Calculus

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64

To solve x^7 = 9

take the 7th root: x = 9^(1/7)

Alternatively,

take logs 7*log(x) = log(9)

log(x) = log(9)/7

x = 10^{log(9)/7}

or use natural logs, so that x = e^{ln(9)/7}

b-30=32

b=30+32

b=62

Factor out -2: -2(x squared +11x-20). This is fully factored.

x+1+x-2=2x-1

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They are elements of the infinite set of ordered pairs of the form (x, 0.1x+1). It is an infinite set and I am not stupid enough to try to list its elements!

No. Not even close! 2 + 2= 4 FOUR, i tell you!

39 is 19 more than 20, so the percentage increase can be determined by dividing 20 by 19. the answer therefore is "to get from 20 to 39, you increase it by 95%" or "39 is 195% of 20". the second answer was obtained because it is including the original value (100%) and adding the extra value to show increase.

2x2

go to y on the bottom and x to the top

8,610,513,192

y=9+3x is linear because there is only one value of x so it will go up proportionally, for instance if x=1 then y=12, x=2 y=15, x=3 y=18.

they will always go up by three, only equations with multiple xs, eg x squared+4x+6 is non linear and x cubed-9 is non linear.

a parabola

4x+1 -3 = 26

first, +1 and -3 = -2

Move the -2 to the other side of the = sign, and it becomes +2.

+26 +(+2) = 28

Now we have 4x = 28

Divide both sides by 4 and you have 4x/4 = 28/4

Perform that division and the answer is x = 7

Any circle centered at the origin fits that description.

Without a second independent equation, it's not a 'system' yet.

The simplified answer would be 6x. In this case, x=1. So, you would add 1 to the 5, making is 6x

A cubic meter of any substance is 1000 liters.

28!EASY

To find the number of strings of length less than 4 that match the regular expression ((x y)y(a , | , ab)), we first analyze the components. The expression can generate strings of length 3: "xyy", "xyab", and also strings of length 2: "xyy" (from the first part) and "xy" (if we consider the empty string for the last part). Therefore, the valid strings of length less than 4 are "xyy", "xyab", and the empty string, leading to a total of 3 valid strings.

An integral freezer unit is a self-contained refrigeration system designed to maintain low temperatures for storing frozen goods. It combines the refrigeration components, such as the compressor and evaporator, within a single unit, making it easier to install and operate. These units are commonly used in commercial settings like restaurants and grocery stores for efficient food preservation. Their compact design allows for flexibility in placement while ensuring optimal freezing performance.

y = x2 - 3x - 20 is a formula linking two variables, x and y. It does not - indeed, it cannot - have a solution.

The equation x2 - 3x - 20 = 0 has solutions at x = -3.217 and x = 6.217 approx.

5X=12

To figure out what X is, you need to get X on it's own.

So simply divide both sides by 5 since there is 5X which makes 12/

So now X=12/5=2.4

X=2.4