

h(x)=|x+8|

i.e. h(x)= -(x+8) when x+8<0

and x+8 when x+8≥0

i.e. h(x)= -x-8 when x<-8

and x+8 when x≥-8

Hence now we find the derivative of the function at c=-8

i.e. we need to find the Left hand derivative (L.H.D.) and Right hand derivative (R.H.D) of the function.

The L.H.D at a point 'a' is calculated as:

$\lim_{x \to a^-} \dfrac{f(x)-f(a)}{x-a}\\\\=\lim_{h \to0} \dfrac{f(a-h)-f(a)}{a-h-a}= \lim_{h\to 0} \dfrac{f(a-h)-f(a)}{-h}$

Similarly R.H.D is given by:

$\lim_{x \to a^+} \dfrac{f(x)-f(a)}{x+a}\\\\=\lim_{h \to 0} \dfrac{f(a+h)-f(a)}{a+h-a}= \lim_{h\to 0} \dfrac{f(a+h)-f(a)}{h}$

Now for L.H.D we have to use the function h(x) =-x-8

and for R.H.D. we have to use the function h(x)=x+8

L.H.D.

we have a=-8

$\lim_{x \to (-8)^-} \dfrac{h(x)-h(-8)}{x-(-8)}\\\\= \lim_{h \to0} \dfrac{h(-8-h)-h(-8)}{-8-h-(-8)}= \lim_{h\to 0} \dfrac{h(-8-h)-h(-8)}{-h}$

= $\lim_{h \to 0} \dfrac{8+h-8-0}{-h}= \lim_{h \to 0}\dfrac{h}{-h}=-1$

similarly for R.H.D.

$\lim_{x \to (-8)^+} \dfrac{h(x)-h(-8)}{x-(-8)}\\\\=\lim_{h \to 0} \dfrac{h(-8+h)-h(-8)}{-8+h-(-8)}= \lim_{h\to 0} \dfrac{h(-8+h)-h(-8)}{h}$

$\lim_{h \to 0} \dfrac{-8+h+8-0}{h}=\lim_{h \to 0}\dfrac{h}{h}=1$

Now as L.H.D≠R.H.D.

Hence, the function is not differentiable.

4 0

3 years ago

0.18 divided by 0.04

tatiyna

If you plug that into a calculator you get 4.5

3 0

3 years ago

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Identify the initial amount and the growth rate of the following:<br> Y = 9.8 (1.35)^t

stiv31 [10]

Assuming t is a time unit.
The initial amount is when t = 0, so it is 9.8 * 1 = 9.8. The growth rate is how much the amount goes up by for every increase of 1 in t. This is 1.35 because that is the part being affected by t. we plug in 0 for t to get 9.8 as the initial amount. The growth rate is just 135% factor, or 35% more each time, because 1.35 is the base of the exponent.

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2 years ago

Mike prepares 10

Andrews [41]

If my thinking is correct, and the numbers:

and

don't mean anything, then the answer would be 8 cups

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3 years ago

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(4,7), (x,19); slope = 3 the pair points lies on the same line with the given slope. Find x

Andrew [12]

So we are given two points, say P1(4,7), P2(x,19).

Slope is given by
m=3=(y2-y1)/(x2-x1)=(19-7)/(x-4)
solve for x
3=(19-7)/(x-4)
cross multiply
3(x-4)=12
3x-12=12
3x=12+12=24
x=8

3 0

3 years ago