The degree of your resultant polynomial (no matter they are added or subtracted) is 7. When you are performing your operations with polynomials of different degrees you are combining only like terms (terms with the same degree). The degree of your resultant
polynomial is the same like of the...

There are 10 numbers from 1 to 100 which are fool squares of digits from 1 to 9 and 10:
1,4,9,16,25,36,49,64,81,100
Thus, there are 90 numbers which are irrational numbers as square roots.

For each point at which a limit is considered (say, x0 for a function y = y(x)) you have to check for left-side and right-side limits:
lim y(x) = a and lim...

Let's rewrite your expression:
2t+4/(12 -3t^2) = 2(t+2)/3(4 - t^2) = 2(t+2)/3(2-t)(2+t) = 2/3(2-t).
Thus, when t approaches -2 your limit will be 2/12 = 1/6.

First, you have to convert km/h into m/sec:
44 km/h = 44,000 m/ 3600 sec = 12.22 m/sec
Then distance by this speed:
...

1) f(g(x)) = g^4 +5g = (7x^3) ^4 + 5(7x^3) = (7^4) x^12 + 35x^3 = 2401 x^12 + 35 x^3
2)g(f(x)) = 7f^3 = 7 (x^4 +5x)^3

Another way to solve the problem. Your function has the first coefficient with negative sign,
which means it may only maximum. The time the ball reaches the ground is double of the time needed to reach to its maximum position. To find that time just calculate derivative of your function and...

Unit rate for the bathroom faucet - 8/12 ounces/min = 0.75 oz/min = 3/4 oz/min
Unit rate for the kitchen faucet - 6/10 = 3/5 oz/min - two rates show different coefficients of proportionality between amounts of water leaked and time.
Unit rate or both faucets = (3/4) + (3/5)...

To calculate then uncertainty of the equivalent capacitor Ceq you have to differentiate the expression for the capacitor shown by Richard, and replace the symbol of differential by Δ symbol (means uncertainty or error of measurement). Let
...

The sum of all 20 munbers is 14x20=280, the sum of first 10 numbers is 10x15 = 150, the sum of next 9 numbers is 9x13= 117. the last number equals 280 - (150+117) = 13.
Answer: 13.

Temperature remains constant. Increase in velocity causes increase in dynamic pressure (ρv2/2) but decrease in static pressure (ρgh). Total pressure (dynamic plus static), remains constant:
...

The sky is blue because of Raleigh scattering of the sunlight in the Earth atmosphere. This type of scattering (while the other portion of the light reaches the Earth's surface) is described by the function inversely proportional to fourth degree of
the light wavelength: ∼λ-4)...

Let v be the Jay's average speed. Then (v + 50)mph is the Mike's average speed. When they met Jay was traveling 5 hours, while Mike has spent just 2 hours. To meet at the same point means to travel the same distance, because the starting is also the same.
Thus, we have
...

This means one square root is positive while another one is negative.
Let x be the number you are looking for. Your word statement can be written as the following equation
√x - (-√x) = 2√x...

The number of segments is equal to the number of couples produced by the set (each segment is defined by two points). The same pair of points produces two identical segments, the number of each is 4x3 = 12. To get unique lines you have to divide this number
by 2. Thus, the number of the unique...

GUIDE PROBLEMS
Let d be the distance traveled by the boat, v0 - speed of the boat in still water, v - speed of the current, t1 = 1/5, and t2 = 3/5.
To find the speed of the boat in still water we have to write two equations: one for motion up the river and another one – against...

Use rules of exponents. First of all
(x5)-8 = x -40
Then if your next term is x4 you will have x-40 x4 = x-36 (you are adding the exponents)
If you have x -4 then your final answer is x -44.

Please type your function again. You have question marks instead of regular symbols.

If you calculate the ratio of distances between Earth and the Sun, and between Earth and the Moon, you will find it is almost 390. When it comes to tidal effects size of the planet (Earth) and its distances from the sources of gravitation (Sun and Moon)
matters. Earth's diameter divided by astronomical...

f(y) is a parabola which is open down, and has two horizontal, intercepts: y=0 and y=2 with maximum
at y = 1. Because g(y) is a straight line, area bounded by the line for 0 ≤y,≤1 is 1/2. Thus, the area bounded by two graphs is the integral of f(y) from 0 to 1 minus 1/2. The answer...