Step-by-step explanation:
<h2><u>☼︎</u><u>Given :</u></h2>
- The floor of a drawing room consist of 2000 tiles .Each tiles is rectangular in shape , of dimensions ,30 cm × 20 cm.
![\rule{200pt}{3pt}](https://tex.z-dn.net/?f=%5Crule%7B200pt%7D%7B3pt%7D)
<h2><u>☼︎</u><u>To Find :</u></h2>
![\rule{200pt}{3pt}](https://tex.z-dn.net/?f=%5Crule%7B200pt%7D%7B3pt%7D)
<h2><u>☼︎</u><u>Solution :</u></h2>
<u>~ Formula </u><u>U</u><u>s</u><u>e</u><u>d</u><u>:</u>
![\large{\blue{\bigstar}} \: \: {\underline{\boxed{\pink{\sf{ Area{\small_{(Rectangle)}} = Length \times Breadth }}}}} \: \: {\blue{\bigstar}}](https://tex.z-dn.net/?f=%5Clarge%7B%5Cblue%7B%5Cbigstar%7D%7D%20%5C%3A%20%5C%3A%20%7B%5Cunderline%7B%5Cboxed%7B%5Cpink%7B%5Csf%7B%20Area%7B%5Csmall_%7B%28Rectangle%29%7D%7D%20%3D%20Length%20%5Ctimes%20Breadth%20%7D%7D%7D%7D%7D%20%5C%3A%20%5C%3A%20%7B%5Cblue%7B%5Cbigstar%7D%7D)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
<u>~ Calculating the</u><u> Area of Tiles </u>
![{➙ \: {\sf{ Area = Length \times Breadth}}}](https://tex.z-dn.net/?f=%7B%E2%9E%99%20%5C%3A%20%7B%5Csf%7B%20Area%20%3D%20Length%20%5Ctimes%20Breadth%7D%7D%7D)
![{➙ \: {\sf{ Area = 30 \times 20 }}}](https://tex.z-dn.net/?f=%20%7B%E2%9E%99%20%5C%3A%20%7B%5Csf%7B%20Area%20%3D%2030%20%5Ctimes%2020%20%7D%7D%7D%20)
![{\sf{➙ \: Area \: of \: 1 Tiles = {\purple{\bf{ 600 \: cm² }}}}}](https://tex.z-dn.net/?f=%7B%5Csf%7B%E2%9E%99%20%5C%3A%20Area%20%5C%3A%20%20of%20%20%5C%3A%201%20Tiles%20%3D%20%7B%5Cpurple%7B%5Cbf%7B%20600%20%5C%3A%20cm%C2%B2%20%7D%7D%7D%7D%7D)
![\qquad{━━━━━━━━━━━━━━━━━━━━━}](https://tex.z-dn.net/?f=%5Cqquad%7B%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%7D)
<u>~ Calculating Area of the </u><u>Drawing Room :</u>
![{➙ \: {\sf{ Area \: of \: Room \: = No. \: of \: Tiles \times Area \: of \: 1 \: Tile }}}](https://tex.z-dn.net/?f=%7B%E2%9E%99%20%5C%3A%20%7B%5Csf%7B%20Area%20%5C%3A%20of%20%5C%3A%20Room%20%5C%3A%20%3D%20No.%20%5C%3A%20of%20%5C%3A%20Tiles%20%5Ctimes%20Area%20%5C%3A%20of%20%5C%3A%201%20%5C%3A%20Tile%20%7D%7D%7D)
![{➙ \: {\sf{ Area \: of \: Room \: = 2000 \times 600 }}}](https://tex.z-dn.net/?f=%20%7B%E2%9E%99%20%5C%3A%20%7B%5Csf%7B%20Area%20%5C%3A%20of%20%5C%3A%20Room%20%5C%3A%20%3D%202000%20%5Ctimes%20600%20%7D%7D%7D%20)
![{\qquad{\sf{ Area \: of \: Room \: = {\color{darkblue}{\bf{ 1200000 \: cm² }}}}}}](https://tex.z-dn.net/?f=%7B%5Cqquad%7B%5Csf%7B%20Area%20%5C%3A%20of%20%5C%3A%20Room%20%5C%3A%20%3D%20%7B%5Ccolor%7Bdarkblue%7D%7B%5Cbf%7B%201200000%20%5C%3A%20cm%C2%B2%20%7D%7D%7D%7D%7D%7D)
![\qquad{━━━━━━━━━━━━━━━━━━━━━}](https://tex.z-dn.net/?f=%5Cqquad%7B%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%E2%94%81%7D)
<u>~ Therefore :</u>
❝ Area of the Drawing room is 1200000 cm² or 12000 m² . ❞
![\begin{gathered} \\ {\blue{\underline{\red{\rule{300pt}{9pt}}}}}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5C%5C%20%7B%5Cblue%7B%5Cunderline%7B%5Cred%7B%5Crule%7B300pt%7D%7B9pt%7D%7D%7D%7D%7D%5Cend%7Bgathered%7D)
Change the order of integration.
![\displaystyle \int_0^1 \int_{2y}^2 \cos(x^2) \, dx \, dy = \int_0^2 \int_0^{x/2} \cos(x^2) \, dy \, dx \\\\ ~~~~~~~~ = \int_0^2 \cos(x^2) y \bigg|_{y=0}^{y=x/2} \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^2 x \cos(x^2) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E1%20%5Cint_%7B2y%7D%5E2%20%5Ccos%28x%5E2%29%20%5C%2C%20dx%20%5C%2C%20dy%20%3D%20%5Cint_0%5E2%20%5Cint_0%5E%7Bx%2F2%7D%20%5Ccos%28x%5E2%29%20%5C%2C%20dy%20%5C%2C%20dx%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Cint_0%5E2%20%5Ccos%28x%5E2%29%20y%20%5Cbigg%7C_%7By%3D0%7D%5E%7By%3Dx%2F2%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Cfrac12%20%5Cint_0%5E2%20x%20%5Ccos%28x%5E2%29%20%5C%2C%20dx)
Substitute
and
.
![\displaystyle \frac12 \int_0^2 x \cos(x^2) \, dx = \frac14 \int_0^4 \cos(u) \, du = \frac14 \sin(u) \bigg|_{u=0}^{u=4} = \boxed{\frac{\sin(4)}4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac12%20%5Cint_0%5E2%20x%20%5Ccos%28x%5E2%29%20%5C%2C%20dx%20%3D%20%5Cfrac14%20%5Cint_0%5E4%20%5Ccos%28u%29%20%5C%2C%20du%20%3D%20%5Cfrac14%20%5Csin%28u%29%20%5Cbigg%7C_%7Bu%3D0%7D%5E%7Bu%3D4%7D%20%3D%20%5Cboxed%7B%5Cfrac%7B%5Csin%284%29%7D4%7D)
Answer:
Number of child tickets = 9
Number of adult tickets = 36
Number of senior tickets = 27
Step-by-step explanation:
Given:
The ratio of adult tickets to child tickets = 4:1
Ratio of adult tickets to senior tickets = 4:3
Number of total tickets = 72
Find:
The number of each ticket.
Computation:
Ratio between Adult to senior to child = 4:3:1
So,
Number of child tickets = [1 / (4+3+1)]Total tickets
Number of child tickets = [1 / (8)]72
Number of child tickets = 9
Number of adult tickets = [4 / (4+3+1)]Total tickets
Number of adult tickets = 36
Number of senior tickets = [3 / (4+3+1)]Total tickets
Number of senior tickets = 27
Answer:
3
Step-by-step explanation:
please remember when dividing letters or numbers of the same base then their exponents will be minused.
The cost of each pen is $50, because you spend $600 on books leaving $200 to buy FOUR pens, making it $50 per pen