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3 years ago

If 27^27+27^27+27^27=3^k What is k?

Mathematics

1 answer:

JulijaS [17]3 years ago

6 0

Answer:

$\large{\boxed{k=82}}$

Step-by-step explanation:

$27^{27}+27^{27}+27^{27}=3^k$

$3 \cdot 27^{27}=3^k$

$3 \cdot (3^3)^{27}=3^k$

$3 \cdot 3^{81}=3^k$

$3^{82}=3^k \implies k=82$

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An aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank.The first pipe alone can f

liq [111]

Answer: it will take them 28 minutes to fill the tank.

Step-by-step explanation:

The first pipe alone can fill the tank in 84 minutes. This means that the rate at which the first pipe fills the tank per minute is 1/84

The second pipe can fill the tank in 42 minutes by itself. This means that the rate at which the second pipe fills the tank per minute is 1/42

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined rate of filling the tank would be

1/84 + 1/42

Assuming it takes t hours for both pipes to fill the tank working together, the working rate per minute would be 1/t. Therefore,

1/84 + 1/42 = 1/t

3/84 = 1/t

t = 84/3

t = 28 minutes

6 0

3 years ago

Read 2 more answers

What are the steps to solving systems of equations and inequalities

Black_prince [1.1K]

Step 1: Line up the equations so that the variables are lined up vertically.

Step 2: Choose the easiest variable to eliminate and multiply both equations by different numbers so that the coefficients of that variable are the same.

Step 3: Subtract the two equations.

Step 4: Solve the one variable system.

Step 5: Put that value back into either equation to find the other equation.

Step 6: Reread the question and plug your answers back in to check.

7 0

3 years ago

A pencil case with a cylinder shape with diameter= 10 cm

Mila [183]

Answer:

length of the longest pencil that can fit must be less than 13cm

Step-by-step explanation:

To get the longest pencil that fit the case, we will use the pythagoras theorem;

diameter = 10cm

radius = 10/2

radius = 5cm

Height = 12cm

Get the length of the longest side

l² = r²+h²

l² = 5²+12²

l² = 25 + 144

l² = 169

l = √169

l = 13cm

Hence the length of the longest pencil that can fit must be less than 13cm

4 0

3 years ago

Find (f^-1)'(7) without finding the inverse function where f(x) = 5 – 2x^3.

faltersainse [42]

Step-by-step explanation:

the derivative of an inverse function is

1/f'(f^-1(x))

f'(x) = -6x²

f^-1(7) is solving the original function equation for x under the knowledge that y = 7

7 = 5 - 2x³

2 = -2x³

-1 = x³

x = -1

f'(-1) = -6×(-1)² = -6×1 = -6

so,

(f^-1)'(7) = -1/6

5 0

2 years ago

Help me with this math question please I'm giving away brainliests

alex41 [277]

Answer:

Step-by-step explanation:

Given function is,

$f(x)=\frac{2x^2+6x}{-4x^2+8x}$

$=\frac{2x(x+3)}{-4x(x-2)}$

This function is not defined at "x(x - 2) = 0"

Therefore, for the values of x = 0 and 2, given function is not defined.

Vertical asymptote → x = 2 [Denominator = 0]

For Horizontal asymptote → $[\frac{2x^2}{-4x^2} =-\frac{1}{2}]$

Therefore, horizontal asymptote → y = $-\frac{1}{2}$

x-intercept,

For f(x) = 0,

Numerator of the function = 0

2x² + 6x = 0

2x(x + 3) = 0

x = -3

Therefore, x - intercept → (-3, 0)

For y-intercept,

x = 0

f(0) = 0

Therefore, graph has no y-intercept.

For holes on the graph,

Since, function is not defined at x = 0,

f(x) = $\frac{(x+3)}{-2(x-2)}$

f(0) = $\frac{(0+3)}{-2(0-2)}$

= $\frac{3}{4}$

Therefore, hole on the graph → $(0, \frac{3}{4})$

8 0

3 years ago