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3 years ago

Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form. HELP PLEASE!!

Mathematics

1 answer:

Nataliya [291]3 years ago

8 0

Answer:

Perimeter = 22*sqrt(2)
Area = 60.5 inches
D

Step-by-step explanation:

Remark

You need 2 facts.

A square has 4 equal sides.
It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

a^2 + a^2 = c^2
2a^2 = c^2

Givens

c = 11

Solution

2a^2 = 11^2
2a^2 = 121 Divide by 2
a^2 = 121/2 Take the square root of both sides
sqrt(a^2) = sqr(121/2)
a = 11/sqrt(2) Rationalize the denominator
a = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]
a = 11 * sqrt(2) / 2

Perimeter

P = 4s

P = 4*11*sqrt(2)/2
P = 44*sqrt(2)/2
P = 22*sqrt(2)

You don't need the area. The answer is D

Area

Area = s^2
Area = (11*sqrt(2)/2 ) ^2
Area = 121 * 2 / 4
Area = 60.5

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Directions - Find the slope ( rise over run)

Zanzabum

Answer:

-1/3

Step-by-step explanation:

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3 years ago

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G verify that the divergence theorem is true for the vector field f on the region

Alenkasestr [34]

$\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1$

Converting to spherical coordinates, we have

$\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi$

On the other hand, we can parameterize the boundary of $E$ by

$\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle$

with $0\le u\le2\pi$ and $0\le v\le\pi$ . Now, consider the surface element

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=36\langle\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v\rangle\,\mathrm du\,\mathrm dv$

So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

$\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv$
$=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi$

as required.

3 0

3 years ago

Solve for X......:) <3

Vedmedyk [2.9K]

Answer:

x = 88

Step-by-step explanation:

All angles in a triangle equal 180 degrees. So our equation will be:

x + 48 + (x - 44) = 180

x + 48 + x - 44 = 180

2x + 48 - 44 = 180

2x + 4 = 180

2x = 176

x = 88

Hope this helps!

8 0

3 years ago

Sally lives in City A and works for the department of transportation. She needs to inspect the weigh stations in each of four di

galben [10]

Answer:

She can visit the cities in 192 ways

Step-by-step explanation:

If Sally starts from city A and after going to 4 cities she returns to home,

then that can be in 4! = 24 ways. (permutation of 4 distinct objects)

If between the time she visits cities, she comes home once,

then cities can be visited in,

$4! \times 3_{C_{1}}$ = 72 ways. (permutation of 4 distinct objects and choosing 1 gap among the 3 )

If between the time she visits cities, she comes home twice,

then cities can be visited in,

$4! \times 3_{C_{2}}$ =72 ways. (permutation of 4 distinct objects and finding 2 gaps among the 3)

If between the time she visits cities, she comes home thrice,

then cities can be visited in,

$4! \times 3_{C_{3}}$ = 24 ways. (permutation of 4 distinct objects and choosing 3 gaps among the 3)

Now, she can't come home more than thrice in between the time she visits cities (since there are 4 cities to visit only)

So, the number of ways she can visit cities = (24+ 72 + 72 + 24)

= 192

6 0

3 years ago

What is the coefficient of x^3 in the expansion of (2x-3)^5?

docker41 [41]

Answer:

309

Step-by-step explanation:

(2x-)^5

step 1

1 5 10 10 5 1

step 2

1(2x¹-3^0) 5(2x²-3^5) 10(2x³-3^4)

10(2x^4-3³) 5(2x^5-3²)

1(2x^0-3¹)

step 3

(2x) (10x²-243) (20x³-81) (20x^4-27)

(10x^5-9) (2-3)

step 4

2 -243-61-7 +1 -1=309

4 0

3 years ago