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mina [271]
3 years ago
5

Determine the area, in square feet, of the smallest square that can contain a circle with a radius of 8 feet.

Mathematics
1 answer:
bixtya [17]3 years ago
3 0

Answer: 256ft Squared

Explanation:

Length= 8 x 2=16ft

Area: 16^2 (16 x 16)= 256ft^2

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POINTS!! I NEED HELP WITH THIS, WILL GIVE BRAINLIEST TO BEST ANSWER
neonofarm [45]

Answer:

Conjecture

Disjunction

Counterexample

Conjunction

Inductive reasoning

Conditional

Step-by-step explanation:

I used Quizlet and I knew most of them.

5 0
3 years ago
Read 2 more answers
Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a funda
pantera1 [17]

Answer:

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

y= c_1x^4+c_2x^6

Step-by-step explanation:

Given equation is

x^2y'' - 9xy+24y=0

This Euler Cauchy type differential equation.

So, we can let

y=x^m

Differentiate with respect to x

y'= mx^{m-1}

Again differentiate with respect to x

y''= m(m-1)x^{m-2}

Putting the value of y, y' and y'' in the differential equation

x^2m(m-1) x^{m-2} - 9 x m x^{m-1}+24x^m=0

\Rightarrow m(m-1)x^m-9mx^m+24x^m=0

\Rightarrow m^2-m-9m+24=0

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

⇒m(m-6)-4(m-6)=0

⇒(m-6)(m-4)=0

⇒m = 6,4

Therefore the auxiliary equation has two distinct and unequal root.

The general solution of this equation is

y_1(x)=x^4

and

y_2(x)=x^6

First we compute the Wronskian

W(x)= \left|\begin{array}{cc}y_1(x)&y_2(x)\\y'_1(x)&y'_2(x)\end{array}\right|

         = \left|\begin{array}{cc}x^4&x^6\\4x^3&6x^5\end{array}\right|

         =x⁴×6x⁵- x⁶×4x³    

        =6x⁹-4x⁹

        =2x⁹

       ≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

y= c_1x^4+c_2x^6

5 0
3 years ago
Find all values of x in the interval [0, 2π] that satisfy the equation.<br> 3 sin(2x) = 3 cos(x)
natita [175]
3 sin ( 2 x ) = 3 cos x
3 · 2 sin x cos x - 3 cos x = 0
6 sin x cos x - 3 cos x = 0   /: 3
2 sin x cos x - cos x = 0
cos x ( 2 sin x - 1 )
cos x = 0,  
x 1 = π/2,  x 2 = 3π/2;
2 sin x - 1 = 0
2 sin x = 1
sin x = 1/2
x 3 = π/6,  x 4 = 5π/6.
7 0
3 years ago
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the
m_a_m_a [10]

Answer:

Required volume is \frac{4864\pi}{3} unit.

Step-by-step explanation:

Given equations of curves,

y=32-x^2, y=x^2

substitute second in first we will get,

x^2=36-x^2\implies x^2=16\implies x=\pm 4

When x=4, y=16 and x=-4, y=16. Thus both curves intersect at the points (4,16),(-4,16). And thus -4.

Considering width of the representative rectangle as \Delta x which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,

V_{Shell}=(\textit{Length of box})\times (\textit{Width of box})\times (\textit{Thikness of box})

Now,

Length of generating box=Length of \Delta x from line x=4(axis of revolution)=circumference of the shell=(4-x)

Width of box=(36-x^2)-x^2

Hence,

V_{Shell}

=\int_{-4}^{4}2\pi (4-x)(36-2x^2)dx

=2\pi\int_{-4}^{4}(144-36x-8x^2+2x^3)dx

=2\pi\{144\big[x\big]_{-4}^{4}-18\big[x^2\big]_{-4}^{4}-\frac{8}{3}\big[x^3\big]_{-4}^{4}+\frac{1}{2}\big[x^4\big]_{-4}^{4}\}

=\frac{4864\pi}{3}

which is required volume of generating area.

3 0
3 years ago
Solve for z<br><br> Z - 4/9 - 1/3 = 5/9
Aleks04 [339]

Answer:

4/3

Step-by-step explanation:

<em>Z-</em><em>4</em><em>/</em><em>9</em><em>-</em><em>1</em><em>/</em><em>3</em><em>=</em><em>5</em><em>/</em><em>9</em>

<em>Z-</em><em>7</em><em>/</em><em>9</em><em>=</em><em>5</em><em>/</em><em>9</em>

<em>Z</em><em>=</em><em>5</em><em>/</em><em>9</em><em>+</em><em>7</em><em>/</em><em>9</em><em> </em>

<em>Z</em><em>=</em><em>4</em><em>/</em><em>3</em><em> </em><em>not</em><em> </em><em>sure</em><em> </em><em />

3 0
3 years ago
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