You would first do 2 multiplied by 2x and that would give you 4x, then you would do 2 multiplied by 3y which would give you 6y, you would put 4x under 2x and put 6y under 3y and bring down your addition symbol
<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
9514 1404 393
Answer:
3
Step-by-step explanation:
The gradient is the ratio of "rise" to "run". Here, it appears the line crosses the y-axis at y = -1. It appears that it also crosses the grid intersection at (1, 2). This represents a "rise" (change in y) of (2 -(-1)) = 3, for a "run" (change in x) of (1 -0) = 1. Then the gradient is ...
m = rise/run = 3/1 = 3
The gradient of the graph is 3.
Answer:
a) f(x) tends to minus infinity
b) (0,768) is the y-intercept, (4,0) and (-3,0) are the x-intercepts.
Step-by-step explanation:
Our function is 
a polynomial of degree 4.
a) The monomial with highest degree determines the behavior of f(x) when x tends to infinity and when x tends to -infinity. This monomial is -4x⁴. Without expanding completely, (x-4)³ has x³ as a summand, which multiplies with -4x from the first factor, to give -4x⁴. When x goes to infinity (or minus infinitive), x²=(x²)² is positive (nonzero squares are always positive) thus -4x² is negative, and f(x) tends to minus infinity.
b). To find the y-intercept, we compute (0,f(0)). Since f(0)=-4(3)(-4)³=768, then (0,768) is the point of the y-intercept.
For the x-intercept, solve f(x)=0. f(x)=0 has the solutions x=-3 and x=4. In this case, the x-intercept is in both x=0 and x=4. Then (-3,0) and (4,0) are x-intercepts.
