Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
X +(x+2) + (x+4) = 5(x+2)-18
3x+6 = 5x+10-18
3x+6 = 5x-8
3x=5x-14
-2x=-14
x=7
(x+2) =9
(x+4) =11
7 + 9+ 11 =27
5(9)-18 =45-18 =27
3 numbers are 7, 9 & 11
Thr probability is calculated from the data gathered from tests on a large number of people. There's undoubtedly some data included with this question that you neglected to copy. Without it, it's not possible to come up with an answer.
In this Problem you can use the Cross Multiplication.
If in 15 seconds the nurse counted 18 beats, so in 60 seconds she will count x beats.
15 seconds = 18 beats
60 seconds = x beats
You use the cross multiplication and multiply 60 by 18 and 15 by x, so you get:
15x = 60 * 18
15x = 1080
Then, you divide 15x and 1080 by 15 each, so you get:
x = 72
So, the Nurse counted 72 beats in 60 seconds
Hope this Helps :)
Answer:
30m²
Step-by-step explanation:
To find the area of a triangle, you need to ensure that the triangle is a right-angled triangle. We can use the Pythagoras Theorem to help us prove that.
a² + b² = c²
5² + 12² = 169
13² = 169
By converse of Pythagoras Theorem, the triangle is a right-angled triangle.
Thus, you can directly find the area of the triangle using the formula: base × height ÷ 2.
Area = 12 × 5 ÷ 2
= 30m²
