<h3>Given</h3>
- length, width, and height of a cuboid are x, x, and 2x, respectively
- the cuboid's surface area is 129.6 cm²
- dx/dt = 0.01 cm/s
<h3>Find</h3>
- dV/dt for the given conditions
<h3>Solution</h3>
The equation for surface area can be written
... A = 2(LW +H(L +W))
Substituting the given values gives an equation that we can solve for x
... 129.6 = 2(x·x +2x(x +x)) = 10x²
... x = √(129.6/10) = 3.6 . . . . . . . cm
The equation for volume can be written
... V = LWH
Substituting the given values gives an expression for volume in terms of x.
... V = x·x·2x = 2x³
Then the rate of change of volume is
... dV/dt = 6x²·dx/dt
... dV/dt = 6·(3.6 cm)²·(0.01 cm/s)
... dV/dt = 0.7776 cm³/s
Y = 7^3 + 1 is a constant value, all of the others include an x variable in the form of a linear function.
Answer:
25.4 miles
Step-by-step explanation:
added them all up
but if i just wants miles than tha answer is 25
Answer:
Step-by-step explanation:
We are given:
And we want to solve this via completing the square.
First, we will subtract 3 from both sides. This yields:
Next, we will factor out the leading coefficient from the left.
In this case, the leading coefficient is simply 1 so we can leave it as is.
Next, we want to add a constant that is half of the b coefficient squared.
In this case, b = -5.
Half of that is -5/2.
Squaring yields 25/4.
So, we will add 25/4 to both sides. Since our leading coefficient is 1, we don't need to multiply by anything when we add it on the right. Hence:
The left side constitutes a perfect square trinomial as shown:
Factor and subtract:
Taking the square root of both sides gives:
Hence:
Approximate: