Answer:
71.6 degrees
Step-by-step explanation:
Given the vectors
u= <8,4> v = <9.-9> (5 points)
u*v = (8, 4)*(9, -9)
u*v = 8(9)+(4)(-9)
u*v = 72 - 36
u*v = 36
|u| = √8²+4²
|u| = √64+16
|u| = √80
|v| = √9²+9²
|v| = √81+81
|v| = √162
Using the formula
u*v = ||u||v| cos theta
36 = √80(√162)cos theta
36 = √12960 cos theta
cos theta = 36/√12960
cos theta = 36/113.8
cos theta = 0.3162
theta = arccos(0.3162)
theta = 71.56 degrees
Hence the angle between the given vectors to the nearest tenth of a
degree is 71.6 degrees
Csc²x - 1
1/sin²x - 1
1/sin²x - sin²x / sin²x
(1 - sin²x) / sin²x
Recall that sin²x + cos²x = 1
So cos²x = 1 - sin²x
So we can replace numerator to cos²x
cos²x / sin²x
= cot²x
Final answer: cot²x
A) x^2 +x -30 = 0 is factored by looking for two factors of 30 that differ by 1. We know ... 30 = 1*30 = 2*15 = 3*10 = 5*6The last two factors differ by 1, so we can factor the trinomial as (x +6)(x -5) = 0
b) The solutions are found by finding values of x that make these factors zero. The only way the product will be zero is if one or more of the factors is zero. x + 6 = 0 x = -6 . . . . . subtract 6
x - 5 = 0 x = 5 . . . . . add 5
The solutions are x = -6 or x = 5These are the values of x that will satisfy the equation (make it true). What they mean depends on the meaning of the variable and the situation the equation is a model of.
Answer:
The answer is y = -1/3x + 5 !
Step-by-step explanation:
If you observe the line, the y-intercept is 5, from the point in the graph (0,5). From that point, we can see that the rise over run is -1/3. Thus, y = -1/3x + 5.
Answer:
3. A=B=70°; C=D=110°
4. A=90°; C=48°
Step-by-step explanation:
Same-side angles of a trapezoid add to 180°.
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3. (2x) +(x+15) = 180
3x + 15 = 180 . . . . simplify
x +5 = 60 . . . . . . . divide by 3
x = 55
A=B=(x+15)° = (55+15)° = 70°
C=D=2x° = 2·55° = 110°
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4. You are given the values of one of the angles on each side, so the other can be found by subtraction:
A=180°-D = 90°
C = 180° -132° = 48°
