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3 years ago

What is the inverse of f(x)=3+2lnx in radical form

1 answer:

8 0

$f(x)=3+2\ln x,\ x > 0\\\\y=3+2\ln x\\\\\text{replace x with y and y with x}\\\\3+2\ln y=x\ \ \ \ |-3\\\\2\ln y=x-3\ \ \ \ |:2\\\\\ln y=\dfrac{y-3}{2}\to e^{\ln y}=e^{\frac{y-3}{2}}\\\\y=e^{\frac{y-3}{2}}\\\\Answer:\ f^{-1}(x)=e^{\frac{y-3}{2}}$

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Is 19 a prime number or composite?

Alexandra [31]

Prime, because the only number that can go into it are 19 and 1

5 0

3 years ago

Read 2 more answers

All the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over. After 60 additional boxe

AveGali [126]

Answer:

(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.

Step-by-step explanation:

Given that all the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over.

This implies that boxes are in multiples of 12

i.e. 12, or 24, or 36 or....

Let us say this as 12m for m an integer

Now additional boxes arrived =60

Total number of boxes now = $12m+60$

This when arranged in stacks of 14,nothing left out

Or this is multiple of 14

$12m+60 = 14n$ for some positive integer n.

By trial and error we find that if 60 is to be divided by 14, 24 should be added and 24 is a multiple of 12.

So we say originally 24 boxes were there now 84 boxes there.

Hence both options are right.

(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.

3 0

3 years ago

(-6,8); perpendicular to y = -3/2x -1

UNO [17]

Answer:

$y = \frac{2}{3} x + 12$

Step-by-step explanation:

$y = - \frac{3}{2} x - 1$

The gradient of a line is the coefficient of x when the equation of the line is written in the form of y=mx+c.

Thus, gradient of given line= $- \frac{3}{2}$ .

The product of the gradients of perpendicular lines is -1.

(Gradient of line)(-3/2)= -1

Gradient of line

$- 1 \div ( - \frac{3}{2} ) \\ = - 1( - \frac{2}{3} ) \\ = \frac{2}{3}$

Substitute m= $\frac{2}{3}$ into y=mx+c:

$y = \frac{2}{3} x + c$

To find the value of c, substitute a pair of coordinates.

When x= -6, y= 8,

$8 = \frac{2}{3} ( - 6) + c \\ \\ 8 = - 4 + c \\ c = 8 + 4 \\ c = 12$

Thus, the equation of the line is $y = \frac{2}{3} x + 12$ .

7 0

3 years ago

Charlotte works at an electronics store as a salesperson. Charlotte earns a 10% commission on the total dollar amount of all pho

olga_2 [115]

Answer: the system of equations are

0.1x + 0.04y = 162

y = 2x

Step-by-step explanation:

Let x represent the total dollar amount of the phone sales she makes.

Let y represent the total dollar amount of the computer sales she makes.

Charlotte earns a 10% commission on the total dollar amount of all phone sales she makes, and earns a 4% commission on all computer sales. If she earned a total of $162 in commission, it means that

0.1x + 0.04y = 162

Charlotte had twice as much in computer sales as she had in phone sales. This means that

y = 2x

3 0

3 years ago

Consider the following pair of equations:

Bond [772]

So the equations are:

y= 3x + 3

y= x- 1

By the transitive property, we know x-1= 3x+3 (Transitive property means if a= b, and b= c, shouldn't a = c if they both equal b?)

so, x- 1= 3x + 3. Now we isolate x and solve:
+1 +1
x= 3x+ 4
-x -x

0 = 2x+ 4
-4 -4

-4 = 2x
/2 /2

x= -2

Now, you can plug that back in to find y:

y = x- 1
y= -2 -1
y= -3

Then plug them both in to make sure it is correct. :o)

6 0

3 years ago