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3 years ago

H(x) = x3 - 64x2. Determine the average rate of change of the function between x = -2 and x = 0

1 answer:

7 0

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
\textit{average rate}\\
\textit{ of change}
\end{array}
\\\\\\
H(x)=x^3-64x^2\quad 
\begin{cases}
x_1=-2\\
x_2=0
\end{cases}\implies \cfrac{H(x_2)-H(x_1)}{x_2-x_1}$

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When trying to find a percent, it is best to multiply everything by 100 (as a percentage is out of 100). 0.03*100= 3 and 1*100=100. Therefore, 0.03 as a percent is 3% Hope this helps :)

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3 years ago

a 400 g of a liquid of density 1.6g/cm3 is made from mixing liquids of density 1.2g/cm3 and 1.8g/cm3 find the mass of the liquid

gogolik [260]

Answer:

133.33g

Step-by-step explanation:

Let the:

Mass of 1.2g/cm³ of liquid = x

Mass of 1.8g/cm³ of liquid = y

From our Question above, our system of equations is given as:

x + y = 400........ Equation 1

x = 400 - y

1.2 × x + 1.8 × y = 1.6 × 400

1.2x + 1.8y = 640..... Equation 2

We substitute, 400 - y for x in Equation 2

1.2(400 - y) + 1.8y = 640

480 - 1.2y + 1.8y = 640

- 1.2y + 1.8y = 640 - 480

0.6y = 160

y = 160/0.6y

y = 266.67 g

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x = 400 - y

x = 400 - 266.67g

x = 133.33g

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3 years ago

All 231 students in math club went on a field trip some rode in vans that held 7 people and some rode on buses that held 25 peop

MariettaO [177]

Answer:

8 vans

7 buses

Step-by-step explanation:

Let there be "b" buses

and "v" vans

Since 7 people is the capacity of vans, the total capacity is

Also, since 25 people is the capacity of 1 bus, the total capacity is

25b

In total 231 people, so we can write our first equation as:

7v + 25b = 231

Now, we know there are 15 vehicles (bus + vans) in total, so we can write our 2nd equation as:

v + b = 15

Now, we solve for v and b. Let's solve the 2nd equation for v and substitute that into 1st and solve for b first:

v + b = 15

v = 15 - b

Now,

$7v + 25b = 231\\7(15-b) + 25b = 231\\105-7b+25b=231\\18b=126\\b=7$

Hence, there are 7 buses

Since 15 vehicles in total, the number of vans is:

15 - 7 = 8 vans

So,

8 vans

7 buses

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4 years ago

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mrs_skeptik [129]

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