Mathematics, 19.09.2019 05:30 kris22elizondop9v1bb

Vector a with arrow has a magnitude of 64 units and points due west, while vector b with arrow has the same magnitude and points due south. specify the direction relative to due west.
find the magnitude and direction of a with arrow and b with arrow.

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Answer from: cyclonenetwork1188

The magnitude is 90.5.

The direction of $(\vec{A}+ \vec{B})$ is 45° south of west.

The direction of $(\vec{A} - \vec{B})$ is 45° north of west.

Step-by-step explanation:

Let suppose the direction of unit vector as follows:

$\hat{i}$ in the eastern direction

$\hat{j}$ in the northern direction

Given:

Vector A with arrow has a magnitude of 64 units and points due west, while vector B with arrow has the same magnitude and points due south.

Therefore,

$\vec{A} = -64 \hat{i}$

$|\vec{A}| = 64$

And

$\vec{B} = -64 \hat{j}$

$|\vec{B}| = 64$

Formula used:

$The\ magnitude\ of\ vector\ (\vec{A}+ \vec{B}) = \sqrt{|A|^{2}+|B|^{2}}$

And the direction is given by:

$tan\theta = \frac{|A|}{|B|}$

Now,

The magnitude of $(\vec{A}+ \vec{B})$ :

$= \sqrt{|A|^{2}+|B|^{2}}$

$= \sqrt{64^{2}+64^{2}}$

$= 64\sqrt{2}$

= 90.5

∴ The magnitude is 90.5.

And,

The direction relative to west is

$tan\theta = \frac{|A|}{|B|}$

θ = tan⁻¹ (B/A) = tan⁻¹ (64/64) = tan⁻¹ 1 = 45° south of west

∴ The direction is 45° south of west.

Again,

The magnitude of $(\vec{A} - \vec{B})$ :

$= \sqrt{|A|^{2}+|B|^{2}}$

$= \sqrt{64^{2}+64^{2}}$

$= 64\sqrt{2}$

= 90.5

∴ The magnitude is 90.5.

And,

The direction relative to west is

$tan\theta = \frac{|A|}{|B|}$

θ = tan⁻¹ (B/A) = tan⁻¹ (64/64) = tan⁻¹ 1 = 45° north of west.

∴ The direction is 45° north of west.

Answer from: Quest

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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Vector a with arrow has a magnitude of 64 units and points due west, while vector b with arrow has t...