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°.
Assuming these are 4^(1/7), 4^(7/2), 7^(1/4) and 7^(1/2), the conversion process is pretty quick. the denominator, or bottom, of your fraction exponent becomes the "index" of your radical -- in ∛, "3" is your index, just for reference. the numerator, aka the top of the fraction exponent, becomes a power inside the radical.
4^(1/7) would become ⁷√4 .... the bottom of the fraction becomes the small number included in the radical and the 4 goes beneath the radical
in cases such as this one, where 1 is on top of the fraction radical, that number does technically go with the 4 beneath the radical--however, 4¹ = 4 itself, so there is no need to write the implied exponent.
4^(7/2) would become √(4⁷) ... the 7th power goes with the number under your radical and the "2" becomes a square root
7^(1/4) would become ⁴√7 ... like the first answer, the bottom of the fraction exponent becomes the index of the radical and 7 goes beneath the radical. again, the 1 exponent goes with the 7 beneath the radical, but 7¹ = 7
7^(1/2) would become, simply, √7
Answer:
The roots of the equation is real and repeated
Step-by-step explanation:
Here, we want to describe the nature of the roots of the given quadratic equation
To get the nature of the roots, we find the discriminant of the equation
The discriminant is;
b^2 - 4ac
In this case, b = -28 , a = 49 and c = 4
The discriminant is thus;
-28^2 - 4(49)(4)
= 784 - 784 = 0
Since the discriminant is zero, this means that the quadratic equation has real roots which are the same
The value of X would be 9
Answer:
You donf have the picture shown, how is anybody supposed to work on it
