James works as a tutor and a lawn mower. both jobs require that he work at least three hours per week. since james attends school, he can only work 15 hours a week. if james is paid $20 per hour as a tutor and $10 per hour as a lawn mower, which of the following is true about the number of hours he can work as a tutor (t) and lawn mower (m)?
pls
a: james can maximize his earnings by working three hours as a tutor and 12 hours as a lawn mower.
b: the critical points (t, m) for this system of equations are (0, 0), (15, 0), and (0, 15).
c: james can maximize his earnings by working 12 hours as a tutor and three hours as a lawn mower.
d: it is possible for james to work eight hours as a tutor and eight hours as a lawn mower.

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Ответ:

normakite

19.04.2021

Mathematics

First, lets note that $tan(\theta)\cdot cos(\theta)=sin(\theta)$ . This leads us with the following problem:

$cos(\theta)-sin(\theta)=0$

Lets add sin on both sides, and we get:

$cos(\theta)=sin(\theta)$

Now if we divide with sin on both sides we get:

$\frac{cos(\theta)}{sin(\theta)}=1$

Now we can remember how cot is defined, it is (cos/sin). So we have:

$cot(\theta)=1$

Now take the inverse of cot and we get:
$\theta=cot^{-1}(1)=\pi\cdot n+ \frac{\pi}{4} , \quad n\in \mathbb{Z}$

In general we have $cot^{-1}(1)=\frac{\pi}{4}$ , the reason we have to add pi times n, is because it is a function that has multiple answers, see the picture:

How do you solve this? cosθ-tanθcosθ=0

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