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3 years ago

Y = 0.115x + 0.0045 , y = 0.499x – 0.22 solve for x

Mathematics

1 answer:

enyata [817]3 years ago

6 0

Answer:

x=0.5612

Step-by-step explanation:

-Given the functions:

$y=0.115x+0.0045\ \ \ \ ...i\\\\y=0.499x-0.22\ \ \ \ \ ...ii$

We subtract equation i from ii to eliminate y and solve for x:

$ii-i\\\\0=0.384x-0.2155\\\\0.384x=0.2155\\\\x=0.5612$

Hence, the value of x is 0.5612

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Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

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Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

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1 year ago

A recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water 3/4 quart of grape juice. Q1: How much sparkling wa

kogti [31]

Answer:

1) 18 Quart of Sparkling water need to mix with 9 quart grape juice

2) 15/2 Quart of grape juice required for 15/4 quarts of sparkling water.

3) Quantity of grape juice and sparkling water in 100 quart of punch are 33 1/3 quart and 66 2/3 quart respectively.

Step-by-step explanation:

1 1/2 quarts = 1 + (1/2) = 3/2 quarts

1) water required for 3/4 quart of grape juice = 3/2 quarts

so water required for 1 quart of grape juice = (3/2) ÷ (3/4) = (3/2)× (4/3) = 2 quarts

so water required for 9 quart of grape juice = 9 * 2 = 18 quart

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For 18 quart of Sparkling water , grape juice require = 9 quart

So for 1 quart of Sparkling water , grape juice require = 9÷18 = 1/2 Quart

so for 15/4 quart of Sparkling water , grape juice require = 1/2 × 15/4 =

15/2 Quart of grape juice required for 15/4 quarts of sparkling water.

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In other words 1 quart of grape juice + 2 quart of sparkling water is 3 quart of punch.

Quantity of Grape juice in 3 quart of punch = 1 quart

so quantity of grape juice in 1 quart of punch = 1/3 quart

And quantity of grape juice in 100 quart of punch = 100×(1/3) = 100/3 =

33 1/3

Quantity of sparkling water in 3 quart of punch = 2 quart

so quantity of sparkling water in 1 quart of punch = 2/3 quart

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