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2 years ago

Use the function f(x) = −16x2 + 24x + 16 to answer the questions.

Mathematics

2 answers:

Anni [7]2 years ago

7 0

Step-by-step explanation:

a) f(x) = -16x^2 + 24x + 16

= -4(4x^2 - 6x - 4)

= -4(2x - 4)(2x + 1)

b) The x-intercepts can be found when y = 0. This happens when

2x - 4 = 0 or x = 2

and

2x + 1 = 0 or x = -1/2

Therefore, the x-intercepts are at (2, 0) and (-1/2, 0)

c) As x approaches positive infinity, f(x) approaches negative infinity. When x approaches negative infinity, f(x) approaches negative infinity. In other words, the graph of this function opens downward.

d) From part (b), we that its graph intersects the x-axis at the 2 points. We also know that it opens downwards. Also, the graph intersects the y-axis at

f(0) = -16(0)^2 + 24(0) + 16

= 16

or at (0, 16)

Mice21 [21]2 years ago

6 0

Answer:

the functionality of element and the researcher in the best pa the best of us the best pa sa bible I don't think I have any other one and only true to size of my module and we will see how I feel after I have to be done by the end the week if I become the

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Step-by-step explanation:

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2 years ago

A gumball has a diameter that is 66 mm. The diameter of the gumball's spherical hollow core is 58 mm. What is the volume of the

grigory [225]

Answer:

Volume of gumball without including its hollow core is 48347.6 cubic mm.

Step-by-step explanation:

Given:

Diameter of Gumball = 66 mm

Since radius is half of diameter.

Radius of gumball = $\frac{diameter}{2}=\frac{66}{2} =33 \ mm$

Now We will first find the Volume of Gumball.

To find the Volume of Gumball we will use volume of sphere which is given as;

Volume of Sphere = $\frac{4}{3}\pi r^3$

Now Volume of Gumball = $\frac{4}{3}\times3.14 \times (33)^3 = 150456.24 \ mm^3$

Also Given

Diameter of gumball's spherical hollow core = 58 mm

Since radius is half of diameter.

Radius of gumball's spherical hollow core = $\frac{diameter}{2}=\frac{58}{2} =29 \ mm$

Now We will find the Volume of gumball's spherical hollow core.

Volume of Sphere = $\frac{4}{3}\pi r^3$

So Volume of gumball's spherical hollow core = $\frac{4}{3}\times3.14 \times (29)^3 = 102108.61 \ mm^3$

Now We need to find volume of the gumball without including its hollow core.

So, To find volume of the gumball without including its hollow core we would Subtract Volume of gumball spherical hollow core from Volume of Gumball.

volume of the gumball without including its hollow core = Volume of Gumball - Volume of gumball's spherical hollow core = $150456.24\ mm^3 - 102108.61\ mm^3 = 48347.63\ mm^3$