The correct structure of the question is as follows:
The function f(x) = x^3 describes a cube's volume, f(x) in cubic inches, whose length, width, and height each measures x inches. If x is changing, find the (instantaneous) rate of change of the volume with respect to x at the moment when x = 3 inches.
Answer:
Step-by-step explanation:
Given that:
f(x) = x^3
Then;
V = x^3
The rate whereby V is changing with respect to time is can be determined by taking the differentiation of V
dV/dx = 3x^2
Now, at the moment when x = 3;
dV/dx = 3(3)^2
dV/dx = 3(9)
dV/dx = 27 cubic inch per inch
Suppose it is at the moment when x = 9
Then;
dV/dx = 3(9)^2
dV/dx = 3(81)
dV/dx = 243 cubic inch per inch
Answer:
Step-by-step explanation:
The given equation is in exponential form:
To find 
we need to write it in logarithmic form:
⇒ 
⇒ 
To prove this, we can substitute the value into the given equation
Therefore, the answer is
Answer:
<h2>(g-f)(10) = - 71</h2>
Step-by-step explanation:
f(x) = x² - 1
g(x) = 2x + 8
To find (g-f)(10) first find ( g - f)(x)
To find ( g - f)(x) subtract f(x) from g(x)
That's
( g - f)(x) = 2x + 8 - ( x² - 1)
Remove the bracket
( g - f)(x) = 2x + 8 - x² + 1
Simplify
( g - f)(x) = - x² + 2x + 9
To find (g-f)(10) substitute the value in the bracket that's 10 into ( g - f)(x)
That is
(g-f)(10) = -(10)² + 2(10) + 9
= - 100 + 20 + 9
= - 100 + 29
= - 71
Hope this helps you
Answer:
i)W = 2500 / T
ii) W = 500 Tons
iii) grad W(10°) = - 25î
iv) The formulation is not practical
Step-by-step explanation:
i) Write an equation describing the use of coal
As use of coal is inversely proportional to the average monthly temperature
if W is use of coal in tons/per month then
W(t) = k / T where k is a constant of proportionality and T is the average temperature in degrees. We have to determine k from given conditions
k = ?? we know that when T = 25° W = 100 tons the by subtitution
W = k/T 100 = k /25 k = 2500 Tons*degree
Then final equation is:
W = 2500 / T
ii) Find the amount of coal when T = 5 degrees
W = 2500 / 5
W = 500 Tons
iii)
The inverse proportionality implies that W will decrease as T increase.
The vector gradient of W function is:
grad W = DW(t)/dt î
grad W = - 2500/T² î
Wich agrees with the fact that W is decreasing.
And when T = 100°
grad W(10°) = - 2500/ 100 î ⇒ grad W(10°) = - 25î
iv) When T = 0 The quantity of coal tends to infinite and the previous formulation is not practical
Answer:
r=0
Step-by-step explanation:
7r-5r+8=9r+8-r
This is already an equation
Combine like terms
2r+8 = 8r+8
Subtract 2r from each side
2r-2r +8 = 8r-2r +8
8 =6r+8
Subtract 8 from each side
8-8 = 6r+8-8
0 = 6r
Divide by 6
0/6 = 6r/6
0 =r
