find the limit as x approaches 0 of x/sin3x

Answers

Answer 1
[tex] \lim_{x \to 0} \frac{x}{sin 3x} = \\ =\frac{0}{0}= \\ = \lim_{x \to 0} \frac{3x}{3sin3x} = [/tex]
= 1/3  ( because the limit as x approaches 0 of  t/sin t = 1 ). 

Related Questions


The decimal number 0.66 is an example of a repeating decimal.

True
or
False

pls answer quick

Answers

If there is a line on top then yes, if not then no, the lone on top means repeating and for .66 repeating would be 2/3 which is something you memorize after typing it into a calc a lot

Answer:

the anwser is FALSE

Step-by-step explanation:


this year 90 students signed up for the group Talent contest if all the groups have the same number of students how many groups could be formed
a. 4 or 5 groups
b. 5 or 6 groups.
c. 4 or 6 groups
d. 4 or 9 groups

Answers

The answer is B. 5 or 6 groups. 90 has to be divisible by the number. 90/5 = 18 90/6 = 15

Given g(x)=x^2-7x+1/4 show that the least possible value of g(x) is -12

Answers

The least vale of the function would be the vertex. To find the vertex first find the x value by using x= -b/2a
x=7/2 or 3.5
Now plug this in for x to find the y value.
y = (7/2)^2 -7(7/2) + (1/4)
y = (49/4) -(49/2) + (1/4)
y = (49/4) -(98/4) + (1/4)
y = (-48/4)
y = -12
The vertex is (3.5,-12)
The minimum (or max) of a function is the y value of the vertex so the min value is -12

What is the value of the discriminant in the equation shown below?
x^2+3x-6=0
...?

Answers

Discriminant = b^2 - 4ac

a = 1

b = 3

c = -6

3^2 - 4(1x-6)

9 - (4 x -6 )

9 - -24 = 33

Therefore it has 2 real roots

Given:ax^2+bx+c=0The discriminant is:b^2−4(a)(c)so it would be 33x^2-4(1)(6)
3^2 - 4(1)(-6)
[a] x^2  [+b] x  [+c] = 0[1] x^2  [+3] x  [-6] = 09 - 4(1)(-6) = 9 - (-24) 
=33

What is 117.28 rounded to the nearest 10 cents?

Answers

117.30                                                                                                                                                                                                                                                              maybe this will help
 
The correct answer is 117.30

Mrs. Curtis wants to buy online tickets for a concert. Two options are given here.

Option 1: $53 for each ticket plus a shipping fee of $10

Option 2: $55 for each ticket and free shipping

What is a system of equations to represent the costs of the tickets?

Express your equations in the form of y=mx+by=mx+b where x is the number of tickets purchased and y is the total cost.

Option 1:______________

Option 2: ______________

Answers

Option 1: y=53x+10
Option 2: y=55x

help :(
Which situations can be represented by a linear function?

Select each correct answer.

a. Every year, Luisa puts $10 into her savings account.

b. Every day, the number of bacteria in the dish is 3 times what it was the previous day.

c. A country's population increases by 0.8% each year.

d. The barrel leaks 0.5 L of water each day.

Answers

The barrel leaks 0.5 L of water each day.

Every year, Luisa puts $10 into her savings account.

Solve (x 6)(x - 4) = -16

Answers

2x+2= -16
2x= -14
x= -7

Answer:

{-4, 2} Original poster forgot to add the + sign

Step-by-step explanation:

Solve (x + 6)(x - 4) = -16

{-4, 6}

{-4, 2}

{-12, 22}

Odyssey

The formula c=5/9(f-32) is used to convert the temperature in degrees fahrenheit (
f. to the temperature in degrees celsius (
c. what is the temperature in degrees celsius (
c. that is equal to 113 degrees fahrenheit (
f.?

Answers

we are going to have to sub in 113 for f and solve for c

c = 5/9(f - 32)
c = 5/9(113 - 32)
c = 5/9(81)
c = 405/9
c = 45 <===

The conversion of fahrenheit to degree celsius for  f = 113 is 45 degree celsius

What is a mathematical expression?

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a mathematical expression.

Given, formula of temperature conversion of degree celsius to fahrenheit

c=5/9(f-32)

If f = 113

then putting the value on the equation, we get

c = 5/9(113-32)

c = 5/9(81)

c = 5*9

c = 45 degree celsius

Therefore, The conversion of fahrenheit to degree celsius for  f = 113 is 45 degree celsius

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What is the range of possible values for x? The diagram is not to scale.?

Answers

Answer:

Range : 0° < x < 17°

Step-by-step explanation:

In any triangle, the smallest angle is opposite to the smallest side.

So, In ΔABD , the side which faces ∠ABD is AD whose length is 22 units.....(1)

And, in ΔCBD, the side which faces ∠CBD is CD whose length is 30 units....(2)

Now, from equations (1) and (2) We get,

∠ABD < ∠CBD

So, ∠ABD lies between 0° to 34°

[tex]\Rightarrow 0 < 2\cdot x<34\\\Rightarrow 0<x<\frac{34}{2}\\\Rightarrow0<x<17[/tex]

∴ Range of x is 0° to 17°


Answer:

Range : 0° < x < 17°

Step-by-step explanation:

In any triangle, the smallest angle is opposite to the smallest side.

So, In ΔABD, the side which faces ∠ABD is AD whose length is 22 units.....(1)

And, in ΔCBD, the side which faces ∠CBD is CD whose length is 30 units....(2)

Now, from equations (1) and (2) We get,

∠ABD < ∠CBD

So, ∠ABD lies between 0° to 34°

∴ Range of x is 0° to 17°

Renna pushed the button for the elevator to go up, but it would not move. The weight limit for the elevator is 450 kilograms, but the current group of passengers weighs a total of 750 kilograms. Renna wants to determine how many 70-kilogram passengers need to get off the elevator.
Let p represent the number of excess passengers. Write an inequality to determine the number of passengers who need to get off the elevator to meet the weight requirement.

Answers

Weigth limit: 450 kg

Passengers weight: 750 kg

Excess weight: 300 kg

Number of 70 kg - passengers: p

Inequality:

70p  ≥ 300 kg 

Solution of the inequality:

p ≥ 300/70

p ≥ 4.3

Given that p is integer, p ≥ 5

Of course, p must also be less than the initial number of passengers.


It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track? ...?

Answers

 Length of outer track = sum of length of 10 pieces = circumference of the outer circle 


if R is the Radius of outer circle then... 

Circumference of the outer track = 2pi*R 


Similarly the circumference of the inner track (with radius r) = 2pi*r 


length of each outer piece is 3.4 inch more than length of inner piece 

So total outer length is 10*3.4 =34 inches more than the inner length. 


=> Outer Circumference - Inner Circumference = 34 inches 

=> 2pi*R - 2pi*r = 34 

=> 2pi(R -r) = 34 

=> R-r = 34/2pi = 5.41 inches 

=> R-r = Width of the track = 5.41 inches
Final answer:

To find the width of the track, add up the lengths of all the inside and outside arcs and subtract the total length of the inside arcs from the total length of the outside arcs.

Explanation:

To find the width of the track, we first need to determine the difference between the inside and outside arcs of each piece. Let's assume the outside arc has a length of A inches. According to the question, the inside arc is 3.4 inches shorter than the outside arc. Therefore, the inside arc has a length of A - 3.4 inches.



Since there are ten identical pieces forming the circular track, we can add up the lengths of all the inside arcs and all the outside arcs to find the total distance covered by the track. The width of the track is then the difference between the total length of the outside arcs and the total length of the inside arcs.



Let's express the width of the track as a function of A. The total length of the outside arcs is 10A inches, and the total length of the inside arcs is 10(A - 3.4) inches. Therefore, the width of the track is:



Width = 10A - 10(A - 3.4) inches.

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(1.8 * 10^2) * (5 * 10^2)

Answers

The answer is 90,000

4. which property is illustrated by the following statement?
2x(6)=(6)2x
A. associative property of addition
B. communtative property of multiplication
C. inverse property of multiplication
D. communtative property of addition

5. which property is illustrated by the following statement?
5g+7=7+5g
A. communtative property of multiplication
B. Inverse property of multiplication
C. communtative property of addition
D. associative property of addition

Answers

2 x ( 6 ) = ( 6 ) 2 x
A B = B A
Answer:
B ) Commutative property of multiplication
Another statement:
5 g + 7 = 7 + 5 g
A + B = B + A
Answer:
C ) Commutative property of addition.

The answer for #5 is C.

the product of two integers is -21. the diference between the two integers is -10. the sum of the two integers is 4. what are the two integers

Answers

The two integers are -3 and 7.
it would be 7 and -3
7 x -3 = -21
difference = -10
the sum = 4

hope this helps you

Which of the following would you round and estimate to a sum of 11?

3.41 + 8.051
3.65 + 7.992
4.25 + 8.103
4.89 + 7.431

Answers

I hope this helps you

Answer:

3.41+8.051

Step-by-step explanation:

whats 64 divided by 8

Answers

Hello :)

[tex] \frac{64}{8}=8 [/tex]

Answer: 8

Step-by-step explanation:

Step 1: eight times one equals eight. Eight times two equals 16, as you keep multiplying, you'll eventually get to 8 times 8 equals 64. To find 64 divided by 8, you find the other "piece" which be what makes 8 times the number equal to 64. :)

If the sum of the measures of the interior angles of a convex polygon is 2160o, how many sides does the polygon have?

Answers

Sum of interior angles of a polygon of n sides is equal to (n. 180 - 360) given 180n - 360 = 2160

180n = 2160 + 360
n = 2520/180
n = 14
so, the polygon have 14 sides.

hope this help

Kevin, while calculating his tax adjustments, notes that he can make adjustments of $3,435 for contributions to his retirement plan, $3,393 for business losses, and $1,128 for business expenses. If Kevin’s gross income is $45,942, what is his adjusted gross income?

a. $53,898
b. $40,242
c. $41,421
d. $37,986

Answers

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Amount of Kevin's gross income = $45942

Amount he contribute to his retirement plan = $3435

Amount he lost in business losses = $3393

Amount he incurred in business expenses = $1128

So, His adjusted gross income will be

[tex]45942-(3435+3393+1128)\\\\=45942-(7956)\\\\=\$37986[/tex]

Hence, his adjusted gross income is $37,986.

Hence, Option 'D' is correct.

For the fruit punch, keira needed 2 gallons of grape juice. she already had 2 quarts of grape juice. grape juice comes in bottles of 1 pint. how many bottles of grape juice does she need to buy? bottles

Answers

 1 gallon = 4 qts....so 2 gallons = 8 qts
so she needed 8 qts.....she had 2....so she still needs 6 qts.

1 qt = 2 pints...so 6 qts = (6 x 2) = 12 pints...and each bottle is 1 pints...so she needs 12 bottles
she needs to buy 12 bottles

divide 56 in a ratio of 5:3

Answers

There are 5 "parts" and 3 "parts"; which total "8 parts" (5 + 3 = 8); so, each part must be 56/8 = 7. so each part must be 56/7 = 8 
5 x 7 is 35
3 x 7 is 21 
___________
So the answer is 35:21 .

Geometry help please! ty
Can you explain to me how to find the area of rectangles and triangles on a coordinate plane? Images below...

Answers

What was it? I`m on this test too.

If all four interior angles of quadrilateral P have the same measure, which of the following statements must be true?

1. All sides of P have equal length.
2. The diagonals of P are perpendicular.
3. The measure of each interior angle of P is 90 degrees.

Thanks in advance! ...?

Answers

3. The measure of each interior angle of P is 90 degrees.

If martha earns $3.25 per hour for baby-sitting, how much will she earn in: 2.5 hours? 4.0 hours? 5.5 hours?

Answers

In 2.5 hours: $3.25 * (2.5) = $8.125 → Round to: $8.13 .

In 4.0 hours: $3.25 * (4)  = $13.00

In 5.5 hours: $3.25 * (5.5) = $ 17.875 → Round to: $17.88 .
____________________________________________

Answer: Martha will earns for 2.5 hours of baby sitting [tex]\approx\$8.13[/tex]

She will earns for 4.0 hours of baby sitting =[tex]\$13[/tex]

She will earns for 5.5 hours of baby sitting =[tex]\approx\$17.88[/tex]

Step-by-step explanation:

Given: Martha earns for each hour of baby sitting = $3.25

Then, Martha will earns for 2.5 hours of baby sitting =[tex]2.5\times3.25=\$8.125\approx\$8.13[/tex]

She will earns for 4.0 hours of baby sitting =[tex]4.0\times3.25=\$13[/tex]

She will earns for 5.5 hours of baby sitting =[tex]5.5\times3.25=\$17.875\approx\$17.88[/tex]

The difference between the square of two numbers is five. Twice the square of the second number is subtracted from three times the square of the first number is 19. Find the numbers. Please show work. The difference between the square of two numbers is five. Twice the square of the second number is subtracted from three times the square of the first number is 19. Find the numbers. Please show work.

Answers

Final answer:

The two possible pairs of numbers that fit the given equations are (√7, 2) and (-√7, -2). We find these by setting up two equations based on the provided conditions and solving them simultaneously.

Explanation:

Let's denote the first number as 'x' and the second number as 'y'. We have two equations from the given information:

1. x² - y² = 5

2. 3x² - 2y² = 19

We can solve these equations simultaneously to find the values of 'x' and 'y'. The first step in solving a system of linear equations is to multiply the equations by what's needed to get the coefficients of one of the variables to match, so it can be eliminated when the equations are added or subtracted. Let's multiply the first equation by 3 and the second equation by 1. We then have:

3x² - 3y² = 15

3x² - 2y² = 19

If we subtract the second equation from the first, we get:

-y² = -4

which leads to y = 2 or y = -2 (squared numbers are always positive). Substituting '2' for 'y' in the first original equation, we find that x = √7 or x = -√7. Therefore, the possible pairs of numbers are (√7, 2) and (-√7, -2).

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please help me with this problem thanks!

Answers

use the formula of a reactangle and a triangle.
Answer= 110400 sq. mi

20 is 50% of what number? If necessary, round to the nearest tenth.
Is it 10.0?

Answers

Because 50% is the same as .5 or 1/2, that means 20 is half of the original number.
20+20=40
40 is the correct answer.

20 is 50 percent of the number 40.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let 20 is 50% of the number x.

Now, 50% of x=20

0.50×x=20

0.5x=20

x=20/0.5

x=40

Therefore, 20 is 50 percent of the number 40.

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If a 16 in. by 24 in. picture has a wooden frame "x" in. wide surrounding it, what equation can be used to find the total area of the picture and frame? ...?

Answers

The total area of the the picture and frame is given by the equation A = (16 + 2x)(24 + 2x) = 384 + 32x + 48x + 4x^2 = 4x^2 + 80x^2 + 384
Area = width x length

Area = (16+2x)*(24+2x)

Give the excluded value(s) for the following fraction.

y+5/y^2+4y-32

Answers

Since we can divide by 0, we can clearly see that  there  is no way denominator can be 0. So, lets start :[tex]y^2+4y-32=0[/tex].
The exluded  values are lying in the y and we hav eto find them :[tex]y^2+4y-32=(y+8)*(y-4)=0[/tex]
According to the info above,[tex]y+8=0 or y-4=0[/tex]
y is -8 and 4. 
That's all!

Answer:

y is -8 and 4.

Step-by-step explanation:

What is the leg length of an isosceles right triangle with a hypotenuse of 32 inches?

Answers

isosceleses means 2 sides have equal legnths
that means that those are the legs
a^2+b^2=c^2
a and b are legs and c is the hypotonuse
 
a=b
2a^2=c^2
c=32
2a^2=32^2
2a^2=1024
divide both sides by 2
a^2=512
sqrt both sides
a=16√2

the legnth of each leg is 16√2 or aprox 22.63 inches
it would be about 22.63 for each leg
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