Question

Find the value of unknown figure plz tell i will mark as brainliest

Answer 1

Answer:

1. $2^{3}$ x $3^{6}$

ii. 18

b. -12

2. nth = a + (n - 1)d

ii. k = 103

3. $x^{o}$ = $27^{o}$

4. Volume = 25.025 $m^{3}$

Step-by-step explanation:

1. Prime factors of 5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

                                       = $2^{3}$ x $3^{6}$

ii. $\sqrt[3]{5832}$ = 18

b. 2$a^{2}$ - 3$b^{2}$ + 3abc

a = 3, b = 2, c = -1

Thus,

2$(3)^{2}$ - 3$(2)^{2}$ + 3(3 x 2 x -1)

= 18 - 12 - 18

= -12

2. The required formula is;

nth = a + (n - 1)d

where: a is the first term, n is the number of terms in the sequence and d is the common difference.

b. kth term = 304, then

304 = -2 + (k - 1) 3

      = -2 + 3k -3

      = 3k - 5

3k = 304 + 5

3k =  309

k = $\frac{309}{3}$

  = 103

k = 103

3. Comparing <DAB and < EBC;

<DAB ≅ <EBC = $x^{o}$

<BEC = $90^{o}$ (right angle property)

<C = $63^{o}$

Thus,

<B + <C + <E = $180^{o}$ (sum of angles in a triangle)

$x^{o}$ + $63^{o}$ + $90^{o}$ = $180^{o}$

$x^{o}$ + 153 = $180^{o}$

$x^{o}$ = 180 - 153

   = 27

$x^{o}$ = $27^{o}$

4. Volume of a cylinder = $\pi$$r^{2}$h

where r is the radius and h is the height of the cylinder.

Diameter = 3.5 m, h = 2.6 m

r = $\frac{3.5}{2}$

r = $\frac{7}{4}$ m

So that,

Volume = $\frac{22}{7}$ x $(\frac{7}{4}) ^{2}$ x 2.6

             = $\frac{22}{7}$ x $\frac{49}{16}$ x $\frac{13}{5}$

             = 25$\frac{1}{40}$

Volume = 25.025 $m^{3}$