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Oksana_A [137]
3 years ago
5

The table shows the concentration of a reactant in the reaction mixture over a period of time.

Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0
<h3>Option C</h3><h3>The average rate of the reaction over the entire course of the reaction is: 2.0 \times 10^{-3}</h3>

<em><u>Solution:</u></em>

Average rate is the ratio of concentration change to the time taken for the change

Average\ rate = \frac{ \triangle c }{\triangle t }

The concentration of the reactants changes 1.8 M to 0.6 M

here, the time interval given is 0 to 580 sec

Therefore,

Average\ rate = \frac{1.8-0.6}{580} \\\\Average\ rate = \frac{1.2}{580} \\\\Average\ rate \approx 2.0 \times 10^{-3}

Thus option C is correct

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The graph h = −16t^2 + 25t + 5 models the height and time of a ball that was thrown off of a building where h is the height in f
Thepotemich [5.8K]

Answer:

part 1) 0.78 seconds

part 2) 1.74 seconds

Step-by-step explanation:

step 1

At about what time did the ball reach the maximum?

Let

h ----> the height of a ball in feet

t ---> the time in seconds

we have

h(t)=-16t^{2}+25t+5

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

so

The x-coordinate of the vertex represent the time when the ball reach the maximum

Find the vertex

Convert the equation in vertex form

Factor -16

h(t)=-16(t^{2}-\frac{25}{16}t)+5

Complete the square

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+5+\frac{625}{64}

h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}\\h(t)=-16(t^{2}-\frac{25}{16}t+\frac{625}{1,024})+\frac{945}{64}

Rewrite as perfect squares

h(t)=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

The vertex is the point (\frac{25}{32},\frac{945}{64})

therefore

The time when the ball reach the maximum is 25/32 sec or 0.78 sec

step 2

At about what time did the ball reach the minimum?

we know that

The ball reach the minimum when the the ball reach the ground (h=0)

For h=0

0=-16(t-\frac{25}{32})^{2}+\frac{945}{64}

16(t-\frac{25}{32})^{2}=\frac{945}{64}

(t-\frac{25}{32})^{2}=\frac{945}{1,024}

square root both sides

(t-\frac{25}{32})=\pm\frac{\sqrt{945}}{32}

t=\pm\frac{\sqrt{945}}{32}+\frac{25}{32}

the positive value is

t=\frac{\sqrt{945}}{32}+\frac{25}{32}=1.74\ sec

8 0
3 years ago
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romanna [79]

Answer:7 mins

Step-by-step explanation:

47 minus 19 equals 28 4 times 7 equals 8

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3 years ago
The square root 2..25 is _____.
nata0808 [166]

Answer:

Hi there!

Your answer is:

B. 1.5

Step-by-step explanation:

The square root of 2.25 = 1.5

Check your work!

1.5×1.5 = 2.25!!✓

Hope this helps!

7 0
3 years ago
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