Write the first 3 numbers of the sequence.

Given the triangle below, what is the length of the third side, rounded to the nearest whole number?

Leno4ka [110]

Answer:

Step-by-step explanation:

You need the Law of Cosines for this, namely:

$x^2=21^2+14^2-2(21)(14)cos58$ where x is the missing side.

$x^2=441+196-311.5925$ and

$x^2=325.4075$ so

x = 18.0 or just 18

7 0

3 years ago

A vector u has a magnitude of 15 and a direction of 0 degrees. A vector v has a magnitude of 9 and a direction of 35 degrees. Fi

umka2103 [35]

Answer:

$\displaystyle \alpha \simeq 13^o$

$\displaystyle \left | \vec{u}+\bar{v} \right |\simeq 23$

Step-by-step explanation:

<u>Sum Of Vectors</u>

Given

$\displaystyle \vec{u}=, \vec{v}=$

the sum of both is

$\displaystyle \vec{u}+\vec{u}=$

Given a vector

$\displaystyle \vec{x}=$

The magnitude of \vec x is

$\displaystyle \left | \vec{x} \right |=\sqrt{m^2+n^2}$

And the angle is forms with the positive x-axis is

$\displaystyle tan\alpha =\frac{n}{m}$

We have

$\displaystyle \vec{u}=$

Also

$\displaystyle \vec{v}=$

$\displaystyle \vec{v}=< 7.372,5.162>$

The sum of both vectors is

$\displaystyle \vec{u}+\vec{v}=$

The magnitude of the sum is

$\displaystyle \left | \vec{u}+\vec{v} \right |=\sqrt{22.732^2+5.162^2}=22.96$

We compute the angle (direction)

$\displaystyle tan\alpha =\frac{5.162}{22.732}=0.227$

$\displaystyle \alpha =12.79^o$

Rounding to the nearest integer

$\displaystyle \alpha \simeq 13^o$

Rounding the magnitude

$\displaystyle \left | \vec{u}+\bar{v} \right |\simeq 23$

5 0

3 years ago

Find the unit rate.<br> 1/3 kilometer in 1/3hour

bagirrra123 [75]

Answer:

1 kilometer in 1 hour

Step-by-step explanation:

unit rate is km(kilometer) per hour(hr)

1/3 km = 1/3 hr

multiply both sides by 3

1 km in 1 hour

6 0

3 years ago

Kay's mother taught her how to make handmade ornaments to sell at a craft fair. Kay rented a table at the fair for $30 and set u

leva [86]

Answer:

profit= 6. 00x - (30+2. 50x)

5 0

3 years ago

In the diagram below of triangle HJKHJK, LL is a midpoint of \overline{HJ}HJ and MM is a midpoint of \overline{JK}JK. If LM=71-9

love history [14]

Answer:

Step-by-step explanation:

Since J is the midpoint of HK, then HJ=JK and 3x+5=9x-3 solve for x

6x=8 x=8/6=4/3 so HJ=3x+5=3(4/3)+5=9 = JK HK=2(9)=18

the full segment HK is 18, each half of it is 9 =HJ=JK

3 0

3 years ago