Answer:
general rule Un=1.8n-21
U100=1.8(100)-21=159
Step-by-step explanation:
a5=a+4d, a5=-12
a10=a+9d, a10=-3
-12=a+4d
-3=a+9d subtract the system of equations
-9=-5d solve for d
d=1.8
substitute d into first equation to find a
-12=a+4(1.8)
a=-19.2
un. = a + (n − 1)d
Un=-19.2+(n-1)(1.8)
Un=1.8n-21
2 more 10s then 11 is 31
1 more 10s then 11 is 21
3 more 10s then 11 is 41.
basic math :)
<u>Answer</u><u> </u><u>:</u><u>-</u>
9(3+√3) feet
<u>Step </u><u>by</u><u> step</u><u> explanation</u><u> </u><u>:</u><u>-</u>
A triangle is given to us. In which one angle is 30° and length of one side is 18ft ( hypontenuse) .So here we can use trignometric Ratios to find values of rest sides. Let's lable the figure as ∆ABC .
Now here the other angle will be = (90°-30°)=60° .
<u>In ∆ABC , </u>
=> sin 30 ° = AB / AC
=> 1/2 = AB / 18ft
=> AB = 18ft/2
=> AB = 9ft .
<u>Again</u><u> </u><u>In</u><u> </u><u>∆</u><u> </u><u>ABC</u><u> </u><u>,</u><u> </u>
=> cos 30° = BC / AC
=> √3/2 = BC / 18ft
=> BC = 18 * √3/2 ft
=> BC = 9√3 ft .
Hence the perimeter will be equal to the sum of all sides = ( 18 + 9 + 9√3 ) ft = 27 + 9√3 ft = 9(3+√3) ft .
<h3>
<u>Hence </u><u>the</u><u> </u><u>perim</u><u>eter</u><u> of</u><u> the</u><u> </u><u>triangular</u><u> </u><u>pathway</u><u> </u><u>shown</u><u> </u><u>is</u><u> </u><u>9</u><u> </u><u>(</u><u> </u><u>3</u><u> </u><u>+</u><u> </u><u>√</u><u>3</u><u> </u><u>)</u><u> </u><u>ft</u><u> </u><u>.</u></h3>
Total distance covered = 5 x 30 = 150 miles
Angle of travel with respect to south pole = 180 - 164°56' = 15°4'
Let the distance southwards covered be x, then
cos 15°4' = x/150
Thus, x = 150 cos 15°4' = 144.84
Therefore, the distance covered southwards = 145 miles to the nearest mile.
