If 3cot^2x - 5cotx = -2, then cotx = _____.

1 answer:

7 0

3cot²x - 5cotx = -2

Lets pretend cotx = t

3t² - 5t = -2
3t² - 5t + 2 = 0

factor polynomial
(3t-2)(t-1) = 0

3t-2 = 0
t-1 = 0

then "t" which is also cotx is equal to 1 or 2/3

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Kimberly is ordering bath towels and washcloths for the inn where she works. The total cost of the order is T=6b+2w, where T is

Setler [38]

Answer:

Step-by-step explanation:

We are given the equation

a) T=6b+2w

T is the total cost

b is the no of bath towels

w is the no of washcloths

so the final equation becomes when T=85

6b+2w=85

b) given budget is $85

6b+2w $\leq$ 85

the maximum no of bath towels will be when wash clothes will be zero

6b + 2(0) $\leq$ 85

6b $\leq$ 85

b $\leq$ 85/6

b $\leq$ 14.16

that means the maximum no of baths towels we can buy is 14

similarly for the maximum no of wash clothes it will be when bath towels will be zero

6(0) + 2w $\leq$ 85

upon solving we get

w $\leq$ 42.5

That means we can buy at most 42 wash clothes.

c) when w = 20

6b + 2(20) $\leq$ 85

6b $\leq$ 45

b $\leq$ 7.5

That means we can buy 7 bath towels when 20 wash clothes are bought to stay in the budget.

Note: omitting the decimal values because a particular objects can't be bought in decimals.

7 0

3 years ago

Jane had a bottle filled with juice. At first she drank 1/5 of the juice in the bottle. After 1 hours she drank 1/4 of the juice

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X is the size of the bottle. So x/5 + (x/5)/4 + ((x/5)/4)/3 = 2/3 cups

x/5 + x/20 + x/60=2/3; (12x+3x+x)/60=2/3; 16x/60=2/3; (16x)3=(2)(60)
48x=120
x= $\frac{120}{48}$ = 2 $\frac{24}{48}$ = 2 $\frac{1}{2} }$

The bottle is 2 $\frac{1}{2}$ cups