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2 years ago

Simplify 4(3x^2y^4)^3 / (2x^3y^5)^4 show your work

2 answers:

8 0

Step by step solution :Step 1 :Equation at the end of step 1 : (((3•(x2))•(y4))3) 4•—————————————————— ((2x3•(y5))4) Step 2 :Equation at the end of step 2 : ((3x2 • (y4))3) 4 • ——————————————— 24x12y20 Step 3 : 33x6y12 Simplify ———————— 24x12y20 Dividing exponential expressions :

3.1 x6 divided by x12 = x(6 - 12) = x(-6) = 1/x6

Dividing exponential expressions :

3.2 y12 divided by y20 = y(12 - 20) = y(-8) = 1/y8

Equation at the end of step 3 : 27 4 • —————— 16x6y8 Step 4 :Final result : 27 ————— 4x6y8

Helga [31]2 years ago

7 0

Answer: The answer is " $432x18y32$ "

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Task 2 a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a

Galina-37 [17]

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

$y = 10000 * 1.04^x$

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

$y = 12000* 0.97^x$

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A exceeds city B, we have the following inequality

$10000 * 1.04^x > 12000 * 0.97^x$

Divide both sides by 10000

$1.04^x > 1.2 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{0.97})^x > 1.2$

$1.07^x > 1.2$

Take the natural logarithm of both sides

$\ln(1.07)^x > \ln(1.2)$

This gives

$x\ln(1.07) > \ln(1.2)$

Solve for x

$x > \frac{\ln(1.2)}{\ln(1.07)}$

$x > 2.69$

This means that, the population of city A will exceed city B after 3 years

<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A is at least twice city B, we have the following inequality

$10000 * 1.04^x \ge 2 * 12000 * 0.97^x$

$10000 * 1.04^x \ge 24000 * 0.97^x$

Divide both sides by 10000

$1.04^x \ge 2.4 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{ 0.97})^x \ge 2.4$

$1.07^x \ge 2.4$

Take the natural logarithm of both sides

$\ln(1.07)^x \ge \ln(2.4)$

This gives

$x\ln(1.07) \ge \ln(2.4)$

Solve for x

$x\ge \frac{\ln(2.4)}{\ln(1.07) }$

$x\ge 12.9$

This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

brainly.com/question/11464095

3 0

3 years ago

Mike received a 10% raise each month for 3

s2008m [1.1K]

Answer:

his salary after three months would be 1300

Step-by-step explanation:

10 percent of 1000 is a hundred and multiply that by 3, it would equal 300 and add that to the 1000.

7 0

3 years ago

What is the sum of the measures of the exterior angles of this triangle?

fgiga [73]

Answer:

360°

Step-by-step explanation:

We need only remember that the sum of the measures of the interior angles of a triangle is 180°. Angle c and 112° form a pair of "straight angles," so they add up to 180°; as a consequence, Angle c = 180° - 112°, or 68°.

With two of the interior angles now known, we can calculate the third, Angle A: It is 180° less (51° + 68°), or 180° - 119°, or 61°.

That means that the measure of Angle B is 180° - 61° = 119°

Looking at the pair C and 112°, we identify the exterior angle as 112°.

Looking at the pair A and B, or 61° and 119°, we identify the exterior angle as 119°.

Finally, looking at the pair 51° and (180° - 51°), or

51° and 129°, we identify the exterior angle as 129°.

Then the sum of the exterior angles 129° and 119° and 112° is 360°.

6 0

3 years ago

Read 2 more answers

Help please I'm stuck show and explain your work

Deffense [45]