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lozanna [386]
2 years ago
6

Tony made 2 fruit pies. After his family ate some of each pie, 13 of one pie remained and 56 of the other pie remained. About ho

w much pie is remaining?
Mathematics
1 answer:
omeli [17]2 years ago
4 0

Answer:

<h2>There remains 7/6 of pie.</h2>

Step-by-step explanation:

Givens

The remaining parts are 1/3 of one pie and 5/6 of the other pie.

To find how much pie is remaining, we just need to sum those fractions.

\frac{1}{3}+\frac{5}{6}=\frac{6+15}{18} =\frac{21}{18} =\frac{7}{6}

Therefore, there remains 7/6 of pie. They ate just 1/6.

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We can use t=x^2 to solve this
Once we do that we will have simple square equation which we know how to solve.

t^2 + 3t + 2 = 0

t1 = -1
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x1 = √-1 = i
x2 = -i

x3 = √-2 = i√2
x4 = -i√2

Make sure you know that i^2 = -1 and (-i)^2 = -1 which gives us solutions we got...
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The recipe makes enough stew for 6 people, and the ingredients cost $9.75. How much would it cost to serve 24 people? Use the ra
maxonik [38]
Well, you have to multiply the 6 by 4 and the 9.75 by 4 because there are going to be 24 people. 6 • 4 is 24 and 9.75 • 4 = 39!
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A bookkeeper needs to post the cost of a desk and chair into his records. The cost of the desk was five times the cost of the ch
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Caleb’s school is five blocks due north of his home, and the library is two blocks due west of his home. If each city block is a
Ilia_Sergeevich [38]

Answer:

The closest straight-line distance from Caleb's school to the library is:

  • <u>1480.92 feet</u>

Step-by-step explanation:

Imagine a triangle, where five blocks are a side and two blocks another side, to obtain the closest straight-line distance from Caleb's school to the library you can use the Pythagoras theorem, where the hypotenuse is the closest straight-line:

  • perpendicular^{2} +base^{2} =hypotenuse^{2}

Clearing the hypotenuse is:

  • \sqrt{perpendicular^{2}+base^{2}}= hypotenuse

Now, you only need to identify the distance in each case:

Five blocks = 275 feet * 5 = 1375 feet.

Two blocks = 275 feet * 2 = 550 feet.

At last, you must replace the distances found in the equation cleared:

  • \sqrt{1375 feet^{2}+550 feet^{2}}= hypotenuse
  • <u>Hypotenuse or closest straight-line = 1480.92 feet</u>.

Identifying this, the closest straight-line distance from Caleb's school to the library is <u>1480.92 feet</u>.

4 0
2 years ago
Use Green's Theorem to evaluate F · dr. C (Check the orientation of the curve before applying the theorem.) F(x, y) = e−x + y2,
Yuki888 [10]

Notice that C is traversed clockwise. Green's theorem applies to curves with a counterclockwise orientation, so we'll have to multiply the area integral by -1.

By Green's theorem, with the vector field \vec F(x,y)=P(x,y)\,\vec\imath+Q(x,y)\,\vec\jmath,

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=-\iint_D\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)\,\mathrm dA

where D is the region with boundary C. The partial derivatives are

\dfrac{\partial(e^{-y}+x^2)}{\partial x}=2x

\dfrac{\partial(e^{-x}+y^2)}{\partial y}=2y

so that the double integral is

\displaystyle\iint_D\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)\,\mathrm dA=\int_{-\pi/2}^{\pi/2}\int_0^{\cos x}2(y-x)\,\mathrm dy\,\mathrm dx=\boxed{\frac\pi2}

3 0
1 year ago
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