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3 years ago

(810^7)(210^6) simplify the expression and write in scientific notation

Mathematics

1 answer:

lesya [120]3 years ago

8 0

Grouping similar factors together makes this easier:

(8)(2)(10^7)(10^6) = 16(10^13) = 1.6(10^14)

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if you practice a musical instrument each day for 2/3 of an hour how many hours of practice would you get in each week?

RideAnS [48]

In order to find the answer of the given problem above, we need to make the solution below:
Given: 2/3 of an hour = practice each day
2/3 of an hour is equivalent to 40 minutes
And per week, there are 7 days. So we will multiply 40 minutes by 7, and the result is 280 minutes. Since there are 60 minutes in an hour, we divide 280 by 60 and we get 4.67 hours. Therefore, each week, you would get 4.67 hours of practice on playing a musical instrument.

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3 years ago

Find (a) arc length and (b) Area of a sector.

barxatty [35]

Answer:

a) 29.45 cm (2 dp)

b) 220.89 cm² (2 dp)

Step-by-step explanation:

<u>Formula</u>

$\textsf{Arc length}=r \theta$

$\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta$

$\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}$

<u>Calculation</u>

Given:

$\theta=\dfrac{5 \pi}{8}$
r = 15 cm

$\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left(\dfrac{5 \pi}{8}\right)\\& = \dfrac{75}{8} \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}$

$\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(15^2) \left(\dfrac{5 \pi}{8}\right)\\\\& = \dfrac{225}{2}\left(\dfrac{5 \pi}{8}\right)\\\\ & = \dfrac{1125}{16} \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}$

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2 years ago

(8*10^7)(2*10^6) simplify the expression and write in scientific notation

(810^7)(210^6) simplify the expression and write in scientific notation