Answer:
<h2>a.) reflect across x-axis</h2>
Step-by-step explanation:
The transformation described is about multiplying the vertical value by -1:
That means all vertical coordinates will change to the opposite side, but all horizontal coordinates will maintain at the same coordinate.
As a result, we'll have a reflection across the x-axis, because the y coordinates were transformed.
Therefore, the right answer is A.
<h2>9.</h2><h3>Given</h3>
<h3>Find</h3>
- linear approximation to the volume when the radius increases 0.4 cm
<h3>Solution</h3>
The equation for volume of a sphere is
... V = (4/3)π·r³
Differentiating gives
... dV = 4π·r²·dr
Filling in the given numbers gives
... change in volume ≈ 4π·(15 cm)²·(0.4 cm)
... = 360π cm³ ≈ 1130.97 cm³ . . . . . . volume of layer 4mm thick
<h2>11.</h2><h3>Given</h3>
- an x by x by 2x cuboid with surface area 129.6 cm²
- rate of change of x is 0.01 cm/s
<h3>Find</h3>
<h3>Solution</h3>
The area is that of two cubes of dimension x joined together. The area of each such cube is 6x², but the two joined faces don't count in the external surface area. Thus the area of the cuboid is 10x².
The volume of the cuboid is that of two cubes joined, so is 2x³. Then the rate of change of volume is
... dV/dt = (d/dt)(2x³) = 6x²·dx/dt
We know x² = A/10, where A is the area of the cuboid, so the rate of change of volume is ...
... dV/dt = (6/10)A·dx/dt = 0.6·(129.6 cm²)(0.01 cm/s)
... dV/dt = 0.7776 cm³/s
Caution: you need to use the same units of measurement throughout. If the spring stretches by 21 cm when a 135 newton object is attached, then you must ask for the mass (in newtons) of a fish that would stretch the spring by 62.1 cm.
We will need to assume that the spring is not stretched at all if and when no object is attached to the spring.
Write the ratio
21.0 cm 135 newtons
------------- = --------------------
62.1 cm x
Solve this for x. This x value represents the mass of a fish that would stretch the spring by 62.1 cm. You can cancel "cm" in the equation above:
21.0 135 newtons
------ = --------------------
62.1 x
Then 21.0x = (62.1)(135 newtons). Divide both sides of this equation by 21.0 to solve it for x.
The answer to the question
