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2 years ago

This negative and positive stuff is really confusing me can anyone please help?

Mathematics

1 answer:

RSB [31]2 years ago

7 0

Answer:

Positive integers have values greater than zero. Negative integers have values less than zero. Zero is neither positive nor negative. The rules of how to work with positive and negative numbers are important because you'll encounter them in daily life, such as in balancing a bank account, calculating weight, or preparing recipes. (THIS EXPLAINS WHT THEY R, HOPE THIS HELPS U)

Step-by-step explanation:

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6 math questions, answer all please for all points

Sergeeva-Olga [200]

Answer:

See below for answers and explanations

Step-by-step explanation:

<u>Problem 1</u>

Recall that the projection of a vector $u$ onto $v$ is $\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v$ .

Identify the vectors:

$u=\langle-10,-7\rangle$

$v=\langle-8,4\rangle$

Compute the dot product:

$u\cdot v=(-10*-8)+(-7*4)=80+(-28)=52$

Find the square of the magnitude of vector v:

$||v||^2=\sqrt{(-8)^2+(4)^2}^2=64+16=80$

Find the projection of vector u onto v:

$\displaystyle proj_vu=\biggr(\frac{u\cdot v}{||v||^2}\biggr)v\\\\proj_vu=\biggr(\frac{52}{80}\biggr)\langle-8,4\rangle\\\\proj_vu=\biggr\langle\frac{-416}{80} ,\frac{208}{80}\biggr\rangle\\\\proj_vu=\biggr\langle\frac{-26}{5} ,\frac{13}{5}\biggr\rangle\\\\proj_vu=\langle-5.2,2.6\rangle$

Thus, B is the correct answer

<u>Problem 2</u>

Treat the football and wind as vectors:

Football: $u=\langle42\cos172^\circ,42\sin172^\circ\rangle$

Wind: $v=\langle13\cos345^\circ,13\sin345^\circ\rangle$

Add the vectors: $u+v=\langle42\cos172^\circ+13\cos345^\circ,42\sin172^\circ+13\sin345^\circ\rangle\approx\langle-29.034,2.481\rangle$

Find the magnitude of the resultant vector:

$||u+v||=\sqrt{(-29.034)^2+(2.481)^2}\approx29.14$

Find the direction of the resultant vector:

$\displaystyle \theta=tan^{-1}\biggr(\frac{2.841}{-29.034}\biggr)\approx -5^\circ$

Because our resultant vector is in Quadrant II, the true direction angle is 6° clockwise from the negative axis. This means that our true direction angle is $180^\circ-5^\circ=175^\circ$

Thus, C is the correct answer

<u>Problem 3</u>

We identify the initial point to be $R(-2,12)$ and the terminal point to be $S(-7,6)$ . The vector in component form can be found by subtracting the initial point from the terminal point:

$v=\langle-7-(-2),6-12\rangle=\langle-7+2,-6\rangle=\langle-5,-6\rangle$

Next, we find the magnitude of the vector:

$||v||=\sqrt{(-5)^2+(-6)^2}=\sqrt{25+36}=\sqrt{61}\approx7.81$

And finally, we find the direction of the vector:

$\displaystyle \theta=tan^{-1}\biggr(\frac{6}{5}\biggr)\approx50.194^\circ$

Keep in mind that since our vector is in Quadrant III, our direction angle also needs to be in Quadrant III, so the true direction angle is $180^\circ+50.194^\circ=230.194^\circ$ .

Thus, A is the correct answer

<u>Problem 4</u>

Add the vectors:

$v_1+v_2=\langle-60,3\rangle+\langle4,14\rangle=\langle-60+4,3+14\rangle=\langle-56,17\rangle$

Determine the magnitude of the vector:

$||v_1+v_2||=\sqrt{(-56)^2+(17)^2}=\sqrt{3136+289}=\sqrt{3425}\approx58.524$

Find the direction of the vector:

$\displaystyle\theta=tan^{-1}\biggr(\frac{17}{-56} \biggr)\approx-17^\circ$

Because our vector is in Quadrant II, then the direction angle we found is a reference angle, telling us the true direction angle is 17° clockwise from the negative x-axis, so the true direction angle is $180^\circ-17^\circ=163^\circ$

Thus, A is the correct answer

<u>Problem 5</u>

A vector in trigonometric form is represented as $w=||w||(\cos\theta i+\sin\theta i)$ where $||w||$ is the magnitude of vector $w$ and $\theta$ is the direction of vector $w$ .

Magnitude: $||w||=\sqrt{(-16)^2+(-63)^2}=\sqrt{256+3969}=\sqrt{4225}=65$

Direction: $\displaystyle \theta=tan^{-1}\biggr(\frac{-63}{-16}\biggr)\approx75.75^\circ$

As our vector is in Quadrant III, our true direction angle will be 75.75° counterclockwise from the negative x-axis, so our true direction angle will be $180^\circ+75.75^\circ=255.75^\circ$ .

This means that our vector in trigonometric form is $w=65(\cos255.75^\circ i+\sin255.75^\circ j)$

Thus, C is the correct answer

<u>Problem 6</u>

Write the vectors in trigonometric form:

$u=\langle40\cos30^\circ,40\sin30^\circ\rangle\\v=\langle50\cos140^\circ,50\sin140^\circ\rangle$

Add the vectors:

$u+v=\langle40\cos30^\circ+50\cos140^\circ,40\sin30^\circ+50\sin140^\circ\rangle\approx\langle-3.661,52.139\rangle$

Find the magnitude of the resultant vector:

$||u+v||=\sqrt{3.661^2+52.139^2}\approx52.268$

Find the direction of the resultant vector:

$\displaystyle\theta=tan^{-1}\biggr(\frac{52.139}{-3.661} \biggr)\approx-86^\circ$

Because our resultant vector is in Quadrant II, then our true direction angle will be 86° clockwise from the negative x-axis. So, our true direction angle is $180^\circ-86^\circ=94^\circ$ .

Thus, B is the correct answer

5 0

2 years ago

Find the perimeter of the triangle with vertices (−2,2), (0,4), and (1,−2). the perimeter is . round to the nearest hundredth.

mina [271]

The answer is about 12.5 (when rounded to the nearest 10th).

This can be found using the distance formula between each point. One distance is 5, one is $\sqrt{2}$ and one is $\sqrt{37}$ . Added together gives you the answer above.

4 0

3 years ago

What is the measure of VKW?

MrRissso [65]

Answer:

107

Step-by-step explanation:

5x + 3 + 7x + 9 = 180

12x + 12 = 180

12x = 168

x = 14

7(14) + 9 = 107

6 0

2 years ago

What is the sum of the first seven terms of the geometric series? 3 12 48 192 ...

Ad libitum [116K]

Hence, the sum of the given GP is 16347

<h2>What is a series?</h2>

a series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers, but much more generality is possible.

<h3>How to solve?</h3>

we can identify from the given geomertric series.

first term = a(say) = 3

geometric factor of progression = r(say) = 4

Sum of the first 7 terms = a( $\frac{r^n-1}{r-1}$ ) ,where n is 7

Sum = 3( $\frac{4^7-1}{3}$ ) = 16348-1

= 16347

Hence, the sum of the given GP is 16347.

to learn more about series: brainly.com/question/12578626

#SPJ4

8 0

2 years ago

I need help asap )/)/)/)

Andrej [43]

Answer:

$49.20

Step-by-step explanation:

6 0

3 years ago