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Elza [17]
3 years ago
5

What is the value of the sin3x/6x; as x approaches to zero

Mathematics
1 answer:
nikklg [1K]3 years ago
6 0

Step-by-step explanation:

When x = 0,

sin3x / 6x = 0 / 0, which is an indeterminate form.

Hence we use L'Hospital's rule:

d/dx (sin3x) = 3cos3x

d/dx (6x) = 6

Now we have 3cos3x / 6 or 0.5cos3x.

When x = 0, 0.5cos3x = 0.5(1) = 0.5.

Hence the limit is 0.5.

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Letter d is s geometric sequence. You multiply or divide by the same number (r), common ratio to be a geometric sequence
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3 years ago
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The sum of the angle measures of a quadrilateral is 360°. Write and solve an equation to find the value of X.​
uranmaximum [27]

Answer:

1). x° + 100° + 120° + 100° = 360°

2). x = 40

Step-by-step explanation:

Formula for the sum of the interior angles of a polygon = (n-2)\times 180

Where n = number of sides of the polygon

From the picture attached,

For n = 4,

Sum of the interior angles of the given polygon = (4 - 2) × 180°

                                                                                = 360°

Therefore, equation for the sum of interior angles will be,

x° + 100° + 120° + 100° = 360°

x° + 320° = 360°

x° = 360° - 320°

x° = 40°

6 0
3 years ago
Choose the triangle that seems to be congruent to the given one.
arsen [322]

AFB, the sides are similar

6 0
3 years ago
In a certain liberal arts college with about 10,000 students, 53% are males. If two students from this college are selected at r
tamaranim1 [39]

Answer:

There is a 50.18% probability that they are of the same gender.

Step-by-step explanation:

We have these following percentages:

53% of the students are males.

47% of the students are females.

If two students from this college are selected at random, what is the probability that they are of the same gender?

The probability that each is male is 53%. So the probability of both being males is

P_{MM} = 0.53*0.53 = 0.2809

The probability that each is female is 47%. So the probability of both being females is

P_{FF} = 0.47*0.47 = 0.2209

The probabilty that both are the same gender is:

P = P_{MM} + P_{FF} = 0.2809 + 0.2209 = 0.5018

There is a 50.18% probability that they are of the same gender.

7 0
4 years ago
Bloomington Nail Salon is having a special this month on services. Over the weekend, they performed 49 manicures and 16 pedicure
marshall27 [118]

Answer: The salon charges $16 for a manicure and $25 for a pedicure.

Step-by-step explanation:

Let x represent the amount charged by the salon for a manicure.

Let y represent the amount charged by the salon for a pedicure.

Over the weekend, they performed 49 manicures and 16 pedicures, bringing in a total of $1,184 in receipts. It means that

49x + 16y = 1184- - - - - - - - - - 1

So far this week, they have administered 31 manicures and 33 pedicures, with receipts totalling $1,321. It means that

31x + 33y = 1321- - - - - - - - - - 2

Multiplying equation 1 by 31 and equation 2 by 49, it becomes

1519x + 496y = 36704

1519x + 1617y = 64729

Subtracting, it becomes

- 1121y = - 28025

y = - 28025/- 1121

y = $25

Substituting y = 25 into equation 1, it becomes

49x + 16 × 25 = 1184

49x + 400 = 1184

49x = 1184 - 400

49x = 784

x = 784/49

x = $16

5 0
4 years ago
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