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Answers by Grigori S.

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...

Word Problems (answer)

Let x be the amount of hours spent by Samantha when she works alone, and 3x - time spent by Logan. First, You have to find how much work can be done each of these girls per unit of time. For Samantha it is 1/x, for Logan - 1/3x. Because 45 minutes is 3/4 of an hour, together they could have...

Word Problems (answer)

Let x0  be the fuel economy in ideal condition (no wind), Δx - change in fuel economy because of thew wind. Thus  we have                         x0 + Δx = 26            ...

Parametric equation has to be of the same kind - quadratic, like this  one, but with free parameters. One parameter is a coefficient of the quadratic term (x^2), and the second one is the coefficient for the linear term - x. Thus, it should be like          ...

Density of mass (answer)

Density of gold is 19.3 g/cm3. Density (by the definition) is mass per unit of volume:                            D = m/V                (D - density, m - mass, V - volume)   If...

I am sorry, Son, do not have enough time to work on the problem right now. Just one advise:   take derivatives of all functions and lim for x →∝. If they are equal - they have the same rate.

The model of an atom supported by J.J.Thomson after discovering electrons in 1897. Also known as plum-pudding model of an atom as a system of positively charged particles with embedded electrons which have negative electric charge (thus, the atom remains electrically neutral). Was replaced by...

Find F'(x)? (answer)

Use chain rule                      F'(x) = dF(x)/dx = (dF(x)/dx2)(dx2/dx) = 2x (dF(x)/dx2)  (1)   When you differentiate the integral with variable upper limit it gives you the function being integrated.   Thus...

Kenneth is right, the answer is    y = 1(1-x)   Here is the solution. If g is an inverse function to f, then we have f(g) =x   meaning that f and g are symmetric with respect to y=x line. Thus, we have   f(g) = 2- (g+1)/g=(g-1)/g...

X^2+x-30=0 (answer)

Factor the expression:               x2 +x - 30 = (x+6)(x-5) = 0   (because 6 and -5 are factors of -30 that make 6x - 5x = x - second term)   The product of two terms is zero if both are equal...

Divide numerator of the second fraction by numerator of the first one. Repeat the same for denominators. If the ratio remains the same then your fractions are proportions.   Check it now. 30/5 = 42/7 = 6 - yes, they are proportions.

Let's put it this way. The repeated part can be written as               7/100 + 7/1000 + ........ = (7/100)[1+ (1/10) +(1/102) + (1/103)......]   What we have in square brakets is a sum of geometric...

It depends on what is given to you in the problem and what s to be found. You need to specify your question. In generally, you can use the formula for angles of regular polygons to find the number of sides, the length of a side and perimeter, you can find the radius and area of a circle in which...

The function 3/x2 is symmetric with respect to chnange in sign: x by - x. This means the integral                          1                   1          ...

Energy E can also be defined as a product of potential difference  V (voltage) and the amount of electricity Q,                                      ...

To balance an equation can be understood like "to solve the equation" meaning to find the value of a variable which is being substituted into the equation balances both sides (makes them equal). Is it what you want?