Answer:
The stone would take approximately 10.107 seconds to fall 500 meters.
Step-by-step explanation:
According to the statement of the problem, the following relationship of direct proportionality is built:
Where:
- Time spent by the stone, measured in seconds.
- Height change experimented by the stone, measured in meters.
- Proportionality constant, measured in 
.
First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:
If 
and 
, then:
Then, the expression is 
. Finally, if 
, then the time is:
The stone would take approximately 10.107 seconds to fall 500 meters.
Answer:
Word problem 3
Step-by-step explanation:
Word Problem one is a subtraction problem since Felicia is giving away two marbles to Lucas. Word Problem two is a division problem since Felicia is evenly dividing the number of marbles she has into two bags. Word Problem three is a multiplication problem because Ryan has two times as many marbles that Felicia does. Word Problem four is an addition problem because she found two more marbles while she already has eight marbles. Keywords for subtraction word problems are: fewer than, decrease, take away, less than, minus, difference, change, lost reduced, and subtract. Keywords for division word problems are: As much, cut up, groups, equally, sharing, half, how many in each, parts, per percent, quotient, ratio, and separated. Keywords for multiplication word problems are: double, every, factor, increased, multiplied product, times, and tripled.
Answer:
Step-by-step explanation:
Simplify expression with rational exponents can look like a huge thing when you first see them with those fractions sitting up there in the exponent but let's remember our properties for dealing with exponents. We can apply those with fractions as well.
Examples
(a) 
From above, we have a power to a power, so, we can think of multiplying the exponents.
i.e.
Let's recall that when we are dealing with exponents that are fractions, we can simplify them just like normal fractions.
SO;
Let's take a look at another example
Here, we apply the 
to both 27 and 
Let us recall that in the rational exponent, the denominator is the root and the numerator is the exponent of such a particular number.
∴
![= \Bigg (\sqrt[3]{27}^{5} \times x^{10} }\Bigg)](https://tex.z-dn.net/?f=%3D%20%5CBigg%20%28%5Csqrt%5B3%5D%7B27%7D%5E%7B5%7D%20%5Ctimes%20x%5E%7B10%7D%20%7D%5CBigg%29)
Answer:
∠ADB≅∠ABC by the Alternate Interior Angles Theorem
∠CAD≅∠ACB by the Alternate Interior Angles Theorem
∠BAD and ∠ADV are supplementary by the Consecutive Interior Angle Theorem
∠ABC and ∠BCD are supplementary by the Consecutive Interior Angle Theorem
