<span>(Y-3)^2 = 4y -12 <=> Y^2 - 6Y + 9 = 4y - 12 <=> 4y = Y^2 - 6Y + 21 <=> y = (Y^2 - 6Y + 21)/4. Solving the equation for y means that we have to express y relative to the other quantities in the equation.</span>
Answer:
Which formula can be used to find the surface area of the hemisphere? ... Recall that the formula for the volume for a sphere is v=4/3πr^3 and the ... Type A is a spherical ball with a radius of 12 inches. ... r=6cm. SA=1/2(4πr^2)+πr^2. SA=2π(6)^2+π(6)^2. SA=72(3.14)+36(3.14) ... The diameter of the hemisphere is 48 feet.
Step-by-step explanation:
Answer:
<em>Option A; the tournament did begin with 128 teams</em>
Step-by-step explanation:
We can see that this equation is represented by compound interest, in other words an exponential function, either being exponential growth or exponential decay;
f ( x ) = a + ( b )^x, where a ⇒ start value, b ⇒ constant, x ⇒ ( almost always considered ) time, but in this case rounds
Option A; The equation is given to be t ( x ) = 128 * ( 1/2 )^x. Given by the above, 128 should represent the start value, hinting that the tournament <em>did indeed begin with 128 teams</em>
Option B; As the rounds increase the number of teams approach 128. Now mind you 128 is the start value, not the end value, which would mean that <em>this statement is false</em>
Option C; The tournament began with 1/2 teams. Theoretically that would not be possible, but besides that the tournament began with 128 teams, only differed by 1/2 times as much every round. <em>This statement is thus false</em>
Option D; This situation actually represents exponential decay. If each round the number of teams differed by 1/2 times as much, the number of teams remaining is less than before, and thus this models exponential decay, not growth<em> ( statement is false )</em>
<em>Answer : Option A; the tournament did begin with 128 teams</em>
Answer:
32.7°
Step-by-step explanation:
Use the formula for law of cosines, for this question we need so solve for angle B, so use...
b² = a² + c² - 2(a)(c)Cos B
We are given a, b, and c, so plug them in...
55² = 90² + 50² - 2(90)(50)Cos B
Now simplify...
3,025 = 8100 + 2500 - (9000)Cos B
-7,575 = -(9000)Cos B (subtract 8100 and 2500 from both sides)
0.841666667 = Cos B (divide both sides by -9000)
Cos^(-1) 0.841666667 = B (use cosine inverse function on calculator)
32.68346376° = B
32.7° = B
