# Tutor profile: Steffan G.

## Questions

### Subject: Geometry

Find the Resultant Vector and Direction of a Force of 12 N acting on an angle of 45 degrees and a second Vector of 20 N acting on 360 degrees.

Since we know a force or line acting on both the x and y planes has 2 components, one on X and another on Y, we first split each vector into its two components, thus: Vector 1: $$ V1x:12 * Cos 45=6 $$ $$ V1y: 12 * Sin 45=6 $$ $$ V2x: 20 * Cos 360=20 $$ $$V2y: 20 * Sin 360=0 $$ We then create Fx and Fy by adding all corresponding X and Y components. $$ Fx : 6 + 20 = 26 $$ $$ Fy: 6 + 0 = 6 $$ Our Resultant is the Root of the sum of both Fx squared and Fy Squared; $$ R= \sqrt{26^{2} + 6^{2}} $$ So $$ R = 26.68 N $$ We have our Resultant, now all we're missing is the direction, which is in the Formula $$ \tan(\alpha) = \frac{Fy}{Fx} $$ Since were looking for an angle, we send inverse Tangent to the right side, and we have our angle; $$ \alpha = \tan^{-1} (\frac{6}{26}) $$ $$\alpha = 13^{o}$$

### Subject: Basic Chemistry

What is the percent composition of Barium Chromate?

We start off our solution by writing the correct chemical formula which is BaCr04, since the second ion is ending in "ate" we know it's a polyatomic ion and thus must look for it on the back of our periodic tables. Once we have have the formula and double check the charge is neutral, we start calculating the mass of each individual element with regards to the total mass of the compound. Our work starts like this: Calculate the Mass of the compound by adding all elements. Like this: Cr = 51.99 g per mol; Ba = 137.327 g per mol; 0 = 15.99 g per mol, This is multiplied by 4 since it's the only subscript giving a total of 63.96 g. If we add everything together we get 253.3207 g per mol of BaCr04. Then we divide each of the individual masses by the total and multiply by 100% Giving us each element in percentage. Ba: 137.327/253.3207 =54.21% Cr: 51.99/253.3207= 20.53% 0: 63.96/253.3207= 25.26% All our percentages must add to 100% or at the very least be between 99.97 and 100%

### Subject: Algebra

Write the following equation in slope intercept form $$3y + 4x = -18$$

First off we want to know what "slope-intercept form" means, thus we write the original SI Form which is Y= mx + b, where m is the slope and b is the y-intercept. Therefore we can clearly see the problem must be solved by leaving the y term alone. After clearly stating our objective and where we want to work our equation to, we move the 4x from left to right, changing its sign in the process and finally we leave the y alone by dividing the entire expression by 3. Giving us a final answer of: $$y = -(4/3)x - 6$$

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