When an object is thrown upwards with a speed of 64 ft/sec, its height above the ground is given by the function h(t)=−16t2+64t , where t is the time in seconds after it has been thrown. At what time will the object reach its highest point?

The object will reach its highest point 0.5 seconds after it has been thrown.

Step-by-step explanation:

The object reaches its maximum height when velocity is equal to zero, the velocity is the derivative of function height. That is:

(1)

Where is the velocity of the object at time , in feet per seconds.

If we know that and , then the time when object reaches its highest point is:

The object will reach its highest point 0.5 seconds after it has been thrown.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form