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3 years ago

If a=i+3j+k and b=i+12j+k, find a unit vector with positive first coordinate orthogonal to both a and

1 answer:

5 0

The cross product of the vectors will be orthogonal to both:
axb
[tex]=<1,3,1>x<1,12,1>
=
i j k
1 3 1
1 12 1
=<3-12, -1+1, 12-3>
=<-9,0,9>
Since it is required to have positive first coordinate, we reverse the sign of the components, namely reverse the direction of the vector, which is still orthogonal to both a and b:
Required vector is <9,0,-9> which is orthogonal to both a and b.

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What graph best represents the solution to the equality y - 2x > -8

Ne4ueva [31]

Answer:

<h2>In the attachment</h2>

Step-by-step explanation:

$y-2x>-8\qquad\text{add}\ 2x\ \text{to both sides}\\\\y>2x-8\\-------------------------\\\\-\ dotted\ line\\\leq,\ \geq-\ solid\ line\\,\ \geq-\ shading\ above\ the\ line\\-------------------------\\\\y=2x-8-\text{It's a linear function.}\\\text{We only need two points to draw a graph.}\\\text{Choice two arbitrary values of x, substitute to the equation,}\\\text{and calculate the values of y}.\\\\for\ x=4\to y=2(4)-8=8-8=0\to A(4,\ 0)\\for\ x=0\to y=2(0)-8=0-8=-8\to B(0,\ -8)$

6 0

3 years ago

Oscar is 16 yrs old and his sister is 12. what will be the ratio of Oscar's age to his sister's age in 2 years?Write as a fracti

just olya [345]

Oscar's age = 16
Sister's age = 12

Current year: 16 / 12
Simplest form: 4 / 3 ; both are divisible by 4.

2 years after: (16 + 2) / (12 + 2) = 18 / 14 ; add two years to both numbers.

Simplest form: of 18 / 14 is 9 / 7; both are divisible by 2.

4 0

3 years ago

Read 2 more answers

Solve the equation using square roots. (X+3)^2=0

Vilka [71]

Answer:

x=3

Step-by-step explanation:

(x−3)^2=0

Set the x−3 equal to 0.

x−3=0

Add 3 to both sides of the equation.

x=3

7 0

2 years ago

The house numbers on the north side of Flynn Street are even. In one block, the house numbers begin 1022, 1032, 1042, and 1052.

never [62]

Answer:

6 houses away

Step-by-step explanation:

You can write down the house numbers and count them:

1032, 1042, 1052, 1062, 1072, 1082

1082 is the 6th house from where Taylor is.

___

You can also recognize that (1082 -1022)/10 = 60/10 = 6 is the number of houses away from the house at 1022.

4 0

3 years ago

The tubs are similar in shape.

faltersainse [42]

Answer:

The tube are similar in shape.

The height of the small tub is 5 cm.

The volume of the small tube is 150 cm3.

The volume of the large tub is 500 cm3.

Work out the height of the large tub.

Give your answer correct to 3 significant figures.

Step-by-step explanation: Hope this help(:

3 0

10 months ago

Read 2 more answers