Answer:
y = 2.4
Step-by-step explanation:
Given y varies inversely with x then the equation relating them is
y = 
← k is the constant of variation
To find k use the condition y = 8 when x = 3
k = yx = 8 × 3 = 24
y = 
← equation of variation
When x = 10, then
y = 
= 2.4
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
Answer:
y = - 
x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
14x + 6y = 36 ( subtract 14x from both sides )
6y = - 14x + 36 ( divide all terms by 6 )
y = - 
x + 6, that is
y = - x + 6 ← in slope- intercept form
The "if" part is the antecedent or hypothesis while the "then" part is the conclusion. The format is "if hypothesis, then conclusion". The given phrase can be translated to "If the number is even, then the number is divisible by 2"
Hypothesis: number is even
Conclusion: number is divisible by 2
That's why the answer is choice D
For the first question, you need to count all of your choices. Kepp in mind, it will be a fraction. Then count all of your "V6".
12/24 = 1/2
Hope this helps!!
