Escreva os numeros racionais na forma de fração: +6,8,-0,375,-0,02 e 0,07
2 answers:
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Answer:
Step-by-step explanation:
<u>Given Equation is:</u>
Adding 9 to both sides
=>
=>
Multiplying 2 to both sides
=> -3x = -18 * 2
=> -3x = -36
Dividing both sides by -3
=> x = 12
Answer:
It weighs 40 pounds on mars
Step-by-step explanation:
Direct proportion is the relationship between two variables when their ratio is equal to a constant value
- It can be expressed as y = k x, where y varies directly as x and k is constant of variation
- It can be expressed as
∵ The weight of an object on mars varies directly as the weight
of the object on earth
∴ w(m) = k × w(e)
∵ The weight of the object on earth is 75 pound
∴ w(e) = 75
∵ The weight of this object on mars is 25 pounds
∴ w(m) = 25
- Substitute them in the equation of variation
∵ 25 = k × 75
- Divide both sides by 75
∴ = k
∴ w(m) = × w(e)
∵ An object weighs 120 pounds on earth
∴ w(e) = 120
- Substitute it in the equation of variation
∴ w(m) = × 120
∴ w(m) = 40
∴ It weighs 40 pounds on mars
The rate of change of the depth of water in the tank when the tank is half
filled can be found using chain rule of differentiation.
When the tank is half filled, the depth of the water is changing at <u>1.213 × </u>
<u>10⁻² ft.³/hour</u>.
Reasons:
The given parameter are;
Height of the conical tank, h = 8 feet
Diameter of the conical tank, d = 10 feet
Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.
Required:
The rate at which the depth of the water in the tank is changing when the
tank is half full.
Solution:
The radius of the tank, r = d ÷ 2
∴ r = 10 ft. ÷ 2 = 5 ft.
Using similar triangles, we have;
The volume of the tank is therefore;
Therefore;
By chain rule of differentiation, we have;
Which gives;
When the tank is half filled, we have;
Solving gives;
h³ = 256
h = ∛256
Which gives;
When the tank is half filled, the depth of the water is changing at <u>1.213 × 10⁻² ft.³/hour</u>.
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