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2 years ago

The magnitude of the resultant vector shown is _____.

Mathematics

1 answer:

Flura [38]2 years ago

6 0

Answer:

2√3

Step-by-step explanation:

You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).

The magnitude of R is 2√3.

_____

In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...

Sin = Opposite/Hypotenuse

sin(30°) = √3/R

R = √3/sin(30°) = √3/(1/2) = 2√3

Of course, doing this on your calculator will give a numerical answer, which you may not want.

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Pencils come in packages of 10.Erasers come in packages of 12. Phillips wants to purpose the smallest number of pencils and eras

balandron [24]

Answer:

The answer to your question is:

Packages of pencils = 6

Packages of erasers = 5

Step-by-step explanation:

Data

Pencils = 10/package

Erasers = 12 / package

Process

Find the least common factor of 10 and 12

10 12 2

5 6 2

5 3 3

5 1 5

LCF = 2 x 2 x 3 x 5 = 60

Finally divide 60 by the number of pencils or erasers in each package

Packages of pencils = 60/10 = 6

Packages of erasers = 60/12 = 5

5 0

2 years ago

What is the inverse one to one function of f(x) = square root of x-2???

alexira [117]

$f(x) = \sqrt{x - 2} \\y = \sqrt{x - 2} \\y^{2} = (\sqrt{x - 2})^{2} \\y^{2} = x - 2 \\x^{2} = y - 2 \\x^{2} + 2 = y \\x^{2} + 2 = f^{-1}(x)$

6 0

2 years ago

Write as an expression " 6 times smaller than 42"

Mademuasel [1]

Answer:

42/6 or 7

Step-by-step explanation:

5 0

2 years ago

Let y′′′−9y′′+20y′=0. find all values of r such that y=erx satisfies the differential equation. if there is more than one correc

DerKrebs [107]

we are given

differential equation as

$y'''-9y''+20y'=0$

we are given

$y=e^{rx}$

Firstly, we will find y' , y'' and y'''

those are first , second and third derivative

First derivative is

$y'=re^{rx}$

Second derivative is

$y''=r*re^{rx}$

$y''=r^2e^{rx}$

Third derivative is

$y'''=r^2*re^{rx}$

$y'''=r^3e^{rx}$

now, we can plug these values into differential equation

and we get

$r^3 e^{rx}-9r^2 e^{rx}+20re^{rx}=0$

now, we can factor out common terms

$e^{rx}(r^3 -9r^2 +20r)=0$

we can move that term on right side

$(r^3 -9r^2 +20r)=0$

now, we can factor out

$r(r^2 -9r +20)=0$

$r(r-5)(r-4)=0$

now, we can set them equal

$r=0$

$r-5=0$

$r=5$

$r-4=0$

$r=4$

so, we will get

$r=0,4,5$ ...............Answer

4 0

3 years ago

Terry practices the same amount of time each day for his soccer tryouts. In 4 days, he has practiced for 360 minutes. Let x repr

n200080 [17]

Answer:

Step-by-step explanation:

390 ( 40; 6 )

7 0

2 years ago