Answer:
3/2
Step-by-step explanation:
The equation 3x-2y=4 can be written in the form of y=mx+c where m is the slope and c is the y intercept.
Therefore
2y=3x-4 and dividing both sides by 2 to have y at the LHS
y=3/2x-2
Therefore, 3/2 represents the gradient/slope
17/3 most likely it depends on what was needed
By "which is an identity" they just mean "which trigonometric equation is true?"
What you have to do is take one of these and sort it out to an identity you know is true, or...
*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5 cscx = 5/3
cosx = 4/5 secx = 5/4
tanx = 4/3 cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!
Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.
Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)
Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 + 3/4)².
By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
Answer:
Step-by-step explanation:
Let the rate of boat in still water be b and the speed of the current be c
- Speed downstream = b + c
- Speed upstream = b - c
<u>We got equations for time:</u>
- 108/(b - c) = 3 ⇒ b - c = 36
- 108/(b + c) = 2 ⇒ b + c = 54
<u>Add up the equations:</u>
- b - c + b + c = 36 + 54
- 2b = 90
- b = 45 km/h
<u>Then finding the values of c</u>
