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3 years ago

11

The points plotted below are on the graph of a polynomial. Some of the roots to this polynomial are integers. Which of the follo

wing x-values are roots of the polynomial? Check all that apply.

1 answer:

Shkiper50 [21]3 years ago

3 0

Answer:

I think its B but I have very little evidence. Don't even put B but I was just saying I think it is.

Step-by-step explanation:

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The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

3 0

3 years ago

What does the strategy 'Dont get bogged down' mean

kap26 [50]

It means not to get too invested in details or to become so invested in something that you can’t focus on anything else.

5 0

2 years ago

A professor has recorded exam grades for 20 students in his class, but one of the grades is no longer readable. If the mean sco

Ivenika [448]

Answer:

5

Step-by-step explanation:

To obtain the total score for all the 20 students, we multiply the average score by the number hence

Total score for all 20 is 81*20=1620

Similarly, for the 19 students, the sum of their total score equals the product of the average and number of students hence

Total score for 19 readable is 19*85=1615

The difference between these two total scores ie for 20 and 19 students equals to the value of unreadable score. Therefore,

Difference=1620-1615=5

Therefore, the value of unreadable score is 5

3 0

3 years ago

Solve by factoring:<br> 5t=t ^2

elena-14-01-66 [18.8K]

Answer:

t=0 and t=5

Step-by-step explanation:

5t = t^2

Subtract 5t from each side

5t-5t = t^2 -5t

0= t^2 -5t

Factor out a t

0= t(t-5)

Using the zero product property

t=0 and t-5 =0

t=0 and t-5+5=0+5

t=0 and t=5

7 0

2 years ago

In the figure below, the two triangular faces of the prism are fight triangles with sides of length 3, 4, and 5. The other three

olasank [31]

The figure of the prism is attached below.

The total surface area of the prism equals the sum of areas of two triangles and the three rectangles.

Surface Area of Prism = Area of 2 Triangles + Area of 3 Rectangles.

Area of a Triangle = 0.5 x Base x Height
Area of a Triangle = 0.5 x 3 x 4 = 6 square units

There are 3 rectangles. From the figure we can see that the bottom most rectangle has the dimensions 4 by 6. The left most rectangle has the dimensions 3 x 6 and the right most rectangle has the dimensions 5 by 6.

So, the Area of 3 rectangles will be = (4 x 6) + (3 x 6) + (5 x 6) = 72 square units

The Surface Area of the prism will be:

Surface Area = 2 (4) + 72 = 84 square units

Thus the correct answer is option A

6 0

2 years ago