Answer:
The Hotel charge without tax in first city is $3500 and The hotel charge before tax in the second city is 2000
Step-by-step explanation:
Let x be the hotel charge without tax in first city
We are given that The hotel charge before tax in the second city was $1500 lower than in the first.
So, Hotel charge without tax in second city =x-1500
Tax% in first city = 10%
So, tax in first city = 0.1x
Tax% in second city =5%
So, tax in second city = 0.05(x-1500)
We are given that The total hotel tax paid for the two cities was $600.
So,0.1x+0.05(x-1500)=600
0.1x+0.05x+75=600
0.15x=600-75
x=3500
Hotel charge without tax in first city = $3500
The hotel charge before tax in the second city =x-1500=3500-1500=2000
Hence The Hotel charge without tax in first city is $3500 and The hotel charge before tax in the second city is 2000
Answer: The correct option is fourth, i.e., 1935 cm³.
Explanation:
It is given that the vase is 30 cm tall and the hexagon base has an area of 64.5 cm².
The area of a hexagon base is,
Where, a is the side length.
The volume of the a hexagon glass is,
Where, A is area of base of hexagon and h is height of the hexagon glass.
Therefore the volume of the glass is 1935 cm³ and the glass can hold 1935 cm³ water. So, fourth option is correct.
Answer:175
Step-by-step explanation:70/40=1.75
1.75x100=175
x*y' + y = 8x
y' + y/x = 8 .... divide everything by x
dy/dx + y/x = 8
dy/dx + (1/x)*y = 8
We have something in the form
y' + P(x)*y = Q(x)
which is a first order ODE
The integrating factor is
Multiply both sides by the integrating factor (x) and we get the following:
dy/dx + (1/x)*y = 8
x*dy/dx + x*(1/x)*y = x*8
x*dy/dx + y = 8x
y + x*dy/dx = 8x
Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).
Since (xy)' turns into y + x*dy/dx, and vice versa, this means
y + x*dy/dx = 8x turns into (xy)' = 8x
Integrating both sides with respect to x leads to
xy = 4x^2 + C
y = (4x^2 + C)/x
y = (4x^2)/x + C/x
y = 4x + Cx^(-1)
where C is a constant. In this case, C = -5 leads to a solution
y = 4x - 5x^(-1)
you can check this answer by deriving both sides with respect to x
dy/dx = 4 + 5x^(-2)
Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.