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3 years ago

Find the center and radius of the with the equation (x + 5) ^ 2 + (y - 2) ^ 2 = 25

Mathematics

1 answer:

iVinArrow [24]3 years ago

8 0

Answer: Center: (5,0)

Radius:5

Step-by-step explanation: Happy to help :)

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Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Maurinko [17]

The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .

6 0

3 years ago

Lucy is going to invest in an account paying an interest rate of 7% compounded daily. How much would Lucy need to invest, to the

Lubov Fominskaja [6]

Answer:

Lucy needs to invest $55,194.16

Step-by-step explanation:

5 0

2 years ago

Translate the given phrase into an algebraic expression and simplify if possible: the difference of −5 and −30.

lawyer [7]

Answer:

IIaI-IbII

Step-by-step explanation:

II-30I-I-5II=

I30-5I=

I25I=

II-5I-I-30II=

I5-30I=

I-25I=

8 0

2 years ago

Yen has 25 dimes she gives the same number of dimes to each of her 5 children how many dimes will each receive?

Brums [2.3K]

Each child will get 5 dimes.
25 ÷ 5 = 5

4 0

3 years ago

Slove the simoltanous equation by using substitution or elimination method 5x-3y=1 3x+2y=1<br>

xxTIMURxx [149]

<u>By substitution method </u>

5x - 3y =1

3x + 2y = 1

_____o____o____

$5x - 3y = 1 \\ 5x = 1 + 3y \\ x = \frac{1 + 3y}{5}$

______o____o_____

$3x + 2y = 1 \\ 3( \frac{1 + 3y}{5} ) + 2y = 1 \\ \frac{3 + 9y}{5} + 2y = 1 \\ \frac{3 +9y + 10y}{5} = 1 \\ \frac{3 + 19y}{5} = 1 \\ 3 + 19y = (1)(5) \\ 3 + 19y = 5 \\ 19y = 5 - 3 \\ 19y = 2 \\ y = \frac{2}{19}$

______o_____o____

$x = \frac{1 + 3y}{5} = \frac{1 + 3 \frac{2}{19} }{5} \\ x = \frac{1 + \frac{6}{19} }{5} = \frac{ \frac{19 + 6}{19} }{5} = \frac{ \frac{25}{19} }{5} \\ x = \frac{25}{19} \div 5 \\ x = \frac{25}{19} \times \frac{1}{5} \\ x = \frac{5}{19}$

I hope I helped you^_^

7 0

2 years ago