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3 years ago

Find the product of 9x(-3x²y-7xz)

Mathematics

1 answer:

kogti [31]3 years ago

4 0

Answer:

$- 27 {x}^{3} y - 63 {x}^{2} z$

Step-by-step explanation:

$9x( - 3 {x}^{2} y - 7xz)$

$= 9x \times ( - 3 {x}^{2} y) + 9x \times ( - 7xz)$

$= - 27 {x}^{3} y - 63 {x}^{2} z$

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Please help <br>cos40∘=sin(x+30∘)

iVinArrow [24]

Answer:

x = 20 degrees.

Step-by-step explanation:

cos40∘=sin(x+30∘)

sin (x + 30) = 0.766

x + 30 = arcsin 0.766 = 50

x = 50 - 30 = 20.

5 0

2 years ago

Read 2 more answers

What is the variable used to predict another variable called________.A. Independent variableB. Dependent variableC. Moderating v

UkoKoshka [18]

Answer:

A. Independent variable

Step-by-step explanation:

The prediction of a variable can be done if we have the independent variable. Which is the required variable that is used to determine the value of the other variable. The variable to be predicted is dependent on the required variable.

An independent variable can also be referred to as a predictor variable. When its value is known, it can be used to obtain the dependent variable.

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3 years ago

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :