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Blababa [14]
3 years ago
5

Find the diagonal of the rectangular solid

Mathematics
1 answer:
earnstyle [38]3 years ago
4 0
There are four (4) diagonals: 3 face diagonals and one space diagonal. We assume you are interested in the space diagonal.

The face diagonal of the 3×4 face has length
  d₃₄ = √((3 ft)² +(4 ft)²) = √(25 ft²) = 5 ft

Taking the 5 ft edge and the 5 ft face diagonal as sides of the triangle with the space diagonal as its hypotenuse, we find the length of the space diagonal to be
  d = √((5 ft)² +(5 ft)²)
  d = 5√2 ft

The space diagonal of the rectangular solid is 5√2 ft ≈ 7.07 ft.
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Problem 9
lapo4ka [179]

Answer:

3:36PM

Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at \frac{1}{4} capacity, we can use the equation:

\frac{1}{4} * 12 = \boxed{3}

This shows \frac{1}{4} of his tank's capacity (12) is equal to 3 gallons. This means he will stop for gas when 3 gallons are remaining.

Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}

This is a simple proportion, and now we know he uses 2.5 gallons of gas per hour.

Now we can how many hours of gas Leon has left.

He has 7 gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

\frac{7-3}{2.5} = 1.6

The 7-3 is because Leon doesn't stop when his tank is empty, he stops 3 gallons earlier. We are dividing by 2.5 because that is how much gas he uses per hour, meaning the result of this division (1.6) is how many hours he has left.

Now we can solve for what time Leon will stop to get gas.

12PM + 2 hours of driving + the remaining 1.6 hours = 3:36PM

(1.6 hours is equal to 1 hour and 36 minutes)

Therefore, Leon will stop for gas at 3:36PM

8 0
2 years ago
The tables below show the values of f (x) and g (x) for different values of x:
dimaraw [331]
<span>2(3)× = 3×+1 is equal when f(x) = g(x).
f(x) is equal to g(x) when x = 0.
Therefore, the solution to the equation </span><span>2(3)×=3×+1 is x = 0.</span>
4 0
3 years ago
Can someone help me with this problem, please?
Masja [62]

Answer:

Length = 2 ft

Width = 7/4 ft = 1.75 ft

Step-by-step explanation:

Length of room on blueprint = 1/8 *16 = 2 ft

Width of room on blueprint = 1/8 *14 = 7/4 ft = 1.75 ft

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3 years ago
Toby pulled weeds and earned $22.50 for three hours of work. How much will he earn tomorrow if he works for 2 hours?
postnew [5]
How many hours total?
8 0
3 years ago
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