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love history [14]
1 year ago
12

Find the magnitude and direction of each resultant for the given vectors. Round each side to the nearest tenth and round each an

gle to the nearest degree.
w = < 5, 6 >, x = < -1, 14 >
Mathematics
1 answer:
marusya05 [52]1 year ago
8 0

The magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

<h3>Magnitude of the resultant vector</h3>

Sum of vectors in x direction, ∑X = 5 - 1 = 4

Sum of the vectors in y direction, ∑Y = 6 + 14 = 20

Resultant vector = √(∑X² + ∑Y²)

Resultant vector = √(4² + 20²) = 20.4 units

<h3>Direction of the vector</h3>

θ = arc tan (ΣY/ΣX)

θ = arc tan (20/4)

θ = arc tan (5)

θ = 78.7⁰

θ ≈ 79⁰

Thus, the magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

Learn more about resultant vectors here: brainly.com/question/19802988

#SPJ1

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CHALLENGE PROBLEM Danny's Department Store advertises savings of
Oksanka [162]

Discount are used to reduce the costs of items

The percent paid to determine the advertisement is incorrect

<h3>How to determine the correct percentage</h3>

The initial prices are given as: $44.00 to $152.00

And the discount is: 45% to 51%

At a discount of 45%, the price of the items would be:

Price = \$44.00 * (1 - 45\%)

Price = \$24.2

Price_2 = \$152.00 * (1 - 45\%)

Price_2 = \$83.6

At a discount of 51%, the price of the items would be:

Price = \$44.00 * (1 - 51\%)

Price = \$21.56

Price_2 = \$152.00 * (1 - 51\%)

Price_2 = \$74.48

The calculates prices show that the percent paid to determine the advertisement is incorrect

Read more about discounts at:

brainly.com/question/23103804

8 0
2 years ago
which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!​
coldgirl [10]

9514 1404 393

Answer:

  (a) -(x+7)/y

  (b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

  \dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}

Likewise, the expression of (b) with the minus sign factored out is ...

  \dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}

On the other hand, simplifying expression (c) gives something different.

  \dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}

__

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

  Given: (-x-7)/y = (-x/y) +(-7/y)

  (a) -(x+7)/y = (-x/y) +(-7/y)

  (b) (x+7)/(-y) = (-x/y) +(-7/y)

  (c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.

__

Of course, you need to know the use of the distributive property and the rules of signs.

  a(b+c) = ab +ac

  -a/b = a/(-b) = -(a/b)

  -a/(-b) = a/b

__

<u>Summary</u>: The given expression matches (a) and (b).

_____

<em>Additional comments</em>

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

  \left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

(c) evaluates to (-1-7)/-2 = 4, different from given

3 0
2 years ago
2. Which is a solution of 2(t-1)+3t 9p+6-5p
insens350 [35]

Answer:

3t9p + 2t - 5p + 4

Step-by-step explanation:

4 0
3 years ago
186 = 6 (3n + 7) answer for N
Vesnalui [34]
N=8 is the correct answer
7 0
2 years ago
Read 2 more answers
The width of a rectangle is 2x²+9x-7 and the length is x²-9. Find the perimeter of the rectangle.​
OLEGan [10]

Answer:

---

Step-by-step explanation:

W=2x²+9x-7

L=x²-9

2(3x²+9x-16)

6x²+18x-32

The bold is the perimeter.

---

hope it helps

6 0
2 years ago
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