The first equation I started with was:

x - 2/3*x = 1/3*x

I then used this equation to solve for the amount of engine oil Eddie had left after selling 4/9 of the remainder and an...

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I know that I need to use the information that there were 288 more red than blue cards at first and that there were 53 more blue cards than red cards left after John used 75% of the red cards and 1/3 of the blue cards. However, I am not sure how to set up an equation to represent this...

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In this case, I am trying to figure out how to solve the problem of John and Peter's erasers. I know that I need to use the information that John gave away 40% of his erasers and Peter gave away 1/7 of his, but I am not sure how to do that. I am also not...

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I have the following challenge.

Some pointers first:

For e.g. a sequence of whole numbers beginning with 1 and ending with 4, the sum will be 10. (1+2+3+4)

For a sequence from 1-6 the sum will be 21.

The sequence I want this formula to work on will always start with 1.

So a sequence that adheres to the above and contains 4 numbers (1,2,3,4) will have the sum of 10.

A sequence that adheres to the above and contains 6 numbers (1,2,3,4,5,6) will have the sum of 21.

What I am looking...

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Presently, I am engaged in conducting a financial assessment for a company. I have encountered a mathematical challenge that is proving to be quite perplexing. However, I am confident that there is a single solution for these equations.

I will try to be more specific: I want to know the revenue for various revenue categories (e.g. from projects, products, trade, etc.) by giving in a total number of available labor hours. Additionally, I give in the revenue distribution among the...

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From what I understand of finding a plane’s equation, you need three points which you will sub into the formula r⋅n = a⋅n.

r is (x,y,z)

n is the normal vector formed by the cross product of two lines originating from one common point.

a is the common point.

In this scenario there is only two - the tee/origin (0,0,0) and the hole (250, 25°, 2°) ≈ (226.44, 105.59, 8.73). How should I proceed?]]>

I am working with dV/dt = 3*pi*a^3 and dV/da = 2pi*a^2.

dh/dt = (3/2)a

I can see that the height at which it is filled is also the radius a, but I'm not sure how to use the volume given for the shaded part of the hemisphere. Maybe that I should replace h with a/2.....?

Thanks]]>

A 36 cm high cone with a base of radius 12cm is filled with water at a constant rate of 3 cm^3 /sec. What is the rate of change of height in cm/sec when the water in the cone has a depth of 9cm?

Any help would be greatly appreciated ]]>

I hope it's correct category, sorry if it's not.

Task for CNC machine to make parametric program, so with different panel sizes holes will follow same pattern.

Some simple trigonometry functions are allowed, like sin, cos but if possible it is better to avoid angles (altho not required).

Red lines are equal to each other.

Green lines are equal to each other.

Thanks in advance!]]>

2.) y^ -3 * dy/dx-5y^ -2=(-5/2) * x

3.) v=y^-2

4.) dv/dx=-2y^ -3 * dy/dx

Shouldn't y^-2 go to zero since there is no x in this expression?

Something I remember from implicit differentiation is that when we say "respect to" it means we are trying to find the relation of rate of change between variables dependent on each other.

Is that how I should see it here?]]>

For the function f(x)= x^2+9x simplify each expression as much as possible

1. [f(x+h)-f(x)]/h, h cannot equal 0

2. [f(w)-f(x)]/(w-z), x cannot equal w]]>

I am after some clarification on squaring negative values and the correct way to apply orders of operation...

I understand that [imath]-13 * -13 = 169[/imath] because multiplying a negative by a negative gives a positive value as the result.

However, I am confused about calculating [imath]-13^2[/imath], Logic tells me this should also be 169 as [imath]-13^2[/imath] seems to be the same as [imath]-13 * -13 = 169[/imath]. But if I think about the order of operations BODMAS or BIDMAS then I should calculate the...

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