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3 years ago

How do logarithmic equations relate to exponential equations?

Mathematics

1 answer:

mash [69]3 years ago

6 0

Logarithmic equations are the inverse of exponential equations.

Say you have the exponential equation of:

$y = 2^x$

This is inversely equivalent to:

$log_{2}(y) = x$

By general definition:

$y = b^x$ = $log_{b} (y) = x$

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What is the value of x?

allochka39001 [22]

Answer:

80°

Step-by-step explanation:

Central Angles and the Arc they create are equal

8 0

3 years ago

A circle has a diameter of 15 meters. Calculate the

Nina [5.8K]

Answer:

15.7 meters

Step-by-step explanation:

Applying,

s = πd∅/360°..................... Equation 1

Where s = length of the arc formed, d = diameter of the circle, ∅ = angle formed by the center of the circle, π = pie.

From the question,

Given: d = 15 meters, ∅ = 120°

Constant: π = 3.14

Substitute these values into equation 1

s = (3.14×15×120)/360

s = 15.7 meters

Hence the lenght of the arc formed is 15.7 meters

4 0

3 years ago

Subtract the equations.

Lostsunrise [7]

Answer:

0x+2y=22

Step-by-step explanation:

Set them equal to each other, (5x+4y=25)-(5x+2y=3). Distribute the negative into the right equation, (5x+4y=25)(-5x-2y=-3). Then combine like terms to get your answer.

6 0

3 years ago

g Given the system of equations: 15 c1 – 5 c2 – c3 = 2400 - 5 c1 + 18 c2 – 6 c3 = 3500 - 4 c1 - c2 + 12 c3 = 4000 (a) Calculate

denpristay [2]

Answer

(a)

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

(b)

$A^{-1} b = \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

Step-by-step explanation:

Remember that when you want to solve a problem like this, you express the equation as following

$Ax = b$

So, if you know the inverse of $A$ then

$x = A^{-1} b$

For this case

$A = \begin{pmatrix} 15 && 5 && -1 \\ -5 && 18 && -6 \\ -4 && -1 && 12 \end{pmatrix}$

Now for this case the inverse of A would be

$A^{-1} = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix}$

Then when you multiply with the vector solution

$A^{-1} b = \frac{1}{3493} \begin{pmatrix} 210 && -59 && -12 \\ 84 && 176 && 95 \\ 77 && -5 && 295 \end{pmatrix} * \begin{pmatrix} 2400 \\ 3500 \\ 4000 \end{pmatrix} = \frac{1}{3493} \begin{pmatrix} 249500 \\ 1197600 \\ 1347300 \end{pmatrix}\\\\\\= \begin{pmatrix} \frac{500}{7} \\\\ \frac{2400}{7} \\\\ \frac{2700}{7} \end{pmatrix}$

So from that information you can conclude that the solution to the system of equations is x = 500/7 y = 2400/7 and z = 2700/7

7 0

3 years ago

Can you ever use a calculator to determine if a number is rational or irrational? Explain.

Nataly [62]

Irrational cannot be represented as a fraction. so your answer is yes.

3 0

3 years ago

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