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3 years ago

Find the value of AB.

Mathematics

2 answers:

grin007 [14]3 years ago

8 0

Step-by-step explanation:

Since all side lengths of smaller squares are equal, we have

$3x+4=4x-1$

$x=5$

Since length of AB is twice of the side length of smaller squares,

$\bar{AB}=2(3x+4)=2(3\cdot5+4)=38$

lukranit [14]3 years ago

4 0

Answer:

AB=38

SEE THE IMAGE FOR SOLUTION

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the cylinder has radius 4√3 and hight h. the total surface area of the cylinder is 56π√6. find the exact value of h giving the a

Arte-miy333 [17]

The area of the cylinder is a function of its height (h) and radius, ( $\mathbf{4\sqrt 3}$ )

The exact value of h is: $\mathbf{7\sqrt 2- 4\sqrt 3}$

The given parameters are:

$\mathbf{Area =56\pi\sqrt 6}$

$\mathbf{r=4\sqrt 3}$

The surface area of a cylinder is calculated as:

$\mathbf{Area = 2\pi rh + 2\pi r^2}$

Substitute values for Area

$\mathbf{56\pi\sqrt 6= 2\pi rh + 2\pi r^2}$

Divide through by pi

$\mathbf{56\sqrt 6= 2 rh + 2r^2}$

Substitute value for r

$\mathbf{56\sqrt 6= 2 (4\sqrt 3)h + 2(4\sqrt 3)^2}$

$\mathbf{56\sqrt 6= 8h\sqrt 3 + 2\times 48}$

$\mathbf{56\sqrt 6= 8h\sqrt 3 + 96}$

Collect like terms

$\mathbf{8h\sqrt 3 = 56\sqrt 6- 96}$

Make h the subject

$\mathbf{h = \frac{56\sqrt 6}{8\sqrt 3}- \frac{96}{8\sqrt 3}}$

$\mathbf{h = 7\sqrt 2- \frac{12}{\sqrt 3}}$

Rationalize

$\mathbf{h = 7\sqrt 2- \frac{12\sqrt 3}{3}}$

$\mathbf{h = 7\sqrt 2- 4\sqrt 3}$

Hence, the exact value of h is: $\mathbf{7\sqrt 2- 4\sqrt 3}$

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