radius = 3 feet
rearrange the formula making r the subject
πr³ = V ( multiply both sides by 3 to eliminate fraction )
4πr³ = 3V ( divide both sides by 4π )
r³ = = ( 3 × 36π ) / 4π = 3 × 9 = 27
take the cube root of both sides
r = = 3
Find the value of each trigonometric ratio.A. 37/35B. 12/37C. 12/35D. 37/12
1 answer:
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Answer:
A) 0.15
B) 0.36
Step-by-step explanation:
First Box consist 1 red pills and 19 blue pills
second box consist 6 red pills and 14 blue pills
Third box consist 2 red pills and 18 blue pills
a) Prob ( randomly chosen pill is red)
b)Prob ( 1 reds and 10 blue pilss) =
m∠1 = 30° (by Vertical angle theorem)
m∠A = 80° (by Triangle sum theorem)
m∠D = 80° (by Triangle sum theorem)
The value of x is 7.5 and y is 9.
Solution:
∠ACB and ∠DCE are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
⇒ m∠DCE = m∠ACB
⇒ m∠1 = 30° (by Vertical angle theorem)
In triangle ACD,
Triangle sum property:
<em>Sum of the interior angles of the triangle = 180°</em>
⇒ m∠A + m∠C + m∠B = 180°
⇒ m∠A + 30° + 70° = 180°
⇒ m∠A + 100° = 180°
⇒ m∠A = 100° – 180°
⇒ m∠A = 80° (by Triangle sum theorem)
Similarly, m∠D = 80° (by Triangle sum theorem)
In ΔACD and ΔDCE,
All the angles are congruent, so ΔACD and ΔDCE are similar triangles.
<em>In similar triangle corresponding sides are in the same ratio.</em>
Do cross multiplication.
90 = 12x
7.5 = x
Now, to find y:
Do cross multiplication.
9y = 72
Divide by 9, we get
y = 8
Hence the value of x is 7.5 and y is 9.