Answer:
The radius of the scoop is r = 3.1 cm
Step-by-step explanation:
Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.
3 gallons = 3 × 3785 cm³ = 11355 cm³
So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.
Since 90 scoops = 11355 cm³, then
1 scoop = 11355 cm³/90 = 126.2 cm³
Now, if each scoop is a sphere, the volume is given by V = 4πr³/3 where r is the radius of the scoop. Since we need to find the radius of the scoop, r, making r subject of the formula, we have
r = ∛(3V/4π)
Substituting V = 126.2 cm³, we have
r = ∛(3× 126.2 cm³/4π)
= ∛(378.6 cm³/12.57)
= ∛30.13 cm³
= 3.1 cm
So, the radius of the scoop is r = 3.1 cm
Answer:
what form?
Step-by-step explanation:
The question is missing the figure. So, it is in the atachment.
Answer: MN = x
LN = 
Step-by-step explanation: The first figure in the attachment is the figure of the question. The second figure is a way to respond this question by tracing the altitude from M to LN as suggested. When an altitude is drawn, it forms a 90° angle with the base, as shown in the drawing. To determine the other angle, you have to remember that all internal angles of a triangle sums up to 180°.
For the triangle <u>on the left</u> of the altitude:
45+90+angle=180
angle = 45
For the triangle <u>on the right</u>:
30+90+angle=180
angle = 60
With the angles, use the Law of Sines, which is relates sides and angles, as follows:

For MN:

MN = 
MN = x
For LN:

LN = 
We can determine sin (105) as:
sin(105) = sin(45+60)
sin(105) = sin(45)cos(60) + cos(45)sin(60)
sin(105) = 
sin(105) = 
LN = 
LN = 
LN = 
The expressions for:
MN = x
LN = 