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Mathematics

2 answers:

Kipish [7]2 years ago

7 0

It is longing because it is the definition of yearning

tatiyna2 years ago

4 0

Answer:

longing

Step-by-step explanation:

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What is the height of an isosceles trapezoid, if the lengths of its bases are 5m and 11m, and the length of a leg 4m

son4ous [18]

In the isosceles trapezoid ABCD, draw two perpendiculars AM and BL from A and B to the side CD.

Now, LM = BA = 5 m

CD = CL + LM + MD

= CL + 5 + CL (CL = MD)

= 2CL + 5

But, CD = 11

Therefore, 2CL + 5 = 11

2CL = 11 - 5

= 6

CL = 6/2 = 3m

MD = 3m

Now, consider the right triangle AMD.

We have,

$AM^{2} = AD^{2} - MD^{2}$

= $4^{2} - 3^{2}$

= 16 - 9

= 7

Hence, height of the isosceles trapezoid = AM = $\sqrt{7} m$

6 0

3 years ago

Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about th

Nezavi [6.7K]

The two curves intersect when

$-x^2=6-5x\implies x^2-5x+6=(x-3)(x-2)=0\implies x=2,x=3$

The region bounded by $x=0$ and the two curves "ends" with a vertex where $x=2$ . So over the interval [0, 2], we have $6-5x\ge-x^2$ , so that the volume is

$\displaystyle2\pi\int_0^2x(6-5x+x^2)\,\mathrm dx=\boxed{\frac{16\pi}3}$

That is, each cylindrical shell has a radius of $x$ and height $(6-5x)-(-x^2)=6-5x+x^2$ , and their contribution to the total volume is $2\pi$ times the radius and height.