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Ghella [55]
3 years ago
14

Add 1/2 liter,3/4 liter and 7/8 liter

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
5 0
First, find a lowest common denominator. The lcd in this equation os 8 so your new fractions would be 4/8, 6/8, and 7/8. You add the numerators (top numbers), which equals 17/8. Then you simplify to 2 1/8 liters.
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If f(x)=2x+sinx and the function g is the inverse of f then g'(2)=
Alexxx [7]
\bf f(x)=y=2x+sin(x)
\\\\\\
inverse\implies x=2y+sin(y)\leftarrow f^{-1}(x)\leftarrow g(x)
\\\\\\
\textit{now, the "y" in the inverse, is really just g(x)}
\\\\\\
\textit{so, we can write it as }x=2g(x)+sin[g(x)]\\\\
-----------------------------\\\\

\bf \textit{let's use implicit differentiation}\\\\
1=2\cfrac{dg(x)}{dx}+cos[g(x)]\cdot \cfrac{dg(x)}{dx}\impliedby \textit{common factor}
\\\\\\
1=\cfrac{dg(x)}{dx}[2+cos[g(x)]]\implies \cfrac{1}{[2+cos[g(x)]]}=\cfrac{dg(x)}{dx}=g'(x)\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}

now, if we just knew what g(2)  is, we'd be golden, however, we dunno

BUT, recall, g(x) is the inverse of f(x), meaning, all domain for f(x) is really the range of g(x) and, the range for f(x), is the domain for g(x)

for inverse expressions, the domain and range is the same as the original, just switched over

so, g(2) = some range value
that  means if we use that value in f(x),   f( some range value) = 2

so... in short, instead of getting the range from g(2), let's get the domain of f(x) IF the range is 2

thus    2 = 2x+sin(x)

\bf 2=2x+sin(x)\implies 0=2x+sin(x)-2
\\\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}\implies g'(2)=\cfrac{1}{2+cos[2x+sin(x)-2]}

hmmm I was looking for some constant value... but hmm, not sure there is one, so I think that'd be it
5 0
2 years ago
Solve for x and then find the measure of B
pogonyaev

Answer:

x=6

b= 126

Step-by-step explanation:

8x+78 = 2x+114

8x-2x = 114-78

6x=36

x=6

--------

b=2x6+114

b= 126

3 0
3 years ago
What is the slope of the line that passes through points (2,-3) and (5,1)
Ivenika [448]

Find the difference in the y-coordinates: -3 - 1 = -4

Find the difference in the x-coordinates in the same order: 2 - 5 = -3

Divide the difference in y by the difference in x: slope = (-4)/(-3)

Reduce the fraction: slope = 4/3

3 0
2 years ago
What is the volume of the cylinder below?
yulyashka [42]

Answer:

A

Step-by-step explanation:

v=πr2h

r=(3)²* 5

45π unit³

4 0
2 years ago
I need the answers for this
velikii [3]

Answer:

q1 9.2

q2 5.9

q3 8.4

Q4 7.5

q5 7.3

q6 5.1

5 0
3 years ago
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