Mary Catherine makes 2 gallons of punch how many cups of punch did she make
1 answer:
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The transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>How to transform the logarithmic function?</h3>The parent logarithmic function is
y = log(x)
When shifted left by 4 units, we have:
y = log(x + 4)
When shifted up by 3 units, we have:
y = log(x + 4) + 3
When compressed vertically by 1/3, we have:
y = 1/3(log(x + 4) + 3)
This gives
y = 1/3(log(x + 4)) + 1
When stretched horizontally by 3, we have:
y = 1/3(log(x/3 + 4)) + 1
Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>The transformation of function f(x)</h3>We have:
f(x) = log[-(x – 5)] + 4
Set the radicand greater than 0
-(x - 5) > 0
Divide by -1
x - 5 < 0
Add 5 to both sides
x < 5 -- this represents the domain
A logarithmic function can output any real number.
So, the range is
In the domain, we have:
x < 5
This means that the interval of decrease is
Rewrite as an equation
x = 5 --- this represents the equation of asymptote
Read more about logarithmic functions at:
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Answer:
120 liters of 60% alcohol solution is needed
Step-by-step explanation:
Let's assume
x liters of 60% alcohol solution is added
so, we get solution as
we are given
40 liters of a 20% alcohol solution is
so, total alcohol solution is
now, we can find total solutions
total solutions is
now, it is making 50% solution
so, we get
now, we can solve for x
So,
120 liters of 60% alcohol solution is needed
Answer:
Step-by-step explanation:
We know two sides and the angle between the sides, so we can use the Law of Cosines. Recall that the Law of Cosines states that:
, where a and b are the sides and C is the angle in between.
Let's substitute 115 for a, 178 for b, and 41 for Angle C.
Thus: