Answer: The height of the palm tree is 21 feet.
Step-by-step explanation:
We can use a ratio to solve this:
Actual height to shadow for both objects. The fraction equivalents must be equal.
6/8 = x/28 . Cross multiply
6(28) = 8x
168 = 8x Divide both sides by 8 (8's "cancel" on the right)
168/8 =8x/8
21 = x . This gives us the tree's height as 21 feet.
<em>Another way to solve this is to use the ratios, but simplify the first fraction</em>
<em>6/8 = 3/4</em>
<em>Then multiply the length of the shadow by 3/4</em>
<em>3/4 × 28 = height</em>
<em>28÷4 = 7 7 × 3 = 21</em>
<em>21 feet= the height of the palm tree.</em>
<h3>
Answer: Aryan spent more time exercising.</h3>
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Explanation:
Use your calculator to convert each fraction into decimal form
2/3 = 0.67 approximately
3/4 = 0.75 exact
The decimal 0.75 is larger than 0.67, in which we can think of it like saying "75 is larger than 67".
So 0.67 < 0.75 which leads to 2/3 < 3/4.
Aryan spent more time exercising.
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We could stop there, but if you wanted to know how much longer he spent exercising, then we subtract the two fractions to get
3/4 - 2/3
9/12 - 8/12
(9-8)/12
1/12
Aryan spent 1/12 of an hour longer exercising compared to Naitik
1/12 hour = (1/12)*60 = 60/12 = 5 minutes
He spent 5 extra minutes exercising.
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Notes:
- 2/3 hours = (2/3)*60 = 40 minutes
- 3/4 hours = (3/4)*60 = 45 minutes
- 45-40 = 5 extra minutes of exercise
Answer:
64 * b * b * b * b * b * b
Step-by-step explanation:
Apply exponent to number first, then expand the variable's exponent into repeated multiplication.
Answer:
4. -2s^9
7. 8b^10
Step-by-step explanation:
First, focus on the number part of the expression. For 4), multiply -2 x -1 x -1 = -2. Then, look at the exponents. When you're multiplying exponents with the same base (in number 4, the base is s), you can add the exponents.
2+3+4 = 9; which makes it s^9. Multiply -2 x s^9, which gives you -2s^9.
Same thing for 7). Multiply all the numbers first. this gives you 8. (Remember two negatives equals a positive). Add all of the exponents of b together, which gives you 10. (when a variable has no exponent, it means that the exponent is 1.) Multiplying 8 and b^10 should give you 8b^10.
It may help to brush up on exponent rules and sign rules.
