Calculus

The derivative with respect to 'x' is 4y3 .

The derivative with respect to 'y' is 12xy2 .

5.7 x 10-6 = 0.0000057

I am interpreting this as:

Find the derivative of:

y=((2x+5)8+4x)3

To find the derivative (y'), the chain rule must be applied. The "outermost" function of this compound function is t3 (t being an arbitrary quantity). The derivative of t3 is 3t2 * dt, where "dt" is the derivative of the quantity "t". Applying this, we arrive at a working definition of y':

y' = 3((2x+5)8+4x)2(derivative of (2x+5)8+4x)

The derivative of (2x+5)8+4x is found using basic derivative definitions and the chain rule again:

8(2x+5)7(2)+4 = 16(2x+5)7+4

So now we can write y' again:

y'= 3((2x+5)8+4x)2(16(2x+5)7+4) = 48((2x+5)8+4x)2((2x+5)7+4)

This can be further simplified, but this is an arduous process. If you need further simplification, feel free to contact me via private message.

3x + 7y = 3*x + 7*y = 3*6 + 7*4 = 18 + 28 = 46

This not a circle, both the squared terms must have the same coefficients if it might be a circle. Different signs indicate a hyperbola.

No because the slope of the second equation is 1/4 and for it to be perpendicular to the first equation it should be 1/3

x3+3x2-22x-90 divided by x-5 equals x2+8x+18

For the answer to be correct then the quotient multiplied by the divisor must be equal to the dividend.

Hence:-

(x-5)*(x2+8x+18)

Multiplying out the brackets term by term:

x3-5x2+8x2-40x+18x-90

Collecting like terms in descending order:

x3+3x2-22x-90

So the answer is correct.

The period of a pendulum is give approximately by the formula

t = 2*pi*sqrt(l/g) where l is the length of the pendulum and g is the acceleration (not accerlation) due to gravity. Thus g is part of the formula for the period.

x = 2

set up your mathematical equation

x+3.2=5

Now solve for 'x'

x+3.2=5

-3.2 -3.2 ( minus 3.2 from both sides)

x=1.8

If: y+15 = 11

Then: y = -4

yes

The zeros of functions are the solutions of the functions when finding where a parabola intercepts the x-axis, hence the other names: roots and x-intercepts.

350x = 350*400 = 140000

so 350x - 70 = 139930

8x + x = 1 -8x + 3x = -3

Clean up

9x = 1

-5x = -3

x = 1/9

x = 3/5

Two different answers. If you were expected to solve them simultaneously, this would be an incompatible set, returning an answer of {Φ} ■

10

12/3 = 4

integration is necessary to make collective sense.

x+2*7x = 20 (I am assuming x+2 isn't in brackets or anything)

x+14x = 20

15x = 20

x = 20/15

x = 4/3 or 1.3333333 reccuring.

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Another answer:

This is a basic algebra problem. The aim is to get the variable (X) by itself, and a number on the other side of the equation.

(I will use a X for the variable, and an x for multiplication)

X + 2 x 7X = 20

X + 14X = 20 (multiply 2 by 7X)

15X = 20 (add 14X and X)

X = 20/15 (divide both sides by 15)

X = 4/3 (Simplify)

The value of X is 4/3 or 1 and 1/3 or 1.333 repeating.

There are several ways to do it - depending, in part, on the kind of equations. Sophisticated methods exist specifically for linear equations, among others.

However, for a start, you can combine equations (1) and (2), eliminating one variable; the same for equations (2) and (3), and for equations (3) and (4) (eliminating the same variable in every case). That leaves you with 3 equations with 3 variables.

Similarly, reduce the 3 equations in 3 variables, to 2 equations in 2 variables (eliminating the same variable in every case). Combine those into a single equation with 1 variable.

Example for eliminating a variable:

(Eq. 1) 5a + 3b - 3c + 8d = 28

(Eq. 2) 8a - 3b + 8c - 6d = 8

If you just add up the equations, you eliminate variable b. If you want to eliminate variable a, multiply the first equation by 8, and the second by (-5), then add the resulting equations.

(20x + 3)(1x + 1)

say it is 1 over 2 is equal to x over 4 you multiply 4 and 1 then 2 and x and you get 4=2x. Solve for x = 2. So the equivalent proportion is 2/4.

There are two solutions and they are: x = -1 and y = 3