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3 years ago

A polynomial is to be constructed that will touch the x axis at most 8 times. What is the minimum degree of the polynomial?

1 answer:

7 0

The maximum number of roots to a polynomial of order n is n roots. Take the example of a quadratic (order 2) which can intersect the x-axis a maximum of 2 times, and similarly a cubic (order 3) 3 times maximum.

Hence for 8 intersections, minimum order = 8

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Use the definition of the derivative to differentiate v=4/2 pie r^3

nata0808 [166]

I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:

$\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)$

$\displaystyle \frac{dV}{dr} = 2\pi \cdot 3r^2 = \boxed{6\pi r^2}$

In Mathematica, you can check this result via

D[4/2*Pi*r^3, r]

3 0

2 years ago

How much interest will be earned in 4 years from $2,450 placed in a savings account at 6.5% simple interest? (Remember the I=PRT

Nikolay [14]

Answer:

6100.80

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Can you please explain how to solve this?

BlackZzzverrR [31]

Answer:

Step-by-step explanation:

hello,

as this is a parallelogram we can write that BE = DE so

15x + 4 = 9x + 6

<=> 15x - 9x + 4 = 6

<=> 6x = 6 - 4 = 2

<=> x = 2/6 = 1/3

so BE = DE = 15/3+4=5+4=9

so BD = BE + DE = 9 + 9 = 18

the correct answer is 18

hope this helps

7 0

3 years ago

The equation f(x)=x-5 translated 4 units to the left is

laila [671]

F(x)=x-5
f(4)=x-5
f(4)=4-5
f(4)=-1

4 0

3 years ago

Find the equation of the tangent line at the point (1, 6). for y = 4 + 4x2 - 2x3.

Lostsunrise [7]

$y = 4 + 4 x^{2}-2x^{3} Lets \ write \ it \ y = -2 x^{3} +4 x^{2} +4
$
The tangential line at a certain point is just the derivative so.
$y ' = -6 x^{2} +8x$ . At the point (1,6) we plug the x value in and get the slope at the point (y ' = 2)

The tangential line at that point is
y - 6 = 2(x - 1) (this is the answer)

6 0

3 years ago