Answer:
(a) Orthogonal, (b) Neither, (c) Parallel, d( Orthogonal
Step-by-step explanation:
a and b are parallel is a=kb
a and b if a dot b = 0
(a) a dot b = (9)(-4)+6(6)=-36+36=0
a and b are orthogonal
(b) a dot b = 40-7-21=12
a=kb -> there is no k value satisfying the equation
a and b are neither parallel or orthogonal
(c) a dot b = -12-108-48=-168
a=kb -> k=-3/4 satisfies the equation
a and b are parallel
(d) a dot b= 9-3-6=0
a and b are orthogonal
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
You can solve this in two ways.
1. Graphical. Plot the graph for x between -5 and 1 (see attachement).
The vertex of the graph is the peak of the curve, which has the coordinates x=-2, y=-9.
2. Analytical. Calculate the derivative of the function f(x)
Solve the equation:
will give the solution x=-2.
Replace x=-2 in the f(x) function and you'll get the value of y:
You get the same answer: x=-2, y=-9
So the answer is
<span>B. (-2, -9)</span>
10 and -7 times each other equals -70.
10 plus -7 equals 3.
Hope this helps you! (:
4/6 = x + 3/ 12 - x
4( 12 - x) = 6( x + 3)
48 - 4x = 6x + 18
-4x - 6x = 18 - 48
- 10x = -30
x = 3
