When a product is raised to a power, it is equal to the product of each factor raised to that power. Show that this rule does no
1 answer:
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Answer:
52 weeks
Step-by-step explanation:
The club starting with $270 (club 1) is increasing their bank balance each week by ...
... $280 -270 = $10
The club starting with $10 (club 2) is increasing their bank balance each week by ...
... $25 -10 = $15
Club 2 is gaining on Club 1 by $15 -10 = $5 each week. So, the initial difference of $270 -10 = $260 will be overcome in ...
... $260/($5/week) = 52 weeks
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The same result is shown in the attached graph, which also shows that both clubs' bank balances will be $790 at that time.
<u>Given:</u>
The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.
We need to determine the height of the tree.
<u>Height of the tree:</u>
Let the height of the tree be h.
The height of the tree can be determined using the trigonometric ratio.
Thus, we have;
Substituting the values, we get;
Multiplying both sides by 25, we have;
Rounding off to the nearest tenth of a foot, we get;
Thus, the height of the tree is 16.9 feet.
Hence, Option B is the correct answer.
To check if a piecewise defined function is continuous, you need to check how the pieces "glue" together when you step from one domain to the other.
So, the question is: what happens at x=3? If you reach x=3 from values slightly smaller than 3, you obey the rule f(x)=log(3x). So, as you approach 3, you get values closer and closer to
Similarly, if you reach x=3 from values slightly greater than 3, you obey the rule f(x)=(4-x)log(9). So, as you approach 3, you get values closer and closer to
So, the function is continuous at x=3, because both pieces approach log(9) as x approaches 3.