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3 years ago

The magnitude of the resultant vector shown is _____.

Mathematics

1 answer:

Flura [38]3 years ago

6 0

Answer:

2√3

Step-by-step explanation:

You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).

The magnitude of R is 2√3.

_____

In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...

Sin = Opposite/Hypotenuse

sin(30°) = √3/R

R = √3/sin(30°) = √3/(1/2) = 2√3

Of course, doing this on your calculator will give a numerical answer, which you may not want.

You might be interested in

Given the midpoint (1.5,1.5) and the endpoint (5,7) where is the other endpoint located

earnstyle [38]

The formula of a midpoint:

$M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)$

We have:

$M(1.5,\ 1.5)\to x_M=1.5,\ y_M=1.5\\A(5,\ 7)\to x_A=5,\ y_A=7$

Substitute

$\dfrac{5+x_B}{2}=1.5\qquad|\cdot2\\\\5+x_B=3\qquad|-5\\\\x_B=-2\\\\\dfrac{7+y_B}{2}=1.5\qquad|\cdot2\\\\7+y_B=3\qquad|-7\\\\y_B=-4$

<h3>Answer: (-2, -4)</h3>

8 0

3 years ago

Gabriel wants to paint the model. How

enyata [817]

Answer:

<h2>The area of the base is 144 square inches.</h2><h2>The area of each triangular face is 66 square inches.</h2><h2>Grabiel needs 408 square inches of paint.</h2>

Step-by-step explanation:

The complete problem is attached.

Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of

$B=12 \times 12 = 144 \ in^{2}$

The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face

$A=\frac{1}{2}bh =\frac{1}{2}(12)(11)= 66 \ in^{2}$

But there are four triangle faces, so $A_{faces} =4(66)=264 \ in^{2}$ .

Therefore, the area of each triangular face is 66 square inches.

So, the total surface area would be the sum

$S=144+264=408 \ in^{2}$

Therefore, Gabriel needs 408 square inches to paint the whole model.

4 0

3 years ago

Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. 6 sqrt 2

Gemiola [76]

Isosceles right triangles have two equal sides (a and b) that are not the hypotenuse (c). And when two sides are equal, so are their opposite angles. There are only 180° degrees in any triangles, thus the right angle = 90°, so 90 left for the two equal, means that 2x=90,
x = 45°.

There are several ways to go about solving a triangle like this. The best and easiest is simply to memorize that the hypotenuse is exactly root2 times the other sides. Or, each isosceles side is the hypotenuse (c) ÷ root2
$a = b = c \div \sqrt{2} \\ c = a\sqrt{2} \\ c = 6 \sqrt{2} \times \sqrt{2} = 6 \times 2 = 12$
Another way to do it is the longer proof of Pythagorean Theorem:
${c}^{2} = {a}^{2} + {b}^{2}... \: \: c = \sqrt{({a}^{2} + {b}^{2})} \\$
$c= \sqrt{({6 \sqrt{2}) }^{2} + ({6 \sqrt{2})}^{2}} \\ = \sqrt{(2 \times{(6 \sqrt{2} )}^{2} )} = \sqrt{2(36 \times 2)} \\ c = \sqrt{144} = 12$

7 0

3 years ago

X-y=3 in slope intercept form and find x and y intercepts

Dominik [7]

Answer:

x intercept is x=3

y intercept is y=-3

Step-by-step explanation:

We can write this equation in a simpler way to find the values needed. Lets do it. Take:

x-y=3

And sum y in both sides, as we know the equality will maintain:

x-y+y=3+y

x = 3+ y

Now subtract 3 in both sides:

x-3 = y+3-3

x-3=y

So, we can rewrite our equation as y=x-3

The x intercept is a value of x such that the equation in equal to zero; in other words, is the value of x when y is zero. It is also called a zero root. Graphically, its the x value when the function passes trough the x-axis. Lets find if, we nned that:

x-3 = 0

If we sum 3 in both sides:

x-3+3=3

x=3

So, x=3 is x intercept

For finding the y intercept we need the value of y when x is zero. Graphically, is the value of y obtained when the function passes trough the y-axis. So, replace x with 0:

0-3=y

y=-3

Another way to get it is knowing that the y intercept in a polynomial is always the independent term, the one that has no x or y, which in this case is -3.

7 0

3 years ago

Which of the following absolute value equations has no solutions?Group of answer choices

Amiraneli [1.4K]

The absolute value measures the distance a number is away from the origin (zero) on the number line. A number can be to the left or right of zero on the number line, but the distance away from zero is always positive. Graphically:

In other words:

• If d is positive and

$\begin{gathered} |x|=d \\ \text{ then} \\ x=d\text{ or }x=-d \end{gathered}$

• If d is negative and

$\begin{gathered} |x|=-d \\ \text{then} \\ \text{ No solution, because distance (d) can not be negative.} \end{gathered}$

Therefore, the equation that has no solutions is:

$\boldsymbol{|x|=-3}$

3 0

1 year ago