Someone help me I need to get this finished by tomorrow ASAP

Given:

The given vector is:

[tex]v=9i-6j[/tex]

To find:

The unit vector in the direction of the given vector.

Solution:

If a vector is [tex]v=ai+bj[/tex], then the unit vector in the direction of the this vector is

[tex]\hat v=\dfrac{v}{|v|}[/tex]

Where, [tex]|v|=\sqrt{a^2+b^2[/tex]

We have,

[tex]v=9i-6j[/tex]

Here, [tex]a=9[/tex] and [tex]b=-6[/tex]. So,

[tex]|v|=\sqrt{9^2+(-6)^2}[/tex]

[tex]|v|=\sqrt{81+36}[/tex]

[tex]|v|=\sqrt{117}[/tex]

[tex]|v|=3\sqrt{13}[/tex]

Now, the unit vector in the direction of the given vector is:

[tex]\hat v=\dfrac{9i-6j}{3\sqrt{13}}[/tex]

[tex]\hat v=\dfrac{9i}{3\sqrt{13}}-\dfrac{6j}{3\sqrt{13}}[/tex]

[tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex]

Therefore, the required unit vector is [tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex].

Answer:

C

Step-by-step explanation:

Because 0 lbs of sugar is required to make 0 muffins

I hope this is right

Answer:

9 ft

Step-by-step explanation:

As length, width and height are same, then it is a square prism / cube

Volume of prism = 729 ft³

side³ = 729

side³ = 9³

Side = 9 ft

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

Perimeter of figure =

[tex]w + x + x + y + y + y + y \\ = 1 \times w + 2 \times x + 4 \times y \\ = w + 2x + 4y[/tex]

Answer:

x= 4 , y= 1

Step-by-step explanation:

confirm the answer was correct

Answer:

John has 4608.171 points

Step-by-step explanation:

4092.1 + 516.071 = 4608.171

Hope this helps

Have a nice day :)

Answer:

2497

Step-by-step explanation:

Answer:

2497

Step-by-step explanation:

53 + 2444

= 0053 + 2444

= 2497

Answer:

20°

Step-by-step explanation:

ok so if 40 degrees is on one side its also on the side parallel from it

a straight line = 180 degrees

so 180 - 40 = 140

so 7x =140

we now divide 7 on both sides and get x=20 because the 7 cancels out

180 -40 =140

7x = 140

7x/7 =140/7

x=20

Hope I helped?

Answer:

Step-by-step explanation:

let x be the population

so we have ,

2x= 6h

?= 3 days or 3×24h

by cross multiplication we have

2x× 72h= 6h×?

?= 2x×72/6 = 24x

So, in three days the bacteria will b 24 times current population.

Answer:

-5.2

Step-by-step explanation:

15.6 ÷ (-3) = -5.2

Answer:

[tex]\displaystyle y' = \frac{-1}{x^4}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{1}{3x^3}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

55.64

Step-by-step explanation:

The range finder is 92 feet from the building and 106 feet from the top of the building i.e. hypotheses

We will use the Pythagorean theorem:

x^2 = 106^2 - 92^2

= 11,236 -  8,464

= 2,772

= √2,772

x = 52.64978632

The height of the building:

h = x + 3

= 52.64978632 + 3

= 55.64978632

or

≈ 55.64 feet

Step-by-step explanation:

the answer to the nearest is 55.64

Answer:

Drink = 1.4

Hot dog = 1.75

x + y = 3.15

Step-by-step explanation:

Let drink = x ; hot dog = y

3x + 2y = 7.70 - - (1)

2x + y = 4.55 - - - (2)

From (2)

y = 4.55 - 2x - - - (3)

Put y = 4.55 - 2x in (1)

3x + 2(4.55 - 2x) = 7.70

3x + 9.1 - 4x = 7.70

-x = 7.7 - 9.1

-x = - 1.4

x = 1.4

Put x = 1.4 in (3)

y = 4.55 - 2(1.4)

y = 4.55 - 2.8

y = 1.75

Drink = 1.4

Hot dog = 1.75

x + y = 3.15

Answer:

50 pack

[tex]\$0.01[/tex]

Step-by-step explanation:

Number of packs at Costco = 30

Cost of 30 packs at Costco = $10.82

Number of packs at the other place = 50

Cost of 50 packs = $17.25

Cost of one pack when 30 packs are bought

[tex]\dfrac{10.82}{30}=\$0.36[/tex]

Cost of one pack when 50 packs are bought

[tex]\dfrac{17.25}{50}=\$0.35[/tex]

It is better to buy the 50 pack.

Difference in the unit prices = [tex]0.36-0.35=\$0.01[/tex].

Answer:

wowo cool

Step-by-step explanation:

Answer:

sounds cheeesyyy

Step-by-step explanation:

Answer:

x = -14

Steps:

Rewrite the equation as -8 = 6+x

Then move all terms not containing x to the right side of the equation.

x = -8-6

Afterwords subtrack.

x = -14.

hope this helps :)

Answer:

Solution given:

radius[r]=2in

π=3.14

we have

volume of sphere=[tex] \frac{4}{3} \pi {r}^{3} [/tex]=[tex] \frac{4}{3} ×3.14× {2}^{3} [/tex]=33.5in³is your answer.

Let's see

Answer:

scalene

Step-by-step explanation:

Answer:

Step-by-step explanation:

So it 22

Answer: 0.007

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

because a straight line is 180 degrees so 140 plus 40 equals 180

Answer:

40

Step-by-step explanation:

straight line is 180 degrees

180=140+x

140+40=180

Answer:

B: y = 3x + 6

Answer: The value of G = 4.5

Step-by-step explanation:

As per given,

[tex]G\propto \dfrac{j^2}{m}[/tex]

When we replace proportional sign with an equal to sign, we get

[tex]G=k\dfrac{j^2}{m}[/tex], where k = constant

If G=0.05 when j = 0.4 and m=1.6, then

[tex]0.05=k\dfrac{0.4^2}{1.6}\\\\ 0.05=k(0.1)\\\\ k=0.5[/tex]

Now,

[tex]G=0.5\dfrac{j^2}{m}\\\\\Rightarrow\ G=0.5\dfrac{6^2}{4}\\\\\Rightarrow\ G=4.5[/tex]

hence, when j =6 and m=4, the value of G = 4.5