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2 years ago

1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.

Mathematics

1 answer:

Troyanec [42]2 years ago

6 0

9514 1404 393

Answer:

p = 3/4n +3

Step-by-step explanation:

Expressing the given equation in terms of powers of 3, we have ...

(27^(n+3))/(81^(p-1)) = 3

(3^3)^(n+3)/(3^4)^(p-1) = 3^1 . . . . as powers of 3

3(n +3) -4(p -1) = 1 . . . . . . . . . . . . log base 3 (or, equate exponents)

3n +9 -4p +4 = 1 . . . . . . . . . . . . . eliminate parentheses

3n +12 = 4p . . . . . . . . . . . . . . . . add 4p -1

p = 3/4n +3 . . . . . . . . . . divide by 4

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2 years ago

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Alvin is 11 years younger than Elga. The sum of their ages is 43. What is elgas age

Neporo4naja [7]

Answer:

Step-by-step explanation:

Lets assume x is Elgas' age

And y is Alvins age

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2 years ago

Solve for x. (X+16) (4x-5) X = 4.3 X = -7 X = 3 X = 7

jeka94

Answer:

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Step-by-step explanation:

1) replace the x with 7

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3 years ago

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2 years ago

the boundary of a rectangular farm field in ireland has a straight rock wall along one side and fences along its other three sid

Inessa [10]

Answer:

781250 $ft^{2}$

Step-by-step explanation:

Let y is the length of the farm field

Let x is the width of the farm field

Given that, no fencing is necessary along the rock wall, so we can find the perimeter of the farm is:

2x + y = 2500 feet

<=> y = 2500 -2x

The are of the farm has the following formula:

A = x*y

<=> A = x(2500 - 2x)

<=> A = 2500x -2 $x^{2}$

To have the maximum area of field in square feet, we need to use differentials to estimate:

$\frac{dA}{dx}$ = 2500 - 4x

Set $\frac{dA}{dx}$ = 0, we have:

2500 - 4x = 0

<=> x = 625 feet.

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So the maximum area of field is:

A = x*y = 625*1250 = 781250 $ft^{2}$

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3 years ago

1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.​

1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.