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4 years ago

The initial freshman class at a college is 10% smaller 1

Mathematics

1 answer:

Harman [31]4 years ago

7 0

Answer:

875 students are enrolled in this year's freshman class after the first week of classes.

Step-by-step explanation:

Last year, there were 950 students.

This year, the class is 10% smaller. So it's number of students is 100 - 10 = 90% of last year.

0.9*950 = 855

Initially, this year class had 855 students.

During the first week, 20 enrolled.

855 + 20 = 875.

875 students are enrolled in this year's freshman class after the first week of classes.

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If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by y = 56t − 1.86t2.

Zina [86]

Answer: (a) (i)50.42 m/s (ii) 51.35 m/s (iii) 52.094 m/s (iv) 52.2614 m/s (v) 52.27814 m/s

(b) 54.14 m/s

Step-by-step explanation:

The average speed over the given time interval [a,b]: = $\frac{y(b)-y(a)}{b-a}$

Given: If an arrow is shot upward on Mars with a speed of 56 m/s, its height in meters t seconds later is given by $y = 56t − 1.86t^2.$

(a)

(i) average speed = $\frac{y(2)-y(1)}{2-1}$

$=\frac{56(2)-1.86(2)^2-(56(1)-1.86(1)^2)}{1}$

$=50.42$ m/s

(ii) average speed = $\frac{y(1.5)-y(1)}{1.5-1}$

$=\frac{56(1.5)-1.86(1.5)^2-(56(1)-1.86(1)^2)}{0.5}$

$=51.35$ m/s

(iii) average speed = $\frac{y(1.1)-y(1)}{1.1-1}$

$=\frac{56(1.1)-1.86(1.1)^2-(56(1)-1.86(1)^2)}{0.1}$

$=52.094$ m/s

(iv) average speed = $\frac{y(1.01)-y(1)}{1.01-01}$

$=\frac{56(1.01)-1.86(1.01)^2-(56(1)-1.86(1)^2)}{0.01}$

$=52.2614
$ m/s

(v) average speed = $\frac{y(1.001)-y(1)}{1.001-01}$

$=\frac{56(1.001)-1.86(1.001)^2-(56(1)-1.86(1)^2)}{0.001}$

$=52.27814
$ m/s

(b) $y(1)=56(1)-1.86(1)^2$

$=56-1.86$

$= 54.14$ m/s

3 0

3 years ago