1.9+n
2.10+6
3.2+10
4.17
5.3+3
6.-3+n
Answer:
z=28
Step-by-step explanation:
10z-10=9z+18
-9z -9z
z-10=18
+10 +10
z=28
Answer:
Time it will take to drain the entire tower = 2.8minutes
Step-by-step explanation:
The question is incomplete as the volume of the tower was not indicated.
Let's consider the following question:
If there are 7.48 gallons in a cubic foot, and the volume of the tower is around 36000in cubed. Residents of the apartment building are using the water from the tower at an average rate of 56 gallons per minute, determine how long it will take to drain the entire tower.
Solution:
Volume = 36000in³
Conversion of in³ to ft³
1 inch = 0.0833 feet
12 inch = 1 ft
1 ft³ = 1ft × 1ft × 1ft
= 12 in x 12 in x 12 in = 1728 in³
36000in³ × [(1ft³)/(1728 in³) = (36000/1728)ft³
= 20.833ft³
Volume = 20.833ft³
There are 7.48 gallons in a cubic foot
In 20.833ft³ = 20.833ft³× (7.48 gallons/1ft³)
= 20.833× 7.48gallons
Volume = 155.83 gallons
The rate of usage = 56 gallons per minute
The rate of usage for 155.83 gallons = 155.83 gallons × (1min/56gallons)
= (155.83/56)minute
= 2.8minutes
Time it will take to drain the entire tower = 2.8minutes
Answer: 5 km walking and 30 km by bus
Step-by-step explanation:
Yochanan walked from home to the bus stop at an average speed of 5 km / h. He immediately got on his school bus and traveled at an average speed of 60 km / h until he got to school. The total distance from his home to school is 35 km, and the entire trip took 1.5 hours. How many km did Yochanan cover by walking and how many did he cover by travelling on the bus?
walking - 5km/h bus - 60km/h
distance walking - d₁ distance bus - d₂
time walking - t₁ time bus - t₂
d₁ + d₂ = 35
t₁ + t₂ = 1.5
v = d/t
vwalking = d₁/t₁
5 = d₁/t₁ ⇒ d₁ = 5t₁
vbus = d₂/t₂
60 = d₂/t₂ ⇒ d₂ = 60t₂
d₁ + d₂ = 35 ⇒ 5t₁ + 60t₂ = 35
_________________________
5t₁ + 60t₂ = 35
t₁ + t₂ = 1.5 (*-5)
5t₁ + 60t₂ = 35
-5t₁ -5t₂ = -7.5 (+)
__________________________
55t₂ = 27.5
t₂ = 27.5/55 = 0.5 h
t₁ + t₂ = 1.5 ⇒ t₁ = 1.5 - 0.5 = 1h
d₁ = 5t₁ ⇒ d₁ = 5.1 = 5 km
d₂ = 60t₂ ⇒ d₂ = 30.0.5 = 30 km
<span>Length = 1200, width = 600
First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as:
W = (2400 - L)/2
And area is:
A = LW
Substitute the equation for width, giving:
A = LW
A = L(2400 - L)/2
And expand:
A = (2400L - L^2)/2
A = 1200L - (1/2)L^2
Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
A = 1200L - (1/2)L^2
A = 1200(1200+e) - (1/2)(1200+e)^2
A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
A = 720000 - (1/2)e^2
And notice that the only e terms is -(1/2)e^2. ANY non-zero value of e will cause this term to be non-zero and negative meaning that the total area will be reduced. Therefore the value of 1200 for the length is the best possible length that will get the maximum possible area.</span>
