Answer:
Hence the distance between automobile and farmhouse is increase at rate of 33.541 mph.
Step-by-step explanation:
Given:
farmhouse distance from highway is 2 miles
An automobile traveling at 75 mph.
To Find:
Distance between automobile and farmhouse when automobile pass 4 miles way from intersection of highway.(rate miles per hr)
Solution:
The solution is required in rate ,(Refer the attachment)
so using derivative with respect to time
Consider Triangle ABC,
<em>AB=2 miles</em>
<em>x=BC=X km distance from highway intersection</em>
<em>y=AC= Distance between car and the farmhouse.</em>
Using Pythagoras Theorem we get ,
y^2=x^2+2^2
y^2=x^2+4
y=Sqrt of{(x^2+4)}
Differentiate w.r.t 't' we get
2y*(dy/dt)=2x*(dx/dt)
dy/dt=(x/y)*(dx/dt)
dy/dt=(x/Sqrt of{(x^2+4)})*(dx/dt)............(here x=4 miles)
dy/dt=(2/Sqrt(20))*(dx/dt)
here dx/dt is the rate of change of distance i.e. speed=75
dy/dt=(2/Sqrt(20))*(75)
=0.44721*75
=33.541 mph
Answer:
x = 3
Step-by-step explanation:
Taking this from the graph:
2x + 5 = 11
2x = 6
x = 3
For this, we use simultaneous equations. Let George's page be g, Charlie's be c and Bill's page be b.
First, <span>George's page contains twice as many type words as Bill's.
Thus, g = 2b.
</span><span>Second, Bill's page contains 50 fewer words than Charlie's page.
Thus, b = c - 50.
</span>If each person can type 60 words per minute, after one minute (i.e. when 60 more words have been typed) <span>the difference between twice the number of words on bills page and the number of words on Charlie's page is 210.
We can express that as 2b - c = 210.
Now we need to find b, since it represents Bill's page.
We can substitute b for (c - 50) since b = c - 50, into the equation 2b - c = 210. This makes it 2(c - 50) - c = 210.
We can expand this to 2c - 100 - c = 210.
We can simplify this to c - 100 = 210.
Add 100 to both sides.
c - 100 + 100 = 210 + 100
Then simplify: c = 210 + 100 = 310.
Now that we know c, we can use the first equation to find b.
b = c - 50 = 310 - 50 = 260.
260 is your answer. I don't know where George comes into it. Maybe it's a red herring!</span>
A. Exactly one quadrilateral exists