Morgan spent $30 on school supplies. He

Mathematics

1 answer:

mestny [16]3 years ago

5 0

To help solve this problem, create an equation.

Let x = number of notebooks

$30 = $22.50 + $1.50x. Subtract $22.50 from each side.

$7.5 = $1.50x. Divide each side by $1.50.

5 = x.

Morgan bought 5 notebooks.

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Scientists are studying a bacteria sample. The function f of x equals 256. 1.15 to the x. gives the number of bacteria in the sa

My name is Ann [436]

Answer:

the number of bacteria increases at a rate of 15% each day

Step-by-step explanation:

Given the function :

f(x) = 256(1.15)^x

The function represents an exponential growth function ; comparing the equation with the general form of an exponential growth function :

f(x) = A(1 + r)^t

A = the initial value of the population, = 256

(1 + r),; r = growth rate

Therefore, to solve for r ;

1 + r = 1.15

r = 1.15 - 1 ; r = 0.15

Hence, growth rate = 0.15 = 0.15 * 100% = 15%

Hence, the number of bacteria increases at a rate of 15% each day

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3 years ago

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m>s and a horizontal velocity compon

natka813 [3]

Draw a diagram to illustrate the problem as shown below.

The ball is thrown from A, rises to a maximum height at B, and returns to the original level at C.
Given:
v = 12.0 m/s, vertical component of launch velocity
u = 20 m/s, horizontal component of launch velocity.
Note that g = 9.8 m/s², the acceleration due to gravity.
Wind resistance is ignored.

Part a.
The time, t, required to reach B from A is given by
0 = 12 - 9.8t
t = 12/9.8 = 1.2245 s

Answer: The time is 1.225 s (nearest thousandth)

Part b.
The height attained is
h = 12*1.2245 - 05*9.8*1.2245²
= 7.347 m

Answer: The height attained is 7.35 m (nearest hundredth) above A.

Part c.
When the ball returns the level of point A or C at time t,
0 = 12t - 0.5*9.8t²
t(12 - 4.9t) = 0
t = 0 (point A), or
t = 4.9/2 = 2.45 s (point C)
Notice that 2.45/2 = 1.225 s, which is equal to the time to reach B from A.

Answer:
The time taken to travel from A to C is 2.45 s.
This time is twice the time taken to travel from A to B.

Part d.
The horizontal distance traveled from A to C is
d = 20*2.45 = 49 m

Answer: 49 m

Part e.
x(t) = 20t for horizontal travel
y(t) = 12t - 4.9t² for vertical travel
vy(t) = 12 - 9.8t for vertical velocity
vx(t) = 20 for horizontal velocity.
Graphs of x-t, y-t, vx-t, vy-t are shown below.