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3 years ago

5

A paving company was hired to make a 4 mile section of the highway. They need 700 tons of concrete to complete the job. How many

pounds of concrete will they need to repave the highway?

1 answer:

Arlecino [84]3 years ago

5 0

Answer:

they will need 1,400,000

Step-by-step explanation:

1 ton is 2,000 pounds. so 700x 2,000=1,400,000

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Laura bought a notebook and pencil for $4.50 the notebook cost twice the amount of the pencil

skad [1K]

Answer: N=3

Step-by-step explanation:

Let's represent notebooks with "N" and pencils with "P".

Then,

N + P = 4.50

Since N =2P, we can substitute that directly into the equation:

(2P) + P = 4.50

3P = 4.50 (divide both sides by 3)

P = 1.50

Now that we have P, we can in turn substitute that into the equation.

N + (1.50) = 4.50

N = 3.00

7 0

3 years ago

Find the maximum and minimum values of the curve y=2x³-3x²-12x+10

Ray Of Light [21]

$\underline{ \orange{\huge \boxed{ \frak{Answer : }}}}$

Let ,

$\sf \large \color{purple} y = 2 {x}^{3} - 3 {x}^{2} - 12x + 10 \: --( \: 1 \: )$

$\: \: \:$

Now , Diff wrt ' x ' , we get :

$\sf \: \frac{dy}{dx} = \frac{d}{dx} (2 {x}^{3} - 3 {x}^{2} - 12x + 10) \\ \sf \: \sf \: \frac{dy}{dx} = \frac{d}{dx} \: 2(3 {x}^{2} ) - \frac{d}{dx} 3 {x}^{2} - \frac{d}{dx} 12x + \frac{d}{dx} 10 \\ \sf \: \frac{dy}{dx} =2(3 {x}^{2} ) - 3(2x) - 12(1) + 0 \\ \sf \: \frac{dy}{dx} =6 {x}^{2} - 6x - 12 + 0 \\ \: \sf \red{\frac{dy}{dx} = 6 {x}^{2} 6x - 12 -- (2)}$

$\: \: \:$

For maxima or minima \frac{dy}{dx} = 0

$\: \: \:$

$\sf \: 6 {x}^{2} - 6x - 12 = 0$

$\: \: \:$

Divided by 6 on both side , we get.

$\: \: \:$

$\sf \: {x}^{2} - x - 2 = 0 \\ \sf \: {x}^{2} - 2x + x - 2 = 0 \\ \sf \: x(x - 2) + 1(x - 2) = 0 \\ \sf \: (x - 2)(x + 1) = 0 \\ \sf \: x - 2 = 0 \: \: \bold or \: \: x + 1 = 0 \\ \sf \fbox{x = 2 \: } \: \bold or \: \fbox{ x = - 1}$

$\: \: \:$

Again Diff wrt ‘ x ’ , we get.

$\sf \: \frac{d}{dx} =(\frac{dy}{dx} ) = 6\frac{d}{dx} - 6\frac{d}{dx}x - \frac{d}{dx}12 \\ \sf \: \frac{ {d}^{2}y }{ {dx}^{2} } = 6(2x) - 6(1) - 0 \\ \sf \: \sf \bold{ \frac{ {d}^{2}y }{ {dx}^{2} } =12x - 6}$

$\: \: \:$

At x = 2

$\: \: \:$

$\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12(2) - 6 \\ \: \: \: \sf \: = 24 - 6 \\ \: \: \: \: \sf \red{ = 18 > 0}$

At x = -1

$\: \: \:$

$\sf \: \frac{ {d}^{2}y }{ {dx}^{2} } =12( - 1) - 6 \\ \: \: \: \sf \: = - 12 - 6 \\ \: \: \: \: \sf \red{ = - 18 < 0 }$

$\: \: \:$

x = 2 gives minima value of function.

$\: \: \:$

x = -1 gives maxima value of function.

$\: \: \:$

Now, put x = 2 in eqⁿ ( 1 )

$\: \: \:$

$\sf \: y \: minima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( {2})^{3} - 3 ({2})^{2} - 12(2) + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: = 2(8) - 3(4) - 24 + 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: = 16 - 12 - 24 + 10 \\\sf \: \: \: \: \: \: \: \: \: \: = - 20 + 10 \\\sf \color{red}{\boxed{ = - 10}}$

$\: \: \:$

<u>The </u><u>Point </u><u>of </u><u>minima </u><u>is </u><u>(</u><u> </u><u>2</u><u> </u><u>,</u><u> </u><u>-</u><u>1</u><u>0</u><u> </u><u>)</u><u>.</u>

$\: \: \:$

Now , put x = -1 in eqⁿ ( 1 )

$\sf \: y \: maxima \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2( { - 1})^{3} - 3 ({ - 1})^{2} - 12( - 1) + 10 \\\sf \color{red}{\boxed{ = 17}}$

$\: \: \:$

<u>The point of maxima value is ( -1 , 17 )</u><u>.</u>

$\: \: \:$

<u> $\: \:$ </u>

Hope Helps! :)

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2 years ago

What is two and five eighths minus one and one half

vladimir2022 [97]

So first you convert
2 and 5/8 and
1 and 1/2
2 and 5/8=16/8+5/8=21/8
1 and 1/2=2/2+1/2=3/2
so 21/8-3/2
convert so that the denominator (bottom number) is the same
21/8-([3/2][4/4])
21/8-12/8
9/8=1 and 1/8

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3 years ago

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kati45 [8]

Answer:

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Step-by-step explanation:

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