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4 years ago

What equation this show The cost of 10 pounds of potatoes is 8 dollars

1 answer:

8 0

To formulate the equation that shows the cost of 10 pounds of potatoes is 8 dollars we proceed as follows;
suppose the cost 1 pound is x;
thus,
total cost=(amount in pounds)*(price of one pound)
total cost=$8
amount=10 pounds
cost of one pound=x
thus the equation is;
8=10x

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Using division to find the ratios that are equivalent to 40:28 and please show the steps.

makkiz [27]

Answer:

10:7

Step-by-step explanation:

40:28 are both divisible by 4. 40/4 is 10. 28/4 is 7. So the ratio would be 10:7 since neither is divisible by both the same number, this is the final ratio.

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2 years ago

Which sentence has the quotation marks placed correctly ?

a_sh-v [17]

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3 years ago

Read 2 more answers

Let C be the curve of intersection of the parabolic cylinder x^2 = 2y, and the surface 3z = xy. Find the exact length of C from

Maslowich

I've attached a plot of the intersection (highlighted in red) between the parabolic cylinder (orange) and the hyperbolic paraboloid (blue).

The arc length can be computed with a line integral, but first we'll need a parameterization for $C$ . This is easy enough to do. First fix any one variable. For convenience, choose $x$ .

Now, $x^2=2y\implies y=\dfrac{x^2}2$ , and $3z=xy\implies z=\dfrac{x^3}6$ . The intersection is thus parameterized by the vector-valued function

$\mathbf r(x)=\left\langle x,\dfrac{x^2}2,\dfrac{x^3}6\right\rangle$

where $0\le x\le 4$ . The arc length is computed with the integral

$\displaystyle\int_C\mathrm dS=\int_0^4\|\mathbf r'(x)\|\,\mathrm dx=\int_0^4\sqrt{x^2+\dfrac{x^4}4+\dfrac{x^6}{36}}\,\mathrm dx$

Some rewriting:

$\sqrt{x^2+\dfrac{x^4}4+\dfrac{x^6}{36}}=\sqrt{\dfrac{x^2}{36}}\sqrt{x^4+9x^2+36}=\dfrac x6\sqrt{x^4+9x^2+36}$

Complete the square to get

$x^4+9x^2+36=\left(x^2+\dfrac92\right)^2+\dfrac{63}4$

So in the integral, you can substitute $y=x^2+\dfrac92$ to get

$\displaystyle\frac16\int_0^4x\sqrt{\left(x^2+\frac92\right)^2+\frac{63}4}\,\mathrm dx=\frac1{12}\int_{9/2}^{41/2}\sqrt{y^2+\frac{63}4}\,\mathrm dy$

Next substitute $y=\dfrac{\sqrt{63}}2\tan z$ , so that the integral becomes

$\displaystyle\frac1{12}\int_{9/2}^{41/2}\sqrt{y^2+\frac{63}4}\,\mathrm dy=\frac{21}{16}\int_{\arctan(3/\sqrt7)}^{\arctan(41/(3\sqrt7))}\sec^3z\,\mathrm dz$

This is a fairly standard integral (it even has its own Wiki page, if you're not familiar with the derivation):

$\displaystyle\int\sec^3z\,\mathrm dz=\frac12\sec z\tan z+\frac12\ln|\sec x+\tan x|+C$

So the arc length is

$\displaystyle\frac{21}{32}\left(\sec z\tan z+\ln|\sec x+\tan x|\right)\bigg|_{z=\arctan(3/\sqrt7)}^{z=\arctan(41/(3\sqrt7))}=\frac{21}{32}\ln\left(\frac{41+4\sqrt{109}}{21}\right)+\frac{41\sqrt{109}}{24}-\frac98$

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4 years ago

The next model of sports car is will cost 14.1% more than the car model. The current model cost $31,000. How will the price incr

Novosadov [1.4K]

Answer: the price of the next model is $35371

Step-by-step explanation:

The cost of the current model of the car is $31,000

The next model of sports car will cost 14.1% more than the car model. This means that the amount by which the cist of the current model of the car will increase is

14.1/100 × 31000 = 0.141 × 31000 =$4371

The price of the next model of the car would be the sum of the previous model's price and the increase in price. It becomes

31000 + 4371 = $35371

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4 years ago

Ms. Yazzie earns $16.40 per hour at her job. She works 372 hours a week for 50 weeks a year

IceJOKER [234]

Answer:

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3 years ago