De l'Hospital rule applies to undetermined forms like
If we evaluate your limit directly, we have
which is neither of the two forms covered by the theorem.
So, in order to apply it, we need to write the limit as follows: we start with
Using the identity , we can rewrite the function as
Using the rule , we have
Since the exponential function is continuous, we have
In other words, we can focus on the exponent alone to solve the limit. So, we're focusing on
Which we can rewrite as
Now the limit comes in the form 0/0, so we can apply the theorem: we derive both numerator and denominator to get
So, the limit of the exponent is -6, which implies that the whole expression tends to
Answer:
0.3056 or 30.56%
Step-by-step explanation:
The volume of the grapefruit with the peel is:
When removing the peel, the grapefruit diameter becomes 10 cm (take out 1 cm of peel from each side). The volume of the grapefruit without the peel is:
The percentage of the volume correspondent to the peel is given by the difference between both volumes, divided by the total volume:
30.56% of volume of the grapefruit is the peel.
Answer:
Ground speed = 131.25 km/h
Bearing = 92.68º
Step-by-step explanation:
If we imagine a triangle to depict the question with one side 134 km/h at an angle of 78º to the right of vertical (the plane's speed vector).
At the end, we have a line 21 km/h at an angle of 180 (from north), a vertical down from the end of the plane's vector. This vertex is angle B
This makes a triangle with the interior angle B of 78º.
The 3rd side is the ground speed which we can find using the Cosine rule:
b² = a² + c² - 2•a•c•cos(78)
b² = 134² + 21² - 2•134•21•cos(78)
b² = 17226.873
b = 131.25 km/h
The true course bearing" is the ground track. Thus;
Using the Sine rule to find angle A, we have;
(sin(A))/34= sin(78)/b
Thus,
sin(A) = (34 x sin(78))/131.25
sin(A) = 0.2534
A = sin^(-1)0.2534
A = 14.68º
Ground track = A + 78 = 14.68 + 78 = 92.68º
The profit which the manufacturer gained from the warranties is a. $105,430,050
<h3>Calculations and Parameters:</h3>
Given that count 12% of 532,475:
532,475 - 100%
x - 12%
x= 63, 897.
This means that 63, 897 guitars were sold with a full-replacement warranty and 532,475-63,897=468,578 electric guitars were sold without a full-replacement warranty.
Hence, to find the gain of the manufacturer, $225·468,578
=$105,430,050 from the warranties.
Option A is correct: $105,430,050
Read more about profit and loss here:
brainly.com/question/2165353
One solution is x = 1 and y = 443 because
0.10(1) + 0.05(443) = 22.25.
So, (1, 443) is a solution.
Since, 1 dime = 2 nickels,
Increment of 1 in x-value = Decrease of 2 in y-value.
Therefore, the set of possible solutions are {(1, 443), (2, 441), (3, 439), (4, 437),......(222, 1)}