MATHEMATICS COLLEGE

If the logarithm of 5832 is 6, what is the base?
$logx(5832) = 6$

Answers

Answer 1

Answer:

Answer:

The base is 4.2426.

Step-by-step explanation:

Logarithm definition:

Suppose we have that:

$log_a(b) = c$

It means that;

$b = a^c$

In this question:

$log_x((5832)) = 6$

It means that:

$x^6 = 5832$

$x = \sqrt[6]{5832}$

$x = (5832)^{(1)/(6)}$

$x = 4.2626$

The base is 4.2426.

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A rectangular window has a length of 81.47 cm and a width of 34.2 CM what is the least

This is the two that go together, but are separate questions

Answers

Answers:

Option 1)

6a + 8s = 102

14a + 4s = 150

each adult ticket costs 9 dollars

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Explanation:

6 adult tickets and 8 student tickets bring in $102, so that means 6a+8s = 102

14 adult tickets and 4 students tickets bring in $150, so 14a+4s = 150

The system of equations is

$\begin{cases}6a+8s = 102\n14a+4s = 150\end{cases}$

If we multiply both sides of the second equation by -2, we get this updated system

$\begin{cases}6a+8s = 102\n-28a-8s = -300\end{cases}$

Add the equations straight down

6a+(-28a) = -22a

8s+(-8s) = 0s = 0 ... the 's' terms go away

102+(-300) = -198

So we end up with the equation -22a = -198 and that solves to a = 9 after dividing both sides by -22.

Each adult ticket costs $9

If you want the value of s, then

6a+8s = 102

6(9)+8s = 102

54 + 8s = 102

8s = 102-54

8s = 48

s = 48/8

s = 6

Meaning each student ticket costs $6

Or you could use the other equation

14a+4s = 150

14(9)+4s = 150

126+4s = 150

4s = 150-126

4s = 24

s = 24/4

s = 6

We get the same value of s

Olga walks 5 blocks to school her friend Louis walks 1/3 of that distance how many blocks does Louis walk to school

Answers

Answer:

Louis walks 1 and 2/3 blocks.

Step-by-step explanation:

To figure this out, what you want to do is multiply 1/3 by 5.

casey has n nickels.meghan has 4 times as many nickels as casey has.write an expression for the total number of nickels casey and meghan have.then simplify the expression.

Answers

Answer:

Step-by-step explanation:

Summarizing what we know:

Casey has n nickels, and Meghan 4 times as many: 4n

Then the total number of nickets these two people have is n + 4n, or 5n.

I need some help with this calculus 1 implicit diffrention problem?

Answers

Answer:

y" = -24 / y³

Step-by-step explanation:

6x² + y² = 4

Take the derivative of both sides with respect to x.

12x + 2y y' = 0

Again, take the derivative of both sides with respect to x.

12 + 2y y" + y' (2y') = 0

12 + 2y y" + 2(y')² = 0

Solve for y' in the first equation.

2y y' = -12x

y' = -6x/y

Substitute and solve for y":

12 + 2y y" + 2(-6x/y)² = 0

12 + 2y y" + 2(36x²/y²) = 0

12 + 2y y" + 72x²/y² = 0

6y² + y³ y" + 36x² = 0

y³ y" = -36x² − 6y²

y" = (-36x² − 6y²) / y³

Solve for y² in the original equation and substitute:

y² = 4 − 6x²

y" = (-36x² − 6(4 − 6x²)) / y³

y" = (-36x² − 24 + 36x²) / y³

y" = -24 / y³

Determine 6th term in the geometric sequence whose first term is 3 and whose common ratio is -4.

Answers

$a_1=3$
$a_2=-4a_1$
$a_3=-4a_2=(-4)^2a_1$
$\cdots$
$a_6=-4a_5=\cdots=(-4)^5a_1$

$\implies a_6=(-4)^5\cdot3=-3072$

Candy Canes BONUSHow many candy canes do I have?
I have more than 15 but less than 30.
If 2 people share them evenly, there will be 1 left over.
If 3 people share them evenly, there will be 2 left over.
If 4 people share them evenly, there will be 3 left over.