Given:
y = x - 6 (1)
for the line
x² + y² = r² (2)
for the circle
When the line intercepts the circle, the x and y values will be equal.
Equate the values of y by substituting (1) into (2).
x² + (x - 6)² = r²
x² + x² - 12x + 36 = r²
2x² - 12x + 36 = r²
Answer: r² = 2x² - 12x + 36
<span>V(h 24) = 30 cm*20 cm*24 cm = 14400 cm³ = 14,4 liters</span>
<span>V(h 15) = 30 cm*20 cm*15 cm = 9000 cm³ = 9 liters</span>
<span> + 6,5 liters = + 6500 cm³ </span>
9 liters + 6,5 liters = 15,5 liters => 15,5 liters -14,4 liters = 1,1 liters
now 15500 cm³ => 1100 cm³ =1,1 liters too much !!
Answer: 1,1 liters of water overflow the container.<span>
</span>
2/5 or 2 divided by 5. 2 pounds are divided up by 5 friends.
Answer:
-16/65
Step-by-step explanation:
Given sinα = 3/5 in quadrant 1;
Since sinα = opp/hyp
opp = 3
hyp = 5
adj^2 = hyp^2 - opp^2
adj^2 = 5^2 = 3^2
adj^2 = 25-9
adj^2 = 16
adj = 4
Since all the trig identity are positive in Quadrant 1, hence;
cosα = adj/hyp = 4/5
Similarly, if tanβ = 5/12 in Quadrant III,
According to trig identity
tan theta = opp/adj
opp = 5
adj = 12
hyp^2 = opp^2+adj^2
hyp^2 = 5^2+12^2
hyp^2 = 25+144
hyp^2 = 169
hyp = 13
Since only tan is positive in Quadrant III, then;
sinβ = -5/13
cosβ = -12/13
Get the required expression;
sin(α - β) = sinαcosβ - cosαsinβ
Substitute the given values
sin(α - β) = 3/5(-12/13) - 4/5(-5/13)
sin(α - β)= -36/65 + 20/65
sin(α - β) = -16/65
Hence the value of sin(α - β) is -16/65
