Answer:
Part A
71°
Part B
The ladder is been used safely
Step-by-step explanation:
Part A
We solve the above question using Trigonometric function of Cosine
cos x = Adjacent/Hypotenuse
Adjacent = The distance between the house and the bottom of the ladder = 4 feet
Hypotenuse = Length of the ladder = 12 feet
x = Angle
Hence:
cos x = 4/12
cos x = 1/3
x = arc cos (1/3)
x = 70.528779366°
Approximately to the nearest degree
= 71°
Part B
According to the manufacturer, if the angle the ladder forms with the ground, x, is between 70° and 75°, then it meets safety standards. Is this ladder being used safely?
Angle x = 71°
Therefore, the ladder is been used safely
The third one
x,y —>-x,-y
Because 2,-1–>-2,1
B is the answer
hope it helped
Answer:
Minimum dimensions are r=3cm, h=9cm
Minimum Cost=$254.47
Step-by-step explanation:
Volume of a Cylinder=πr²h
Volume of the Open Top Cylinder=81π cm³.
Therefore:
πr²h=81π
The bottom costs $3 per cm² and the side costs $1 per cm².
Total Surface Area of the open top Cylinder= πr²+2πrh
Cost, C=3πr²+2πrh
As the Volume is fixed.
πr²h=81π
r²h=81
h=81/r²
Modifying C,


We differentiate C with respect to r
C'=
At the minimum cost, C'=0.
Next we solve C'=0 for r

6πr³-162π=0
6πr³=162π
r³=27
r=3
The dimensions of the cylinder at minimum cost are therefore:
r=3 cm
h=81/9=9cm
The minimum cost of the Cylinder
C=3πr²+2πrh
=(3XπX3²)+(2XπX3X9)
=$254.47
Answer:
(x+6) feet, 110sq ft
Step-by-step explanation:
Area = width * length = something * (x + 7)
Width = (x+6) as 6 and 7 add to 13 and times to 42.
To confirm expand (x+6)(x+7)=x^2+6x+7x+42=x^2+13x+42
(x+6) feet
4^2+13(4)+42=16+52+42=110 sqft