A basketball is rolling with a velocity of 0.5 meters/second relative to the ground and due north. A tennis ball is rolling with
1 answer:
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Answer:
50 Educators
Step-by-step explanation:
To tackle this question, the initial step is to calculate the amount of teachers prior to the addition of new staff. For this, I devised Model 1. In this model, teachers are positioned at the top of the ratio and students at the bottom. The variable X represents the number of teachers we are determining. Utilizing this model, I computed 2,100 multiplied by 1 (2,100) and then divided by 14 to conclude there were 150 teachers. Next, I formed a similar model with the updated student-teacher ratio (Model 2). This time, I multiplied 2,100 by 2 (which is 4,200) and divided by 21 to ascertain there are 200 teachers. Having established both the initial and the increased counts of educators, subtracting the original from the new gives you the tally of new teachers, which results in an increase of 50 teachers.
Answer:
The tangent plane equation for the hyperboloid
.
Step-by-step explanation:
We have
The ellipsoid's equation is
The equation for the tangent plane at the point
(Given)
The hyperboloid's equation is
F(x,y,z)=
The tangent plane equation at point
The tangent plane equation for the hyperboloid is
The tangent plane equation
Hence, the required tangent plane equation for the hyperboloid is
a) The sequence is geometric.
b) The subsequent term is 486
c) The rule is:
The 20th term will be: a_{20}=6973568802
Step-by-step explanation:
The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.
Part a) Is this sequence arithmetic or geometric?
An arithmetic sequence has a constant difference between consecutive terms.
In the given series 6, 18, 54, 162,
18-6 = 12
54-18= 36
The differences are not constant, thus it isn’t arithmetic.
A geometric sequence maintains a constant ratio between consecutive terms.
In this series 6, 18, 54, 162,
18/6 = 3
54/18 = 3
162/54 = 3
The ratios remain constant; therefore, the sequence is geometric.
The sequence in question is geometric.
Part b) How can you determine the next number in the series?
The next number can be calculated using the following formula:
where a_n= nth term
a= first term
r= common ratio
The next number represents the 5th term of the sequence.
To find the 5th term:
Thus, the next term in the sequence is 486
Part c) What is the rule for determining the 20th week? Calculate the 20th week.
The rule for determining the 20th week is:
Here n=20
Calculating the 20th week
Purchasing the first 10 bricks at $4.50 each totals $45. The subsequent 10 bricks at $3.50 each add $35. This uses $80, leaving $20 to buy bricks priced at $2.50 each, allowing for 8 more bricks. Altogether, $100 can buy 28 bricks.
