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## Grigori S.'s Resources

If you asolve this equation for x you will see that x^2 term will be canceled, and you will find        x = [(a+1-(b+c)]/(b+c+a+1)   That means x = 0 if a+1 = b+c.  (1)   In the maentime we have to exclude the...

You are, probably, asking about meters per second (m/s).  One mile is equal to 1612 meters (some resources use 1610 oe 1609 meters).  Also we have to change 1hour (1h) to seconds. 1h = 3600 s.   Thus, we have       70 mi/3h = 70x1612 m/(3x...

The perimeter is           2(w+l ) = 130 ft   (1) In the meantime        l = 4w                   (2) Thus, by substituting (2) into (1) we can write:   2(5w) =...

Write the quadratic equation in standard form:   y = ax2 +bx +c     (1)    Plug x-s from the table into  (1). You will have:   c = -4   4a - 2b + c = -18   4a + 2b + c = -14   By...

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...

boat speed (answer)

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...