The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of
1 answer:
Answer:
It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.
Step-by-step explanation:
The filling time of a gas tank can be given by a first order function in this format:
In which is the current amount of fuel in the tank(in L),
is the volume of the tank(in L),
is the discharge rate of the tank(in L/s) and t is the time in seconds.
Finding the values of the parameters:
The tank is completly empty, so .
The volume of the tank is 14 gallons. However, the problem states that the volume of the tank is measured in liters.
Each gallon has 3.78L.
So
The discharge rate for the gas is 38.0 l/min. However, the problem states that the discharge rate is in L/s. So, to find the value of r, we solve the following rule of three.
38 L - 60s
r L - 1s
Solving the equation:
It is going 84.12s = 1 minute and 24.12 seconds to fill the tank.
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Answer:
Option A is correct.
The system of equation is inconsistent is;
2x+8y=6
5x+20y=2
Explanation:
* A system of equations is called an inconsistent system, if there is no solution because the lines are parallel.
* If a system has at least one solution, it is said to be consistent .
*A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.
(A)
2x+8y=6
5x+20y=2
This is inconsistent, because as shown below in the graph of figure 1 that the lines do not intersect, so the graphs are parallel and there is no solution.
(B)
5x+4y=-14
3x+6y=6
this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 2 and also it is independent.
(C)
x+2y=3
4x+6y=5
this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 3.
(D)
3x-2y=2
6x-4y=4
this is a consistent system and has an infinite number of solutions, it is dependent because both equations represent the same line. as shown below in the graph of Figure-4.
Therefore, the only Option A system of equation is inconsistent.
Answer:
<em><u>Expression (19m-28) is equivalent to -4(7 - 2m) + 11m.</u></em>
Answer:
<em>96π units²</em>
Step-by-step explanation:
Find the diagram attached
Area of a sector is expressed as;
Area of a sector = θ/2π * πr²
Given
θ = 3π/4
r = 16
Substitute into the formula
area of the sector = (3π/4)/2π * π(16)²
area of the sector = 3π/8π * 256π
area of the sector = 3/8 * 256π
area of the sector = 3 * 32π
<em>area of the sector =96π units²</em>
Note necessary facts about isosceles triangle ABC:
- The median CD drawn to the base AB is also an altitude to tha base in isosceles triangle (CD⊥AB). This gives you that triangles ACD and BCD are congruent right triangles with hypotenuses AC and BC, respectively.
- The legs AB and BC of isosceles triangle ABC are congruent, AC=BC.
- Angles at the base AB are congruent, m∠A=m∠B=30°.
1. Consider right triangle ACD. The adjacent angle to the leg AD is 30°, so the hypotenuse AC is twice the opposite leg CD to the angle A.
AC=2CD.
2. Consider right triangle BCD. The adjacent angle to the leg BD is 30°, so the hypotenuse BC is twice the opposite leg CD to the angle B.
BC=2CD.
3. Find the perimeters of triangles ACD, BCD and ABC:
4. If sum of the perimeters of △ACD and △BCD is 20 cm more than the perimeter of △ABC, then
5. Since AC=BC=2CD, then the legs AC and BC of isosceles triangles have length 20 cm.
Answer: 20 cm.