The arc length (s) is given in terms of the radius (r) and central angle (θ) by
s = r*θ . . . . . . . where θ is in radians
For your arc, the length is
s = (15 ft)*(π/4) ≈ 11.78 ft
_____
45° can be converted to radians by multiplying by π/180°.
45° * (π/180°) = π*(45/180) = π/4 . . . . radians
Answer:
Rectangular area as a function of x : A(x) = 200*x + 2*x²
A(max) = 5000 m²
Dimensions:
x = 50 m
l = 100 m
Step-by-step explanation:
"x" is the length of the perpendicular side to the wall of the rectangular area to be fenced, and we call "l" the other side (parallel to the wall of the barn) then:
A(r) = x* l and the perimeter of the rectangular shape is
P = 2*x + 2*l but we won´t use any fencing material along the wll of the barn therefore
P = 2*x + l ⇒ 200 = 2*x + l ⇒ l = 200 - 2*x (1)
And the rectangular area as a function of x is:
A(x) = x * ( 200 - 2*x) ⇒ A(x) = 200*x + 2*x²
Taking derivatives on both sides of the equation we get:
A´(x) = 200 - 4*x ⇒ A´= 0
Then 200 - 4*x = 0 ⇒ 4*x = 200 ⇒ x = 50 m
We find the l value, plugging the value of x in equation (1)
l = 200 - 2*x ⇒ l = 200 - 2*50 ⇒ l = 100 m
A(max) = 100*50
A(max) = 5000 m²
hope this help Answer:( x - 3i√2)(x + 3i√2)
solve x² + 18 = 0
x² = - 18 ⇒ x = ±√- 18 = ±3i√2
factors are ( x - (3i√2))(x - (-3i√2))
x² + 18 = (x - 3i√2)(x + 3i√2
Step-by-step explanation:
Answer:
<h2>The specific heat of the metal is 0.274951 calories/gram-degree C.</h2>
Step-by-step explanation:
Let, the specific heat of the container is x calories/gram-degree C.
The container and water gains (18 - 15) = 3 degrees C.
Hence, the transfer of heat is 
.
The metal, which is dropped in the water, losses (164 - 18)= 144 degrees C.
Hence, the transfer of heat is 
.
As per the given conditions,
.
Answer:
The correct answer is €10.00
Step-by-step explanation:
50% of 40 is 20. 50% of 50 is 25, so what you do is just take 20 and multiply that by 0.5 or you can just take 40 and multiply that by 0.25.
I really hope this helps you out!
