Answer:
x= 35 gallons consumed by 1st car
and y= 40 gallons consumed by 2nd car
Step-by-step explanation:
Fuel efficiency of 1st car = 15 miles per gallon
Fuel efficiency of 2nd car = 35 miles per gallon
Let x= gallons consumed by 1st car
and y= gallons consumed by 2nd car
Total gallons consumed by both cars = 75
so, we can write
x + y = 75
Miles covered by both cars = 1925 miles
and we know, Fuel efficiency of 1st car = 15 miles per gallon
Fuel efficiency of 2nd car = 35 miles per gallon
we can write the equation as
15 x + 35 y = 1925
where x and y are gallons consumed by 1st and 2nd car.
We have two equation now,
x + y = 75 (1)
15 x + 35 y = 1925 (2)
Multiplying eq(1) with 15 and subtracting eq (1) and 2
15 x + 15 y = 1125
15 x + 35 y = 1925
- - -
_______________
0 - 20 y = -800
y= -800 / -20
y = 40
Putting value of y in equation 1
x + y = 75
x + 40 = 75
x= 75 - 40
x = 35
x= 35 gallons consumed by 1st car
and y= 40 gallons consumed by 2nd car
<span><span><span>1. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Find the equations of the altitudes of the triangle with vertices (4, 5),(-4, 1) and (2, -5). Do this by solving a system of two of two of the altitude equations and showing that the intersection point also belongs to the third line. </span>
(Scroll Down for Answer!)</span><span>Answer by </span>jim_thompson5910(34047) (Show Source):You can put this solution on YOUR website!
<span>If we plot the points and connect them, we get this triangle:
Let point
A=(xA,yA)
B=(xB,yB)
C=(xC,yC)
-------------------------------
Let's find the equation of the segment AB
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through AB is
-------------------------------
Let's find the equation of the segment BC
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through BC is
-------------------------------
Let's find the equation of the segment CA
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through CA is
So we have these equations of the lines that make up the triangle
So to find the equation of the line that is perpendicular to that goes through the point C(2,-5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex C is
Now to find the equation of the line that is perpendicular to that goes through the point A(4,5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex A is
Now to find the equation of the line that is perpendicular to that goes through the point B(-4,1), simply negate and invert the slope to get
Now plug the slope and the point (-4,1) into
Solve for y and simplify
So the altitude for vertex B is
------------------------------------------------------------
Now let's solve the system
Plug in into the first equation
Add 2x to both sides and subtract 2 from both sides
Divide both sides by 3 to isolate x
Now plug this into
So the orthocenter is (-2/3,1/3)
So if we plug in into the third equation , we get
So the orthocenter lies on the third altitude
</span><span>
</span></span>
Answer:
<h2>x = 1, y = 3 → (1, 3)</h2>
Step-by-step explanation:
<span>Equivalent ratios are ratios that name the same comparison. Meanwhile, equivalent fractions </span><span>are fractions that name the same amount or part. Equivalent ratios and equivalent fractions are similar in that the two quantities refer to ratios and fractions that ultimately have the same value but are expressed in a different way. For example, 48/64 is equivalent to 72/96, both have the value of 3/4. </span>
Answer:
3π square units.
Step-by-step explanation:
We can use the disk method.
Since we are revolving around AB, we have a vertical axis of revolution.
So, our representative rectangle will be horizontal.
R₁ is bounded by y = 9x.
So, x = y/9.
Our radius since our axis is AB will be 1 - x or 1 - y/9.
And we are integrating from y = 0 to y = 9.
By the disk method (for a vertical axis of revolution):
![\displaystyle V=\pi \int_a^b [R(y)]^2\, dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%20%5Cint_a%5Eb%20%5BR%28y%29%5D%5E2%5C%2C%20dy)
So:
Simplify:
Integrate:
![\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5CBig%5By-%5Cfrac%7B1%7D%7B9%7Dy%5E2%2B%5Cfrac%7B1%7D%7B243%7Dy%5E3%5CBig%7C_0%5E9%5CBig%5D)
Evaluate (I ignored the 0):
![\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cpi%5B9-%5Cfrac%7B1%7D%7B9%7D%289%29%5E2%2B%5Cfrac%7B1%7D%7B243%7D%289%5E3%29%5D%3D3%5Cpi)
The volume of the solid is 3π square units.
Note:
You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:
We acquire the exact same answer.
