A rectangle has a perimeter of 28 units, an area of 48 square units, and sides that are either horizontal or vertical. If one ve
rtex is the point (−5, −7) and the origin is in the interior of the rectangle, find the vertex of the rectangle that is opposite (−5, −7).
1 answer:
Answer:
Opposite coordinate of (−5, −7) = (1,1)
Step-by-step explanation:
Let the sides of rectangle be a and b
Perimeter = 2 ( a+b ) = 28
a + b = 14
Area = ab = 48
The sides with sum 14 and product 48 is 8 and 6.
a = 8 and b = 6
Since origin is inside the circle, the side with 8 unit is parallel to y axis and side with 6 unit is parallel to x axis
Opposite coordinate of (−5, −7) = (−5+6, −7+8) =(1,1)
You might be interested in
Answer:
- <u>0.075 m/min</u>
Explanation:
You need to use derivatives which is an advanced concept used in calculus.
<u>1. Write the equation for the volume of the cone:</u>
<u />
<u>2. Find the relation between the radius and the height:</u>
- r = diameter/2 = 5m/2 = 2.5m
- h = 5.2m
- h/r =5.2 / 2.5 = 2.08
<u>3. Filling the tank:</u>
Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.
The ratio x/y is the same r/h
- x/y=r/h
- y = x . h / r
The volume of water inside the cone is:
<u>4. Find the derivative of the volume of water with respect to time:</u>
<u>5. Find x² when the volume of water is 8π m³:</u>
m²
<u>6. Solve for dx/dt:</u>
<u />
<u>7. Find dh/dt:</u>
From y/x = h/r = 2.08:
That is the rate at which the water level is rising when there is 8π m³ of water.