Answer:
f(x) = 
Step-by-step explanation:
Let the equation of the give cubic function is,
f(x) = p(x - a)(x - b)(x - c)
Here, a, b, c and d are the x-intercepts of the given graph.
Since, x-intercepts given in the graph are x = -5, 1 and 4,
Equation of the curve will be,
f(x) = p(x + 5)(x - 1)(x - 4)
Since, the graph of this function passes through (2, -2) also
-2 = p(2 + 5)(2 - 1)(2 - 4)
-2 = -p(14)
p = 
p = 
Therefore, equation will be,
f(x) =
<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
To find the missing dimension you will use the formula for finding the volume of a prism and solve for the missing dimension. In this case 2ft is how deep the pool is and you will solve for the width of the pool.
V = Bh, where B is the area of the base. In this case, use the area of a trapezoid formula.
286 = 1/2h(8 +13)2
<u>286</u> = <u>21h</u>
21 21
h = 13.6
The width of the wading pool is approximately 13.6 feet.
Answer:
nr. 1 and 3 is a Dilation 2 and 4 are not Dilations
Step-by-step explanation:
Dilation is an elnargment or shink of a figure by a x(factor) that makes the SAME image but smaller or larger
Answer:
I think it's prove the midpoints are the same
Step-by-step explanation:
I'm not completely sure but I'm taking it right now and I believe that's the most logical answer because if they meet up at the same midpoint then they could bisect each other.
