Your yard is in a shape of a trapezoid

Mathematics

1 answer:

g100num [7]3 years ago

4 0

Answer: You would tell him 1,425ft².

Step-by-step explanation:

First, you need to know the equation for finding the area of a trapezoid, which is ½h(b1+b2) .

When you plug in all the number you have into the equation, you have a new equation essentially that says, ½×30(65+50) .

When you start solving the equation, you need to do parentheses first, so 65+30, which would get you 95. This would then turn the equation into ½×30(95) .

Next, you have to do 30×95, which would come out to be 2850. When you do this, your equation would now be ½×2850 , or essentially 2850÷2 .

When you do the last and final step of the problem, which is ½×2850, you would get 1425. But since it's area, your answer would 1425ft².

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A ball is thrown vertically upwards from the ground. It rises to a height of 10m and then falls and bounces. After each bounce,

Citrus2011 [14]

${\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}$

(i)

$\sf{a_n = 20 \times {( \frac{2}{3} )}^{n - 1} }$

(ii)

$\sf S_n = 60 \{1 - { \frac{2}{3}}^{n} \}$

Step-by-step explanation:

$\underline\red{\textsf{Given :-}}$

height of ball (a) = 10m

fraction of height decreases by each bounce (r) = 2/3

$\underline\pink{\textsf{Solution :-}}$

(i) We will use here geometric progression formula to find height an times

${\blue{\sf{a_n = a {r}^{n - 1} }}} \\ \sf{a_n = 20 \times { \frac{2}{3} }^{n - 1} }$

(ii) here we will use the sum formula of geometric progression for finding the total nth impact

$\orange {\sf{S_n = a \times \frac{(1 - {r}^{n} )}{1 - r} }} \\ \sf S_n = 20 \times \frac{1 - ( { \frac{2}{3} })^{n} }{1 - \frac{2}{3} } \\ \sf S_n = 20 \times \frac{1 - {( \frac{2}{3}) }^{n} }{ \frac{1}{3} } \\ \sf S_n = 3 \times 20 \times \{1 - ( { \frac{2}{3}) }^{n} \} \\ \purple{\sf S_n = 60 \{1 - { \frac{2}{3} }^{n} \}}$