Calculus

315

No.

There is not enough information in the equation x + 2y = 2, by itself, to solve it. There are an infinite number of solutions. A second equation, or information to allow a second equation to be derived, must be given to find a solution.

If: y = 4x^2 -2x -1 and y = -2x^2 +3x+5

Then: 4x^2 -2x-1 = -2x^2 +3x+5 or 6x^2 -5x -6 = 0

Factorizing the above: (3x+2)(2x-3) = 0 meaning x = -2/3 or x = 3/2

By substitution points of contact are at: (-2/3, 19/9) and (3/2, 5)

Sorry, need more info! is it 3 times 2x = 8?

No. One argument of function may have only one value. So, if it has more than one value, it is not a function.

x2 + 9x + 20 = 0

∴(x + 4)(x + 5) = 0

∴x ∈ {-5, -4}

Integral of x dx / sqrt(x+2)

Make the substitution sqrt(x+2)=u

(x+2)^(1/2) = u

(1/2)(x+2)^(-1/2) dx = du

1/2(x+2)^(1/2) dx = du

1/2sqrt(x+2) dx = du

1/sqrt(x+2) dx = 2 du

Integral of x dx / sqrt(x+2) = Integral 2 x du

sqrt(x+2) = u

(x+2)=u^2

x=u^2-2

Integral 2 x du = Integral 2(u^2-2) du

= Integral 2u^2 du - 4 du

= 2 u^3/3 - 4u + C

= (2/3) (x+2)^(3/2) - 4 sqrt(x+2) + C

There are 16 ounces in one pound.

Therefore you have

19 lbs (16 ounces/1 lb) + 2 ounces= 306 ounces

306 ounces/3= 102 ounces

102 ounces (1lb/16 ounces)= 6 lbs 5 ounces

x works out as 5/3

3 + z

All variables if they have no visible coefficient have an implied coefficient of 1.

A single value for x and a single value for y represent a point, not a line. A point cannot have a slope.

It equals 12

The inverse of a function is its reflection in the line y=x.

so the only function that returns its own inverse is the line y=x or any part of the line y=x

42 x 5 = 210

x = +5 or -5

If you factor this you would first factor out a common multiple
4(c^2+3c-18)
4(c+6)(c-3)
The 6 and -3 were arrived by thinking,"What adds together to get +3 and mu;tiplies to get -18?"

Because it can't be written as a fraction

with whole numbers on top and bottom.

(t+3)3 is already factored.

Could write it as (t+3)(t+3)(t+3).

14 + 19 = 33

First, you have to have domain and range, a graph, or an equation in slope-intercept form ( y=mx + b) to determine if an equation is a function. The slope intercept form here is Y=3/1x + 1. So Yes, this equation is a function. If you want to know how to convert into y=mx + b form, ask how to do it here, or look it up on the internet. Hope I helped :-)

no .it will not form

9x + 4 - x + 8 = 8x + 12

x = 7.375

because...

3 over 2x -15 = -12

3 = -12(2x-15)

3 = -24x + 180

0 = -24x + 177

24x = 177

x = 7.375