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2 years ago

8/x = 32 ..................

Mathematics

1 answer:

krok68 [10]2 years ago

6 0

Answer:

Step-by-step explanation:

x= 1/4

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Math Correct answers only please!!

aksik [14]

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Rewrite and add each vector:

$p=\langle40cos70^\circ,40sin70^\circ\rangle\\q=\langle50cos270^\circ,50sin270^\circ\rangle\\r=\langle60cos235^\circ,60sin235^\circ\rangle\\p+q+r=\langle40cos70^\circ+50cos270^\circ+60cos235^\circ,40sin70^\circ+50sin270^\circ+60sin235^\circ\rangle\\p+q+r\approx\langle-20.73,-61.56\rangle$

Find the magnitude of the resulting vector:

$||p+q+r||=\sqrt{x^2+y^2}\\||p+q+r||=\sqrt{(-20.73)^2+(-61.56)^2}\\||p+q+r||\approx64.96$

Therefore, the best answer is D) 64.959

Problem 2

Think of the vectors like this:

$t=\langle7cos240^\circ,7sin240^\circ\rangle\\u=\langle10cos30^\circ,10sin30^\circ\rangle\\v=\langle15cos310^\circ,15sin310^\circ\rangle$

By adding the vectors, we have:

$t+u+v=\langle7cos240^\circ+10cos30^\circ+15cos310^\circ,7sin240^\circ+10sin30^\circ+15sin310^\circ\rangle\\t+u+v\approx\langle14.8,-12.55\rangle$

Since the direction of a vector is $\theta=tan^{-1}(\frac{y}{x})$ , we have:

$\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{-12.55}{14.8})\\\theta\approx-40.3^\circ$

Don't forget to take into account that the resulting vector is in Quadrant IV since the horizontal component is positive and the vertical component is negative, so we will add 360° to our angle to get the result:

$\theta=360^\circ+(-40.3)^\circ\\\theta=319.7^\circ$

Therefore, the best answer is D) 320°

Problem 3

Again, rewrite the vectors and add them:

$u=\langle30cos70^\circ,30sin70^\circ\rangle\\v=\langle40cos220^\circ,40sin220^\circ\rangle\\u+v=\langle30cos70^\circ+40cos220^\circ,30sin70^\circ+40sin220^\circ\rangle\\u+v\approx\langle-20.38,2.48\rangle$

Using the direction formula:

$\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{2.48}{-20.38})\\\theta\approx-6.94^\circ$

As the vector is located in Quadrant II, we need to add 180° to our angle:

$\theta=180^\circ+(-6.94)^\circ\\\theta=173.06^\circ$

Therefore, the best answer is D) 173°

Problem 4

Using scalar multiplication:

$-3u=-3\langle35,-12\rangle=\langle-105,36\rangle$

Find the magnitude of the resulting vector:

$||-3u||=\sqrt{x^2+y^2}\\||-3u||=\sqrt{(-105)^2+(36)^2}\\||-3u||=111$

Find the direction of the resulting vector:

$\theta=tan^{-1}(\frac{y}{x})\\\theta=tan^{-1}(\frac{36}{-105})\\\theta\approx-18.92^\circ$

As the vector is located in Quadrant II, we need to add 180° to our angle:

$\theta=180^\circ+(-18.92)^\circ\\\theta=161.08^\circ$

Therefore, the best answer is C) 111; 161°

Problem 5

Using scalar multiplication:

$5v=5\langle25cos40^\circ,25sin40^\circ\rangle=\langle125cos40^\circ,125sin40^\circ\rangle$

Since the direction of the angle doesn't change in scalar multiplication, it only affects the magnitude, so the magnitude of the resulting vector would be $||5v||=125$ , making the correct answer C) 125; 200°

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2 years ago

Please help last question please. Mimi measures a circular magnet and calculates that it has an area of 3.14 square inches. What

sineoko [7]

Circle is 3.14 #ZedTheZom

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2 years ago

A snowboard originally costs $120, but it is on sale for 45% off. If a customer buying the snowboard has a coupon for $15.00 off

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2 years ago

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Evaluate - 4/8 ./. 8 2/3

LenaWriter [7]

Answer:

The answer is 13/3.

Step-by-step explanation:

8 2/3 is an improper fraction and is expressed as 26/3. CCF (copy, change, flip) is then applied to the division statement and 26/3 to becomes 4/8*26/3. The final answer is 104/24 which simples to 13/3.

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2 years ago

What are whole number dimensions?

Sphinxa [80]

When you get to the point where the width is larger than the length, you can stop because you have exhausted all the possibilities. The greatest area will be the rectangle that is closer in to a square than any of the others.

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3 years ago

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