Answer:
Step-by-step explanation:
First, we apply the Pythagorean theorem to determine the distance from Manuel’s home to the resort.
S1 = √50²+20²
S1 = √2500+400
S1 = √2900
S1 = 53.85m
Next, we find the distance from Manuel's home to his friend’s residence.
S2 = √15²+10²
S2 = √225+100
S2 = √325
S2 = 18.03m
The distance between the two boys and the resort will be represented as ∆S = S2 - S1.
∆S = 53.84 - 18.03
∆S = 35.81m
Answer: The cube root of 10 is 2.1544, using an initial value of -0.003723.
Step-by-step explanation: The Newton-Raphson method is utilized for root finding, and its formula is NR: X=Xo-(f(x)/f'(x)). Before applying this formula, the derivative of the equation must be determined. Given that X =10, this method was implemented to identify the best root to ascertain the cube root of 10 to 5 significant figures. Utilizing software like Excel for quicker iteration calculations is advisable. The found root in this instance was -0.003723.
To determine how many 3/64 gallon servings can be filled from a total of 2/3 gallon of punch, perform the division of 2/3 by 3/64. The outcome is not a whole number, but this method illustrates the solution. Vinny's total is 2/3 of a gallon of punch, with each guest receiving a measure of 3/64 gallon, which tells us how many can be accommodated by performing<span> (2/3) / (3/64).</span>
Let the number of years Brad has been on the soccer team be represented by x, and let y represent the number of years Scott has been on the same team.
From the information given, we formulate the equations:
5y - 2 = x -----(1)
x + y = 10 -----(2)
Now, substituting equation (1) into equation (2):
5y - 2 + y = 10
6y - 2 = 10
6y = 12
y = 2
Next, substituting this value back to find x:
x = 5×2 - 2
x = 8
So, Brad has spent a total of 8 years in the team.
