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Yanka [14]
1 year ago
13

Expand: In (4a)^3 help please

Mathematics
1 answer:
Gala2k [10]1 year ago
4 0

Answer: 3ln4 + 3lna

Step-by-step explanation:

\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}

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Determine if the equation below is a function with independent variable x. If so, find the domain. If not, find a value of x to
Andre45 [30]

Answer:

No because it contains points (3,4) and (3,-4).  You cannot have a x assigned to more than one y-value if you want it to be a function.

Step-by-step explanation:

A function has one output per input.

If we are trying to determine if the given is a function of x, then x is the input.

However I can get two outputs from plugging in x=3.

3^2+y^2=25

9+y^2=25

Subtract 9 on both sides:

y^2=25-9

y^2=16

Take the square root of both sides:

y=\pm \sqrt{16}

y=\pm 4.

So input x=3 yields y=4 and y=-4.

Since this input has more than one output then the given is not a function of x.

----Also!

If you graph the equation, it is a circle with radius 5 and center (0,0). So I could I plug in any number for x between -5 and 5 excluding -5 and 5 which would yield only one output each. Since plugging in either one gives:

(\pm 5)^2+y^2=25

25+y^2=25

Subtract 25 on both sides:

y^2=25-25

Simplify:

y^2=0

There is only one value y such that when you square it gives you 0. That is 0.

x=5 only gives y=0 and x=-5 only gives y=0.

There is no circle, unless it is a circle with radius 0 which means it really wouldn't be a circle, that is a function.

8 0
3 years ago
9. Whats is the equivalent fraction for 0.625
Tatiana [17]

Answer:

5/8

Step-by-step explanation:

You need to convert to a simplified fraction by placing the numbers to the right of the decimal over 1000. Then reduce the fraction.

6 0
3 years ago
Read 2 more answers
What is greater 8ft or 3yr
timama [110]
3yr is greater than 8ft
3 0
3 years ago
Read 2 more answers
What is the rule help I’m to stupid
aalyn [17]

Answer:

2/24

5/60

7/84

10/120

12/144

Step-by-step explanation:

rule is y=12x (Flavoring = x, Water = y)

Ex: y=12x

24=2x

\frac{24}{2} =\frac{2x}{2}

2=x

3 0
3 years ago
if you place a 5ft ladder against the top of a 4ft building how many feet will the bottom of the ladder be from the bottom of th
nika2105 [10]

Answer:

3 ft.

Step-by-step explanation:

When you imagine the sentence, it is a right angled triangle. In this case, it's a Pythagoras Theorem. The formula for it is:

a²(opposite) + b²(adjacent) = c²(hypotenuse)

The building is the opposite, the distance between the foot of the ladder and the building is the adjacent, while the ladder is the hypotenuse.

We have the measurements except for the adjacent. So it will be:

c² - a² = b²

5² - 4² = b²

25 - 16 = b²

9 = b²

√9 = b

b = 3 ft

The answer is 3 ft.

5 0
3 years ago
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