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3 years ago

Y - 10 = 32. Solve for x. Thanks Sooooo MUCH!! :-)

2 answers:

6 0

To solve this we will use inverse operations.

The inverse operations for subtraction is addition.

y - 10 = 32

32 + 10 = 42

So, y = 42 BUT lets check our work.

42 - 10 = 32.

So y = 42.

Paraphin [41]3 years ago

4 0

Y - 10 = 32

First, we have to make the variable (y) equal something. To do that, we have to do everything on one side of the problem. We can first start off by adding 10 to each side. This will make the variable equal the unknown answer.
$y = 32 + 10$

Second, we can now add 32 + 10. Once adding that, you will have the answer to the unknown variable. 32 + 10 = 42.
$y = 42$

Answer: $\fbox {y = 42}$

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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 $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

3 0

3 years ago

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coldgirl [10]

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6 0

3 years ago

Read 2 more answers

PLEASE HELP ! 15 POINTs!

Lapatulllka [165]

Answer:

Perimeter = 101.496 cm

Step-by-step explanation:

draw line from point C that is perpendicular to line AD. Call that point E.

tan 43° = 16.7/ED

0.9325 = 16.7/ED

ED = 17.909 cm

sin 43° = 16.7/CD

0.6820 = 16.7/CD

CD = 24.487 cm

Perimeter = AB + BC + CD + ED + AE

Perimeter = 16.7 + 21.2 + 24.487 + 17.909 + 21.2 = 101.496 cm

8 0

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What is the maximum Number of different sizes of faces that a rectangular Prism can have.

telo118 [61]

Answer:

Step-by-step explanation:

For a rectangular prism of dimensions L × W × H, pairs of opposite faces will have dimensions ...

L × W
W × H
H × L

These will be three different sets of dimensions if L, W, and H are all different lengths.

7 0

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murzikaleks [220]

Answer:

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Step-by-step explanation:

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