Answer:
Step-by-step explanation:
cotx/cscx=cosx
Start on the left side.
cos(x) csc(x)
Apply the reciprocal identity to csc (x) .
cos(x) 1/sin(x)
Simplify
cos(x) 1/sin(x)cos(x)/sin(x)
Rewrite cos(x)/sin(x) as cot(x) .
cot(x)
Because the two sides have been shown to be equivalent, the equation is an identity.
cos(x) csc(x)=cot(x) is an identity
cot(x)−tan(x)/sin(x)cos(x)=csc^2(x)−sec^2(x) is an identity
You are correct :)
Answer:
94.6
Step-by-step explanation:
100% of 44 = 44
⇒ 200% of 44 = 44 + 44 = 88
15% = 15/100 = 0.15
⇒ 15% of 44 = 0.15 x 44 = 6.6
Therefore, 215% of 44 = 88 + 6.6 = 94.6
Answer: the rate at which the distance between the boats is increasing is 68 mph
Step-by-step explanation:
The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.
Let x represent the length the shorter leg(south) of the right angle triangle.
Let y represent the length the longer leg(east) of the right angle triangle.
Let z represent the hypotenuse.
Applying Pythagoras theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156
z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
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Jk, I got you fam
12(t + 2) + 4 ≥ - 8
12t + 24 + 4 ≥ - 8
12t + 28 ≥ - 8
12t ≥ - 8 - 28
12t ≥ - 36
t ≥ - 36 ÷ 12
t ≥ - 3
Solution:
t ≥ -3
Answer:
Below
Step-by-step explanation:
Let's say that each square on the grid represents 1 cm
First find the area of the two triangles
For the larger one: A = bh/2
A = 3 x 3 / 2
= 4.5 cm^2
For the smaller one : A = bh/2
A = 2 x 2 / 2
= 2 cm^2
For the rectangle : A = lw
A = 4 x 5
= 20 cm^2
Add them all up to get the area
4.5 + 2 + 20 = 26.5 cm^2
Hope this helps!
