Answers
The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
⇒ lim θ → 0 ( sin θ / θ ) = 1
Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.
⇒ lim θ → 0 ( sin θ / θ ) = 1
Take LHS;
⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )
⇒ lim θ → 0 ( cos θ / 1 )
⇒ ( cos 0 )
⇒ 1
⇒ RHS
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Related Questions
Please hurry!
Which best describes the relationship between the two triangles below?
Triangle M N L. Angle M is 51 degrees and angle L is 36 degrees. Triangle F H G. Angle F is 51 degrees and angle G is 36 degrees.
Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the third angle is unknown.
Triangle M L N is similar to Triangle F G H because of the angle-angle criterion, Angle M is similar to angle F, Angle L is similar to angle G, and Angle N is similar to angle H.
Triangle M L N may or may not be similar to Triangle F G H because the side lengths are unknown.
Answers
Answer:
Triangle M L N is similar to Triangle F G H because of the third angle theorem, Angle M is congruent to angle F, Angle L is congruent to angle G, and Angle N is congruent to angle H.
Step-by-step explanation:
Triangles are similar if all of the angles are congruent and corresponding to the other triangle and the sides are proportionate. It is important to note that if the angles are congruent then the sides must be proportionate; so, the side lengths are not necessary. Additionally, the third angle theorem states that if two known angles are congruent then the third angles must also be congruent. So, the two triangles must be similar because all of the angles are congruent to their corresponding angles.
A university just acquired more land which is shown by the triangle in the diagram. What is the area of the land that the university just aquired?
Answers
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Area = length x breadth.
Here,
Given : A triangle land which has
height = 2miles
and base = 1.5+ 1.5 = 3 miles
Thus,
To find the area of triangle :
=> Area = 1/2*b*h
=>Area = 3*2/2
=> Area = 3 miles square
Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.
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How does the value of a number change when you divide by 10 100 1000?
Answers
Answer: It gets smaller
Step-by-step explanation: When you divide something by anything, the place value of the digits decreases. The digits move to the right since the number gets smaller, but remember, the decimal point does not move.
True or false? The graph represents a function.
Answers
Answer:
true :)
Step-by-step explanation:
Answer the following as the website for my hwk says I am incorrect:
a) 6/24 as its simplest form (I put 1/4)
b) 52.491 to 2 decimal places (I put 52.49)
c)how many 0.125m drinking straws are needed for a bridge which is 0.85m long (I put both 6.8 and 7)
d) 756.985 × 45 - 14.325 ( I put 34,050)
Answers
b) 52.49
c) 7
d) 34,050
Derrick cut a square cake vertically to make two rectangle slices. Each rectangle had a perimeter of 51 inches.
Answers
Answer:
17 inches
Step-by-step explanation:
Given
[tex]P = 51[/tex] --- Perimeter of rectangle
Required
The length of the original square
The perimeter is calculated as
[tex]51 = 2(L + W)[/tex]
Divide by 2
[tex]25.5 = L + W[/tex]
The rectangle and the square have the same length.
So:
[tex]L = 2W[/tex]
[tex]25.5 = L + W[/tex] becomes
[tex]25.5 = 2W + W[/tex]
[tex]25.5 = 3W[/tex]
Divide both sides by 3
[tex]W = 8.5[/tex]
Recall that:
[tex]L = 2W[/tex]
[tex]L = 2 * 8.5[/tex]
[tex]L = 17[/tex]
A cleaning company charges a fixed amount for a house call and a second amount for each room it cleans the total cost to clean six rooms is $250 and the total cost to clean eight rooms is $320 how much would this company charge to clean two rooms
Answers
The cleaning company would charge $150 for cleaning two rooms according to the fixed charges.
What is fixed amount?A fixed amount is a fixed amount or amount established by agreement or contract. This amount is usually a specified amount, does not change over time, and is usually paid on demand or by a certain date. Fixed amounts are commonly used in loans, insurance, and other financial contracts.
This cost is calculated by dividing the difference between the total cost of 6 and 8 rooms by the number of rooms cleaned (6 - 2 or 4).
= ($250 - $320)/4
= $40
This will give you a price of for each additional room.
To calculate the cost of two rooms, simply add the fixed amount of the home visit and double the cost ($40) for each additional room. That's a total of $150 for two rooms.
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I want to know why D is the correct answer
Answers
Answer:
Cause it is
Step-by-step explanation:
ya know?
Answer:
It's B
Step-by-step explanation:
To find the surface area of a pyramid, you'll multiply L*W*H/3
810 divided by 3 is 405
During January 2012, 50 000 new vehicles were sold in Ontario. About 20% of these were leased. How many vehicles were leased?
Answers
Answer:
10,000 vehicles.
Step-by-step explanation:
20 percent of 50,000 is 10,000.
put this equation in Slope-Intercept form
Y + 2 = -5 ( X + 3 )
Answers
Answer: y=-5x-17
Step-by-step explanation:
Slope-intercept form follows the formula y-mx+b, where m is slope and b is y-intercept. All we have to do is to manipulate the equation to look like y=mx+b.
[tex]y+2=-5(x+3)[/tex] [distribute right side]
[tex]y+2=-5x-15[/tex] [subtract both sides by 2]
[tex]y=-5x-17[/tex]
Now, our equation matches y=mx+b with m=-5 and b=-17.
find asymptotes for y=x^3 + 3^x
Answers
Answer:
No asymptotes
Step-by-step explanation:
The equation provided does not have any asymptotes. Neither for the y-axis or x-axis. It instead goes towards infinity endlessly. Meanining that there is no value that is equal to zero in this equation. The graph below shows the equation graphed, but could not be zoomed out because the equation is endless.
What would the approximate amperage setting be if a welder were set to the high range (150 to 350 amps) and the fine adjustment knob were painting at 5 on a 10 point scale
Answers
On solving the provided question, we can say that the approximate amperage setting be if a welder were set to the high range would be 350 amps.
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.
here,
the approximate amperage setting be if a welder were set to the high range would be 350 amps
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What is the value of 5 + 5.3^4?
810
410
O65
120
Answers
Therefore , the solution of the given problem of expression comes out to be 794.0481.
Describe expression.combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.
• 3 x/2 variable is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.
Here,
Given : 5 + [tex](5.3)^{4}[/tex]
=> 5 + (5.3)*(5.3)*(5.3)*(5.3)
=> 789.0481 + 5
=> 794.0481
Therefore , the solution of the given problem of expression comes out to be 794.0481.
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4cm multiplies 3 whole 1/2
Answers
A 7th-grade class has 14 girls and 10 boys. An 8th-grade class has 11 girls and 13 boys. What is the probability of picking a student from each class and having them both be girls? (Write answer as simplified fraction)
Answers
Answer:
14>10 11<13
Step-by-step explanation:
Please help me on this
Answers
Answer:
12. C
13. B
14. B
Step-by-step explanation:
12 - length of ramp = hypotenuse
given the angle 20, we have hypotenuse and opposite, so we use sin
sin 20* = 10/r
13- tan 46 = x/11, x = 11(tan46) = 11.4
14- cos 46 = 12/x = 17.3
1. r-h=rh
make r the subject and show the steps plz
2. V= pir^2h
make r the subject and show the steps plz
Answers
Answer:
1. N/A
2. √V/pi*h= r
Step-by-step explanation:
1. when you try to get r on one side, the r's cancel out
2. V/pi*h= r^2
√V/pi*h= r
What is the radius and diameter of the following circle?
Answers
Answer:
Diamter is 14 and radius is 7
Step-by-step explanation:
May I have barinliest answer please?
Which expression is equivalent to 4 - 10 (9m – 7:)
0-3 - 90m
O 42 – 54m
O 74 - 90m
O-7 - 54m
Answers
The correct choice will be 74 - 90m
This year, there was 40% more snow than last year. The amount of snow this year is 140% of the amount of snow last year.
1. This year, there were 25% fewer sunny days than last year. The number of sunny days this year is (BLANK)% of the number of sunny days last year.
2. Compared to last month, there was a 50% increase in the number of houses sold this month. The number of houses sold this month is (BLANK)% of the number of houses sold last month.
3. The runner’s time to complete the marathon was 10% less than the time to complete the last marathon. The runner's time to complete the marathon was (BLANK)% of the time to complete the last marathon.
PLEASE FILL IN THE BLANKS. This is in fact the full question
Answers
Answer:
75%150%90%Step-by-step explanation:
You want the percentage multiplier associated with the following changes:
25% decrease50% increase10% decreaseMultiplierTo find the multiplier, add 1 to the change. When you want the multiplier in percent, then add 100% to the change expressed as a percent. (1 = 100%)
1. 25% fewer100% -25% = 75% . . . . of last year
2. 50% increase100% +50% = 150% . . . . of sales last month
3. 10% less100% -10% = 90% . . . . of last marathon's time
please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
sin w = 15/17
Step-by-step explanation:
sin w = opp/hyp
opp of W is VX = 15
hyp is the longest = 17
sin w = 15/17
=========================================================
Explanation:
A drawing may help. See the image below.
Angle X is the 90 degree angle, so angles W and W are the acute angles of right triangle VWX.
The reference angle here is W. Since this is the reference angle, the side opposite angle W is VX = 15. We simply call this "opposite".
The hypotenuse is always opposite the 90 degree angle. This is true no matter what acute reference angle you pick. Since X = 90, this makes WV = 17 the opposite side. Also, the hypotenuse is always the longest side.
The sine of an angle is the ratio of the opposite and hypotenuse
sin(angle) = opposite/hypotenuse
sin(W) = VX/WV
sin(W) = 15/17
Side note: The side XW = 8 isn't used at all. If you wanted to compute cos(W) or tan(W), then you would use side XW.
PLEASE HELP ME GUYS! WILL GIVE 5 stars, brainliest, and everything!!!!
Answers
Answer:
I think it's 388.335
Step-by-step explanation:
I did
(12.75 x 3.75) x2
(3.75 x 8.87) x2
(8.87 x 12.75) x2
and added them all up
Where is the x-intercept in a quadratic formula?
Answers
The x-intercept in a quadratic formula is where the graph of the function crosses the x-axis.
An x-intercept is a point on the graph of a function where the y-coordinate is equal to zero. In other words, it's a point on the graph where the function intersects the x-axis. The x-intercepts of a quadratic formula can be found by setting the y-value equal to zero and solving for x.
The quadratic formula is typically in the form of ax^2 + bx + c =0, thus by setting y=0 we get x = -b/2a and x = -b/2a, these are the x-intercepts where the graph of the function will cross the x-axis. The x-intercepts are also known as the roots or zeroes of the function, and are important for understanding the overall shape of the graph.
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7.4 1; 2; 4; 7; 11; 16; 22;
Describe this pattern:
Answers
Answer:
minus 3 plus 1 plus 2 plus 3 plus 5
Step-by-step explanation:
lines a and b are parallel. which angles is congruent to angle? 4
Answers
Answer:
ANGLE 5 IS CONGURENT TO ANGLE 4
PLEASE MARK BRAINLIEST
what is 629 divided by 8
Answers
Answer:
78.625
Step-by-step explanation:
629 / 8 = 78.625
Answer:
629/8=78.625
OR
[tex]\frac{629}{8}=78\frac{5}{8}[/tex]
what's the equation of a line in slope-intercept form of a line that has a slope of -6 and contains (3,-4)
HELP ME PLEASE!!!!!!
Answers
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]
i need hlep with this q
Answers
The slope of the line is 40 if the points are joined.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
given:
Take two points from the graph as (2, 80) and (4, 160)
Then, the slope of line is
slope, m = ( 160- 80) / ( 4- 2)
slope, m = 80 /2
slope , m = 40
Hence, the slope is 40.
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Find the value of x.
Answers
Answer:
60°
Step-by-step explanation:
as they are a linear pair
120°+x=180
x=180-120
x=60°
WILL MARK BRANLIEST
Question 2 of 5 | Page 2 of
Question 2 (1 point)
The table shows the depth of water in a pond as it is being filled.
What is the average rate of change, in meters per minute, of the depth of the
water in the pond, between t = 2 and t = 5? Round your answer to the nearest
hundredth.
Answers
Answer:
0.47metres per minute
Step-by-step explanation:
you would minus t 5 from 3 which would be 1.34- 0.87 which equals 0.47