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andreev551 [17]
4 years ago
14

julie will build a rectangular pen for her dog against a barn. A wall from the barn will from one side of the pen. She has 32m o

f fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area. What will be the dimensions of julie's pen?
Mathematics
2 answers:
Scorpion4ik [409]4 years ago
5 0
The answer is 8 m by 16 m. I just answered this on my quiz.
charle [14.2K]4 years ago
3 0

the answer is 8 and 16

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azamat

Answer:

area = 45

Step-by-step explanation:

triangle = 7*6. / 2 = 21

rectangle 4*6=24

24+21= 45ft squared

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What would 526 ÷by 2 be
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Evaluate the indefinite integral of: arctan(4x) dx.
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Let vector F = (6 x^2 y + 2 y^3 + 4 e^x) i + (7 e^{y^2} + 54 x) j . Consider the line integral of vector F around the circle of
balu736 [363]

Denote the circle of radius a by C. C is simple and closed, so by Green's theorem the line integral reduces to a double integral over the interior of C (call it D):

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_C(6x^2y+2y^3+4e^x)\,\mathrm dx+(7e^{y^2}+54x)\,\mathrm dy

=\displaystyle\iint_D\left(\frac{\partial(7e^{y^2}+54x)}{\partial x}-\frac{\partial(6x^2y+2y^3+4e^x)}{\partial y}\right)\,\mathrm dx\,\mathrm dy

=\displaystyle\iint_D(54-6x^2-6y^2)\,\mathrm dx\,\mathrm dy

D is a circle of radius a, so we can write the double integral in polar coordinates as

\displaystyle\iint_D(54-6x^2-6y^2)\,\mathrm dx\,\mathrm dy=\int_0^{2\pi}\int_0^a(54-6r^2)r\,\mathrm dr\,\mathrm d\theta

a. For a=1, we have

\displaystyle\int_0^{2\pi}\int_0^1(54-6r^2)r\,\mathrm dr\,\mathrm d\theta=2\pi\int_0^1(54r-6r^3)\,\mathrm dr=\boxed{51\pi}

b. Let I(a) denote the integral with unknown parameter a,

I(a)=12\pi\int_0^a(9r-r^3)\,\mathrm dr\,\mathrm d\theta

By the fundamental theorem of calculus,

I'(a)=12\pi(9a-a^3)

I(a) has critical points when

12\pi(9a-a^3)=12\pi a(9-a^2)=0\implies a=0,a=\pm3

If a=0, then line integral is 0, so we ignore that critical point. For the other two, we would find I(\pm3)=243\pi.

8 0
3 years ago
What is the measure of AX, in degrees?<br> N<br> 6<br> Х<br> 6<br> 70<br> у
Alexus [3.1K]

Answer:

C

Step-by-step explanation:

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The base angles are therefore congruent, that is

∠ Y = ∠ Z = 70°

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6 0
3 years ago
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