Hello :
v . w = <span>| | v | | × </span><span>| | w | | cos(</span><span>θ) ....(1)
v(2,0,1) w(0,1,-3)
</span>v . w = (2)(0)+(0)(1)+(1)(-3) = - 3
| | v | | = √((2)²+(0)²+(1)²) = <span>√5
</span>| | w | = √((0)²+(1)²+(-3)²) = √10
by (1) :
cos(θ) = (v . w ) / | | v | | × | | w | |
cos(θ) = = - 3/√50
θ =..... calculate by 2ind function ( calculator)
Equation of this circle is
x^2 + (y - 2)^2 = 36
y = 2.5x + 2
Substitute for y in the equation of the circle:-
x^2 + (2.5x + 2 - 2)^2 = 36
x^2 + 6.25x^2 = 36
x^2 = 36 / 7.25
x = +/- 6 / 2.693 = +/- 2.228
when x = 2.228 y = 2.5(2.228) + 2 = 7.57 to nearest hundredth
when x = -2.228 y = 2.5(-2.228) + 2 = -3.57
So they intersect at 2 points but the intersect in the first quadrant is at (2.23, 7,57) to nearest hundredth.
This is experimental probability.
If 12 were found to be defective out of 280 the experimental probability of a purifier being defective is:
12/280 which is:
4.3% (to nearest tenth of a percent)
Answer:
Obtuse
Step-by-step explanation:
The sum of squares of the short sides is 130, so is less than the square of the long side. The long side (12) is longer than it would need to be for a right triangle, so the largest angle is bigger than 90°.
The triangle is obtuse.
_____
A triangle solver app or calculator can confirm this. Note angle C is about 96°, an obtuse angle.
Total number of sheets are 12.
Total number of white sheets= 9
Total number of red sheets = 3
Probability = Number of favorable outcomes/ total number of outcomes.
Hence
When Calvin throws the sheets in the air, the probability that he gets a white sheet is
which equals to 
that becomes 0.75
