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kolbaska11 [484]
3 years ago
11

HELP! Find v × w if v = 3i + 8j – 6k and w = –4i – 2j – 3k.

Mathematics
2 answers:
wolverine [178]3 years ago
8 0

Using the determinant method, the cross product is

\begin{vmatrix}\vec\imath&\vec\jmath&\vec k\\3&8&-6\\-4&-2&-3\end{vmatrix}=\begin{vmatrix}8&-6\\-2&-3end{vmatrix}\,\vec\imath-\begin{vmatrix}3&-6\\-4&-3\end{vmatrix}\,\vec\jmath+\begin{vmatrix}3&8\\-4&-2\end{vmatrix}\,\vec k=-36\,\vec\imath+33\,\vec\jmath+26\,\vec k

so the answer is B.

Or you can apply the properties of the cross product. By distributivity, we have

(3i + 8j - 6k) x (-4i - 2j - 3k)

= -12(i x i) - 32(j x i) + 24(k x i) - 6(i x j) - 16(j x j) + 12(k x j) - 9(i x k) - 24(j x k) + 18(k x k)

Now recall that

  • (i x i) = (j x j) = (k x k) = 0 (the zero vector)
  • (i x j) = k
  • (j x k) = i
  • (k x i) = j
  • (a x b) = -(b x a) for any two vectors a and b

Putting these rules together, we get

(3i + 8j - 6k) x (-4i - 2j - 3k)

= -32(-k) + 24j - 6k + 12(-i) - 9(-j) - 24i

= (-12 - 24)i + (24 + 9)j + (32 - 6)k

= -36i + 33j + 26k

AleksandrR [38]3 years ago
7 0

Answer:

B. –36i + 33j + 26k

Step-by-step explanation:

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Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in s
wolverine [178]

Answer:

x^4 - 14x^2 - 40x - 75.

Step-by-step explanation:

As complex roots exist in conjugate pairs the other zero is -1 - 2i.

So in factor form we have the polynomial function:

(x - 5)(x + 3)(x - (-1 + 2i))(x - (-1 - 2i)

= (x - 5)(x + 3)( x + 1 - 2i)(x +1 + 2i)

The first 2 factors  = x^2 - 2x - 15 and

( x + 1 - 2i)(x +1 + 2i) = x^2 + x + 2ix + x + 1 + 2i - 2ix - 2i - 4 i^2

=  x^2 + 2x + 1 + 4

= x^2 + 2x + 5.

So in standard form we have:

(x^2 - 2x - 15 )(x^2 + 2x + 5)

= x^4  + 2x^3 + 5x^2 - 2x^3 - 4x^2 - 10x - 15x^2 - 30x - 75

= x^4 - 14x^2 - 40x - 75.

7 0
4 years ago
The distance between X and Y is 6 1/2 units. Which number could represent the point Y?
tiny-mole [99]

Answer:

\huge\boxed{\sf 3.5}

Step-by-step explanation:

Distance = \sf 6 \frac{1}{2} \ units = 6.5 \ units

Here X is -3

So,

Point Y = -3 + 6.5 = 3.5

\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
6 0
3 years ago
Read 2 more answers
17/10 - 2/5 = *<br> Helpppp
uysha [10]
17/10-(2/5x2/2)
17/10-4/10
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8 0
3 years ago
5. h(x)=0.5x - 1 with domain (-♾, 4) what is the range
Rudiy27

We have a domain of a function, that is, which x-es can we throw in. But we are asking which y-s will we get given that we can only throw x-es in (-\infty,4).

Let's try x=4 even though we are forbidden to put 4 inside h we are still able to do so.

So h(4)=0.5\cdot4-1=2-1=1 what we just got is the upper limit of the range. The lower limit is h(-\infty)=-\infty.

So the range is just (-\infty, 1).

Hope this helps :)

6 0
3 years ago
Kevin runs a farm stand that sells apples and raspberries. Each pound of apples sells for $3.50 and each pound of raspberries se
krek1111 [17]

Kevin sold 10 pounds of apples and 20 pounds of raspberries.

Step-by-step explanation:

Given,

Cost per pound of apples = $3.50

Cost per pound of raspberries = $4

Total amount earned = $115

Let,

x represent the pounds of apples sold

y represent the pounds of raspberries sold

According to given statement;

3.50x+4y=115     Eqn 1

y = 2x                  Eqn 2

Putting value of y from Eqn 2 in Eqn 1

3.50x+4(2x)=115\\3.50x+8x=115\\11.50x=115

Dividing both sides by 11.50

\frac{11.50x}{11.50}=\frac{115}{11.50}\\x=10

Putting x=10 in Eqn 2

y=2(10)\\y=20

Kevin sold 10 pounds of apples and 20 pounds of raspberries.

Keywords: linear equation, substitution method

Learn more about linear equations at:

  • brainly.com/question/4279146
  • brainly.com/question/4354581

#LearnwithBrainly

5 0
3 years ago
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