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forsale [732]
3 years ago
10

Double vision can be the result of _________________.

Mathematics
1 answer:
Tasya [4]3 years ago
3 0
The answer is eye muscles relaxed from fatigue, drugs, or alcohol. Double vision is usually related with alcohol and other drugs. This is often triggered by alcohol intoxication, benzodiazepines, opioids, or certain types of drugs for seizures and epilepsy. Head injuries, like concussions, can also cause double vision. 
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1-cot^2a+cot^4a=sin^2a(1+cot^6a) prove it.​
aliina [53]

Step-by-step explanation:

We have

1-cot²a + cot⁴a = sin²a(1+cot⁶a)

First, we can take a look at the right side. It expands to sin²a + cot⁶(a)sin²(a) = sin²a + cos⁶a/sin⁴a (this is the expanded right side) as cot(a) = cos(a)/sin(a), so cos⁶a = cos⁶a/sin⁶a. Therefore, it might be helpful to put everything in terms of sine and cosine to solve this.

We know 1 = sin²a+cos²a and cot(a) = cos(a)/sin(a), so we have

1-cot²a + cot⁴a = sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

Next, we know that in the expanded right side, we have sin²a + something. We can use that to isolate the sin²a. The rest of the expanded right side has a denominator of sin⁴a, so we can make everything else have that denominator.

sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a

= sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

We can then factor cos²a out of the numerator

sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a

= sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

Then, in the expanded right side, we can notice that the fraction has a numerator with only cos in it. We can therefore write sin⁴a in terms of cos (we don't want to write the sin²a term in terms of cos because it can easily add with cos²a to become 1, so we can hold that off for later) , so

sin²a = (1-cos²a)

sin⁴a = (1-cos²a)² = cos⁴a - 2cos²a + 1

sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-2cos²a+1-sin²a+cos²a)/sin⁴a

= sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

factor our the -cos²a-sin²a as -1(cos²a+sin²a) = -1(1) = -1

sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a

=  sin²a + cos²a (cos⁴a-1 + 1)/sin⁴a

= sin²a + cos⁶a/sin⁴a

= sin²a(1+cos⁶a/sin⁶a)

= sin²a(1+cot⁶a)

8 0
2 years ago
Haj mixes gallon of water with every 1 cup of a laundry powder. How many gallons of water does he mix with 7 cups of laundry pow
Sergeu [11.5K]
Between 6 and 7

1 cup per 1 gallon 
 1x7 gallons is 7
7 0
3 years ago
Read 2 more answers
A store sells black ink pens for $5 and red ink pens for $4. John wishes to buy 20 pens but doesn’t wish to spend more than $92.
Zina [86]

Answer:  4r + 5(20-r) \le 92

=======================================

Explanation:

r = number of red pens

4r = cost of buying r red pens

example: if r = 10, then 4r = 4*10 = 40 is the total cost of buying 10 red pens

If John buys r red pens, then he must buy 20-r black pens so that r and 20-r add to 20.

John buys 20-r black pens, and at $5 each, so it will cost 5(20-r) dollars for just the black pens alone.

In total, John spends 4r + 5(20-r) dollars for all the pens (red & black)

We want $92 be the most he spends. This is the ceiling or highest value possible.

Therefore,

4r + 5(20-r) \le 92

--------------------

Extra info:

If you want to solve for r, then

4r + 5(20-r) \le 92

4r + 5(20)+5(-r) \le 92 distribute

4r + 100 - 5r \le 92  

100 - r \le 92

100-r+r \le 92+r add r to both sides

100 \le 92+r

100-92 \le 92+r-92 subtract 92 from both sides

8 \le r

r \ge 8

So John must buy at least 8 red pens. The most he can buy is 20 red pens since he wants 20 pens total.

8 0
2 years ago
It about math and I not good at it so I need help and it about adding division subtract multiplication word problems
ikadub [295]

Ok I can help but what am I supposed to do?

8 0
2 years ago
Read 2 more answers
Simplify -2x3 yx xy2
NeTakaya

Answer:

Umm can you please rewrite that

Step-by-step explanation:

its not really anything to simplfy

6 0
3 years ago
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