Let y be the temperature
Let m be the rate of temperature drop in degrees per hour
Let x be the number of hours elapsed since 8PM
The initial temperature (at x = 0) is 0
y = mx
Four hours from 8 PM, the temperature was -16.8 degrees
-16.8 = m(4)
m = -4.2 degrees per hour
At 9PM, one hour will have elapsed.
y = -4.2(1)
y = -4.2 degrees
The result can be shown in both exact and decimal forms.Exact Form:<span><span>−<span>14</span></span><span>-<span>14</span></span></span>Decimal Form:<span>−<span>0.25
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(2x)^4 = 16x^4 is the continued product
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
Y = 1/2x - 3. Slope here is 1/2. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So the perpendicular line will have a slope of -2.
y = mx + b
slope(m) = -2
(1,-1)...x = 1 and y = -1
now we sub and find b, the y int
-1 = -2(1) + b
-1 = -2 + b
-1 + 2 = b
1 = b
so ur perpendicular equation is : y = -2x + 1