Answer:
B. 6 1/4
Step-by-step explanation:
The computation of the more flour Nicholas needed for making the cake and cookies is shown below:
= 11.75 - 5.50
= 6.25 more cups of flour
Therefore to make the cookies and cakes, 6.25 more cups of flour is required or needed and the same is to be considered
hence, the correct option is B. 6 1/4
Answer: C. 17.5 feet
Step-by-step explanation:
The attached photo shows the triangle ABC formed by the ladder and the wall. It is a right angle triangle because one of its angles is 90 degrees. The ladder is the hypotenuse of the triangle. To determine the height of the wall, we would find BC by applying Pythagoras theorem
Hypotenuse^2 = opposite ^2 + adjacent^2
18^2 + 4.5^2 + BC^2
BC^2 = 324 - 20.25 = 303.75
BC = √303.75 = 17.5 feet.
Answer:
-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
Step-by-step explanation:
Let
x= distance between the wall and ladder
Ф = angle between the ladder and ground
The rate of change is: dx/dt = 0.8 ft/s
We need to find dФ/dt when x = 8 ft/s
From the triangle in the figure we see that:
cos Ф = x/10
=> x = 10 cosФ
Now, the rate of change will be
d(x)/dt = d/dt (10cosФ)
dx/dt = -10 sin Ф dФ/dt
dx/dt = 0.8 (given)
to find dФ/dt
we need to find sin Ф when x = 8
By Pythagoras theorem
(hypotenuse)^2 = (Perpendicular)^2+(base)^2
(10)^2 = (8)^2+ (Perpendicular)^2
100 = 64 + (Perpendicular)^2
=> (Perpendicular)^2 = 100-64
(Perpendicular)^2 = 36
Perpendicular = 6
sin Ф = Perpendicular/hypotenuse
sin Ф = 6/10 = 3/5
Putting values in:
dx/dt = -10 sin Ф dФ/dt
0.8 = -10(3/5) dФ/dt
0.8 = -6 dФ/dt
=> dФ/dt = 0.8 / -6
dФ/dt = - 0.133 radians/s
So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
