Answer:
dy/dx = -1/√(1 - x²)
For 0 < y < π
Step-by-step explanation:
Given the function cos y = x
-siny dy = dx
-siny dy/dx = 1
dy/dx = -1/siny (equation 1)
But cos²y + sin²y = 1
=> sin²y = 1 - cos²y
=> siny = √(1 - cos²y) (equation 2)
Again, we know that
cosy = x
=> cos²y = x² (equation 3)
Using (equation 3) in (equation 2), we have
siny = √(1 - x²) (equation 4)
Finally, using (equation 4) in (equation 1), we have
dy/dx = -1/√(1 - x²)
The largest interval is when
√(1 - x²) = 0
=> 1 - x² = 0
=> x² = 1
=> x = ±1
So, the interval is
-1 < x < 1
arccos(1) < y < arxcos(-1)
= 0 < y < π
Answer:
5/y-5
Step-by-step explanation:
y/5+1/y^2/25-1=1/y/5-1
Answer:
Step-by-step explanation:
Small order of fries at Wendy’s = x calories
Small order of fries at McDonald’s = y calories
<u>Substitute x in the second equation</u>
- y + 90 + y = 550
- 2y = 550 - 90
- 2y = 460
- y = 230
<u>Then, x is:</u>
- x = 230 + 90 = 320 calories
The custodian will be able to repaint 4 6/7 bookcases with 1 4/7 gallons of paint because you have to divide the fractions 1 4/7 and 1/3. 1 4/7 divided by 1/3. You’d turn 1 4/7 into a mixed fraction, change the division sign to a multiplication sign, and flip 1/3. Now the equation is 11/7 • 3/1. Multiply 11 and 3 which equals 33 then multiply 7 and 1 which equals 7. The fraction you get should be 33/7 and then you simplify it and it becomes 4 6/7 which is the answer.
Answer:
Answer is given below under explanation
Step-by-step explanation:
We are told that the domain is a set of real numbers. Let's depict by a & b.
We will use the following symbols;
∀ means for all
Ǝ there exists
∧ means logical conjuction
Thus;
A) Ǝ a,b : ( a/b < 1, b/a < 1 )
B) ∀ a : ( a > 0 = 1/a > 0 )
C) Ǝ a,b : (a + b = ab)
D) ∀ a,b : [ ( a > 0 ) ∧ ( b > 0 ) = (( a/b > 0 ) ∧ ( b/a > 0 ))]
E) ∀ b : [( b > 0 ) ∧ ( b < 1) = ( 1/b > 1 )]
F) n ( ( Ǝ x ∀ b ( a < b ) )
