Answer:
119.05°
Step-by-step explanation:
In general, the angle is given by ...
θ = arctan(y/x)
Here, that becomes ...
θ = arctan(9/-5) ≈ 119.05°
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<em>Comment on using a calculator</em>
If you use the ATAN2( ) function of a graphing calculator or spreadsheet, it will give you the angle in the proper quadrant. If you use the arctangent function (tan⁻¹) of a typical scientific calculator, it will give you a 4th-quadrant angle when the ratio is negative. You must recognize that the desired 2nd-quadrant angle is 180° more than that.
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It may help you to consider looking at the "reference angle." In this geometry, it is the angle between the vector v and the -x axis. The coordinates tell you the lengths of the sides of the triangle vector v forms with the -x axis and a vertical line from that axis to the tip of the vector. Then the trig ratio you're interested in is ...
Tan = Opposite/Adjacent = |y|/|x|
This is the tangent of the reference angle, which will be ...
θ = arctan(|y| / |x|) = arctan(9/5) ≈ 60.95°
You can see from your diagram that the angle CCW from the +x axis will be the supplement of this value, 180° -60.95° = 119.05°.
Answer:
Step-by-step explanation:
Given
Required
Determine the number of miles driven on the highway and on the city
Represent the gallons used on highway with h and on city with c.
So, we have:
---- gallons used
and
--- distance travelled
In the first equation, make c the subject
Substitute 10 - h for c in the second equation
Open bracket
Collect like terms
Make h the subject
Substitute 5 for h in
If on the highway, he travels 31 miles per gallon, then his distance on the highway is:
If in the highway, he travels 26 miles per gallon, then his distance on the highway is:
Alright so basically what you have to do here is realize that 130 miles is 2 hours, so if you divide by 2, you’ll have 65 miles in one hour ,, so 6mph, and if you divide again by two, you have 32.5 miles ,, therefore he travels 32.5 miles in 30 minutes
Let us say ,
x=number of students who passed
y=number of students who failed
total number of students =276
x+y=276..................(1)
We are given 5 times the number of students passed as failed.
x=5y.............(2)
plugging value of x from (2) in (1),
5y+y=276
6y=276
y=46
x=5y=46*5=230
x=number of students who passed=230
6²/2(3) +4
6²=36
2(3)=6
So now we have
36/6 + 4 which is 6 + 4 which is 10.
