# Tutor profile: John T.

## Questions

### Subject: Trigonometry

If a=5, b=8 and c=10 Find $$\cos A$$

Using the law of cosines, we have $$\cos A=\frac{b^2+c^2-a^2}{2bc}$$ Plug in the values $$\cos A=\frac{8^2+10^2-5^2}{2\times8\times10}=\frac{139}{160}=0.8688$$ Hence, $$\cos A=0.8688$$

### Subject: Calculus

Find the equation of the normal to the curve $$y=2x^2-3x+5$$ at the point (5,8)

Answer: We know that the slope of the tangent at any point (x,y) is given as $$m=y'$$ We will find the slope of tangent at (5,8) Here $$y'=4x-3$$ So the slope of tangent at (5,8) is $$m=4\times5-3=20-3=17$$ But the slope of normal is $$m_n=-\frac{1}{m}=-\frac{1}{17}$$ And using the point slope form, we have equation of normal as $$y-k=m_n(x-h)$$ where (h,k) is the point. Here h=5 and k=8 for the point (5,8) So the equation of normal is $$y-8=-\frac{1}{17}(x-5)$$ Simplify $$y=-\frac{1}{17}x+\frac{141}{17}$$ Hence, the required equation of the normal is $$y=-\frac{1}{17}x+\frac{141}{17}$$

### Subject: Algebra

What would be the remainder when $$f(x)=3x^3-2x^2+5x-2$$ is divided by $$(x-3)$$

Remainder theorem states that when a polynomial f(x) is divided by $$(x-a)$$, the remainder is equal to $$f(a)$$. According to the remainder theorem, Remainder$$=f(3)=3\times3^3-2\times3^2+5\times3-2\\=81-18+15-2\\=76$$ Hence, the remainder is 76

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