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3 years ago

In the notation "s(x) = ...," what does "s(x)" represent?

Mathematics

2 answers:

Neporo4naja [7]3 years ago

6 0

Option 3. The value of s (x) depends on the value of x, since s is a function of x

ser-zykov [4K]3 years ago

6 0

For this case, the first thing you should know is that in the given expression we have the following:
s: represents a function whose value we want to know.
x: represents a term (numerical value) that we must use to know the function s.
Therefore, s depends on x.
We have then:
The value of s (x) depends on the value of x, since s is a function of x.
Answer:
The value of s (x) depends on the value of x, since s is a function of x.

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2 years ago

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(4x2 – 4x – 7)(x + 3)
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2 years ago

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Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the ra

bearhunter [10]

Answer:

$\frac{dh}{dt}=-\frac{1}{2\pi}cm/min$

Step-by-step explanation:

From similar triangles, see diagram in attachment

$\frac{r}{4}=\frac{h}{16}$

We solve for $r$ to obtain,

$r=\frac{h}{4}$

The formula for calculating the volume of a cone is

$V=\frac{1}{3}\pi r^2h$

We substitute the value of $r=\frac{h}{4}$ to obtain,

$V=\frac{1}{3}\pi (\frac{h}{4})^2h$

This implies that,

$V=\frac{1}{48}\pi h^3$

We now differentiate both sides with respect to $t$ to get,

$\frac{dV}{dt}=\frac{\pi}{16}h^2 \frac{dh}{dt}$

We were given that water is drained out of the tank at a rate of $2cm^3/min$

This implies that $\frac{dV}{dt}=-2cm^3/min$ .

Since we want to determine the rate at which the depth of the water is changing at the instance when the water in the tank is 8cm deep, it means $h=8cm$ .