10 classrooms
With 2 left over.
It's a simple question, make sure that you know that the key is 32/3, and because it's not fully divisible use the whole number (10)
Supplementary angles add up to 180 degrees, so look for two angles by each other that add up to 180 degrees.
Hope this Helps!
Answer:
H. the number of orchestra seat is 900
Step-by-step explanation:
Step one:
let the number of orchestra seat be x
and balcony seat be y
cost of orchestra= $50 each
cost of balcony =$40 each
total tickets= 1500
x+y= 1500----------1
amount earned= $69000
50x+40y=69000--------2
The system of equation for the situation is
x+y= 1500----------1
50x+40y=69000--------2
from 1, x=1500-y
put this in equation 2
50(1500-y)+40y=69000
75000-50y+40y=69000
-10y=69000-75000
-10y=-6000
divide both sides by -10
y=-6000/-10
y=600
put y= 600 in equation 1
x+600= 1500
x=1500-600
x=900
<h2>9.</h2><h3>Given</h3>
<h3>Find</h3>
- linear approximation to the volume when the radius increases 0.4 cm
<h3>Solution</h3>
The equation for volume of a sphere is
... V = (4/3)π·r³
Differentiating gives
... dV = 4π·r²·dr
Filling in the given numbers gives
... change in volume ≈ 4π·(15 cm)²·(0.4 cm)
... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick
<h2>11.</h2><h3>Given</h3>
- an x by x by 2x cuboid with surface area 129.6 cm²
- rate of change of x is 0.01 cm/s
<h3>Find</h3>
<h3>Solution</h3>
The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².
The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is
... dV/dt = (d/dt)(2x³) = 6x²·dx/dt
We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...
... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)
... dV/dt = 0.7776 cm³/s
Answer: B. 8 x 10^3
Step-by-step explanation:
