Answer:
76 quarters and 83 dimes
Step-by-step explanation:
From the information given, you can write the following equations considering that a quarter represents $0.25 and a dime $0.10:
y=x+7 (1)
0.25x+0.10y=27.30 (2)
x is the number of quarters
y is the number of dimes
Now, you can replace (1) in (2):
0.25x+0.10(x+7)=27.30
0.25x+0.10x+0.7=27.30
0.35x=27.30-0.7
0.35x=26.6
x=26.6/0.35
x=76
Then, you can replace the value of x in (1) to find the value of y:
y=76+7
y=83
According to this, the answer is that there are 76 quarters and 83 dimes in the jar.
Answer:
12.57
Step-by-step explanation:
2
π
r
d=
2
r
Solving for C
C=
d
=
π
4
≈12.56637
Answer:
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Step-by-step explanation:
Volume of a right circular cone:
The volume of a right circular cone, with radius r and height h, is given by the following formula:

Implicit derivation:
To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So

Radius is 107 in. and the height is 151 in.
This means that 
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.
This means that 
At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
This is
. So




Positive, so increasing.
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Answer:
0.3125
Step-by-step explanation: