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3 years ago

How would we find the unit vector in the direction of v= i+j?

1 answer:

4 0

The vector i=<1,0> and j=<0,1> so the i+j=<1+0,0+1>=<1,1>. The length of this vector is easy: |i+j|=2–√ to make the vector i+j=<1,1> a unit vector we rescale it by it's length (i.e. divide i+j by its length) , v=(i+j)/(|i+j|) thus we have v=1/2–√<1,1> or <1/2–√,1/2–√> If you check the length of this vector v, you see it indeed does have length =1. It is parallel to the vector i+j because it's components are proportional to the components of i+j=<1,1>.

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Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th

saul85 [17]

Answer:

The standard form of the ellipse is $\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$ .

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

$(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)$ (1)

If we know that $V_{1} (x,y) = (4,0)$ and $V_{2}(x,y) = (4, 14)$ , then the coordinates of the center are, respectively:

$(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)$

$(h,k) = (2,0) + (2, 7)$

$(h, k) = (4, 7)$

The length of each semiaxis is, respectively:

$a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}$

$a = 3$

$b = \sqrt{(4-4)^{2}+(0-7)^{2}}$

$b = 7$

The standard equation of the ellipse is described by the following formula:

$\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1$

Where:

$h$ , $k$ - Coordinates of the center of the ellipse.

$a$ , $b$ - Length of the orthogonal semiaxes.

If we know that $h = 4$ , $k = 7$ , $a = 3$ and $b = 7$ , then the standard form of the ellipse is:

$\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$

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3 years ago

ALGEBRAIC PROOF!!!! PLS HELP!!! The area of a rectangular blanket is 20 square feet. The blanket's length is (2x + 1) ft and the

Fynjy0 [20]

Answer:

Length: 5 ft; width: 4 ft.

Step-by-step explanation:

A = LW formula for area of rectangle

(2x + 1)(2x) = 20 substitute length, width, and area into formula

4x² + 2x - 20 = 0 use the distributive property to multiply out left side

2x² + x - 10 = 0 divide both sides of equation by 2

(2x + 5)(x - 2) = 0 factor out trinomial

2x + 5 = 0 or x - 2 = 0 use zero product rule to solve for x

2x = -5 or x = 2 subtract 5 from both sides; add 2 to both sides

x = -5/2 or x = 2

We discard x = -5/2 since it would give negative length and width, and the length and width cannot be negative.

Length: 2x + 1 = 2(2) + 1 = 5

Width: 2x = 2(2) = 4

Length: 5 ft; width: 4 ft.

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3 years ago

Which of the following properties are used

Lady bird [3.3K]

First, we can see that he used the Distributive property. Then after that, he used the Additive property. After that, he combined like terms and the used the additive property again. Finally, he used the divisive property.

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3 years ago

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16. If a customer's check subtotal comes to $27.14,

horsena [70]

Answer:

$28.77

Step-by-step explanation:

If the subtotal is $27.14, and the tax to add is 6%, the total would be:

$27.14*(1+0.06)=$28.77

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3 years ago

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PLEASE HELP ASAP 25 PTS + BRAINLIEST TO RIGHT/BEST ANSWER

Aliun [14]

Answer:

c ln (x^3/y^3)

Step-by-step explanation:

3 ln x - 3 lny

We know that a ln b = ln b^a

ln x^3 - ln y^3

We also know ln a - ln b = ln (a/b)

ln (x^3/y^3)

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3 years ago