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This statement is a simply consequence from the definition of adjacent angles. They have common side.    If angles x and y are adjacent and x=y then, because x+y = 2x= 1800, then x = 180/2 = 900.

The binding energy of an atom refers to the binding energy of its nuceleus, which is defined by the Einstein's mass-energy relation                                              ΔE...

If these two elements belong to an Abelian group, then including the fact that the group is commutative, we can assume that a and b are elements of a vector space definied in one dimension (R1 space). Then their commutativity will be definied with respect to the scalar product, the magnitude...

If you mean to find the sum of first 10 terms of the series, then you have to use the formula for a geometric series:               Sum (of n first terms) = (qn - 1)/(q-1)               (1)   In your example...

I think, some information is missing in your problem. Only force of friction between the car and the grond will stop the car. Othervise, it will keep moving straightline with the same speed gained after coming down (Newton's law of inertia). If the car starts from rest and comes down the ramp...

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 polynomial...

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:                            ...