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2 years ago

I don't understand number 6 please help

Mathematics

2 answers:

ycow [4]2 years ago

7 0

X^-n = 1/x^n
Your fraction becomes:
1/ {(m^5 t^2)(27m^6t^3)} now combine the powers in the denominator
1/ (27 m^11 t^5)

Elanso [62]2 years ago

5 0

On the top, you take both bases and exponents and put them on the denominator, which changes the exponents to positive. You then apply the exponent outside of the parentheses to 3, m^2, and t, changing them to 27m^6t^3. Then combine the like terms, combining m6 and m5 into m11, and combining t2 and t3 into t5. The remaining answer should be 1/27m^11t^5

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

(i)

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(ii)

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Step-by-step explanation:

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

height of ball (a) = 10m

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

(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

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

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