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3 years ago

Which of the number(s) below are potential roots of the function?

Mathematics

1 answer:

Katena32 [7]3 years ago

6 0

Step-by-step explanation:

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Consider two vectors A and B A=14i and B= -4i+8j

DaniilM [7]

Assuming $\mathbf a,\mathbf b\in\mathbb R^3$ , you have

$\mathbf a\cdot\mathbf b=(14)(-4)+(0)(8)=-56$

so

$((\mathbf a\cdot\mathbf b)\,\mathbf i)\cdot\mathbf a=(-56\,\mathbf i)\cdot(14\,\mathbf i)=(-56)(14)=-784$

Next,

$\mathbf a+\mathbf b=(14\,\mathbf i)+(-4\,\mathbf i+8\,\mathbf j)=10\,\mathbf i+8\,\mathbf j$

Then

$(\mathbf a+\mathbf b)\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\10&8&0\\-4&8&0\end{vmatrix}=112\,\mathbf k$

$((\mathbf a+\mathbf b)\times\mathbf b)\times\mathbf k=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\0&0&112\\0&0&1\end{vmatrix}=\mathbf 0$

4 0

3 years ago

The endpoints of (MP)are M(2,1) and P(12,6). If point K partitions (MP) in a ratio of MK:KP = 3:2, what are the coordinates of K

GREYUIT [131]

Answer:

K(8, 4)

Step-by-step explanation:

Given:

M(2, 1), P(12, 6)

MK:KP = 3:2

Required:

Coordinates of K

SOLUTION:

Coordinates of K can be determined using the formula below:

$x = \frac{mx_2 + nx_1}{m + n}$

$y = \frac{my_2 + ny_1}{m + n}$

Where,

$M(2, 1) = (x_1, y_1)$

$P(12, 6) = (x_2, y_2)$

$m = 3, n = 2$

Plug in the necessary values to find the coordinates of K:

$x = \frac{mx_2 + nx_1}{m + n}$

$x = \frac{3(12) + 2(2)}{3 + 2}$

$x = \frac{36 + 4}{5}$

$x = \frac{40}{5}$

$x = 8$

$y = \frac{my_2 + ny_1}{m + n}$

$y = \frac{3(6) + 2(1)}{3 + 2}$

$y = \frac{18 + 2}{5}$

$y = \frac{20}{5}$

$y = 4$

The coordinates of K = (8, 4)

3 0

2 years ago

How do you know if a whole number is a perfect square

kirill [66]

Answer:

you simply think of a number that when multiplied by itself it will give you that whole number

Step-by-step explanation:

let's take for instance the number 4 it's a whole number and still a perfect square because when you think of a number from 1to 10, which number when you multiply by itself will give you four apart from 2

4 0

2 years ago

Question 4.

Ludmilka [50]

Answer:

9.80 m

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.

<h3>setup</h3>

The geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...

Tan = Opposite/Adjacent

Using the given values, we have ...

tan(24°) = AC/AB = (tree height)/(distance from tree)

tan(24°) = AC/(22 m)

<h3>solution</h3>

Multiplying by 22 m gives ...

tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m

The height of the tree is about 9.80 meters.

5 0

1 year ago

write an equation in standard form with integer coefficients for the line with slope 6/11 going through the point (-1,-6)

yKpoI14uk [10]

If the slope is 6/11 then, in y=mx+b form, m will be 6/11. When you multiply 6/11 and -1 you get -6/11. To get the y (-6), you have to add -60/11. So in, y=mx+b form the equation is y=6/11x+(-60/11). To make it standard form, you add negative 6/11x to both sides and then multiply by 11 to get rid of the fractions. So therefore the equation would be:

-6x + 11y = - 60

4 0

3 years ago