Answer:
Solution of the equations is (1, -2).
Step-by-step explanation:
Two linear equations given in the question are
y = -3x+1-------------(1)
and y = 2x-4 ------------(2)
To solve these equations by substitution method we will substitute the value of y from equation (1) to equation number (2).
-3x+1 = 2x-4
Now we add 3x on both the sides of the equation
3x-3x+1 = 3x+2x-4
1 = 5x-4
we will add 4 on both the sides
1+4 = 5x-4+4
5 = 5x
Then we divide the equation by 5
5/5 = 5x/5
x = 5/5 = 1
Now we solve the equation (1) for the value of y by putting x = 1
y = -3(1)+1 = -3+1 = (-2)
So the solution will be (1 -2).
Answer:
Ryan takes 6n+36m -42 seconds to reach the nth flag for the mth time.
Step-by-step explanation:
It takes Ryan to run from 1st to 6th flag in 30 seconds, so it takes him
30 * 6/3 = 36 seconds to make one complete round.
or it takes 6 seconds to run from one flat to the next.
To reach the nth flag (n=1,2,3,4,5, or 6)
Ryan takes 6(n-1) seconds.
To reach it the mth times, he needs to add 36(m-1) seconds.
So time it takes Ryan to reach the nth flag for the mth time takes
6(n-1) + 36(m-1)
= 6n - 6 + 36m - 36
= 6n+36m -42 seconds
The work done by the gas when the gas expands will be 878.89 ft-lb.
<h3>What is the work done for an isothermal process?</h3>
The Pressure is inversely proportional to the volume.
Let the initial pressure and initial volume be P₁ and V₁, and the final volume be V₂.
Then the work done by the gas will be
WD = P₁ V₁ ln (V₂ / V₁)
A quantity of the gas with an initial volume of 1 cubic foot and an initial pressure of 400 pounds per square foot.
The gas expands to a volume of 9 cubic feet.
Then the work done by the gas will be
WD = 400 x 1 x ln (9/1)
WD = 400 x 2.197
WD = 878.89 ft-lb
The work done by the gas when the gas expands will be 878.89 ft-lb.
More about the work done for the isothermal process link is given below.
brainly.com/question/4218306
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Answer:
The answer to your question is 684 ft²
Step-by-step explanation:
Data
Rectangle Triangle 1 Triangle 2
base = 20 ft base = 20 ft base = 18 ft
height = 18 ft height = 9 ft height = 8 ft
Process
1.- Calculate the area of the rectangle
Formula
Area = base x height
Substitution
Area = 20 x 18
Result
Area = 360 ft²
2.- Calculate the area of the triangle 1
Formula
Area = base x height / 2
Substitution
Area = 20 x 9 / 2
-Result
Area = 90 ft² x 2 = 180 ft²
3.- Calculate the area of the triangles 2
Substitution
Area = 18 x 8 / 2
Result
Area = 72 ft² x 2 = 144 ft²
4.- Calculate the area of the pyramid
Total area = 360 + 180 + 144
= 684 ft²
Answer:
f(x) = 2·3^x
Step-by-step explanation:
We have the general equation of exponential functions as
y= a*b^x
We are given that the point (0,2) is on the graph so
when x= 0, y= 2
If we substitute in the general equation we see that
2 = a*b^0, any number to the power 0 is 1
2 = a
We were also given that point (1, 6 ) is on the graph;
If we substitute in our new found equation we see that
y=2·b^x
6 = 2·b^1 , any number to the power 1 is itself and
divide both sides by 2
3 = b
f(x) = 2·3^x
