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.
Using limits, it is found that the value of the function is of 0.5.
The limit given is:
[tex]\lim_{x \rightarrow 0} \frac{\sin{(3x)}}{6x}[/tex]
The following property is used:
[tex]\lim_{x \rightarrow 0} \frac{\sin{(ax)}}{ax} = 1[/tex]
Hence, multiplying the numerator and denominator by 0.5:
[tex]\lim_{x \rightarrow 0} \frac{\sin{(3x)}}{6x} = 0.5\lim_{x \rightarrow 0} \frac{\sin{(3x)}}{3x} = 0.5(1) = 0.5[/tex]
The value of the function is of 0.5.
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The price of Stock A at 9 A.M. was $12.98. Since then the price has been increasing at the rate of $0.07 each hour. At noon the price of Stock B rates continue, in how many hours will the prices of the two stocks be that same?
Can someone plz help me with this
Answer:
m<ABC = 40
m<FEC = 90
because the triangle is isoscles
A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. How far will it travel in ? In 1 hour?
Answer:
45 miles.
Step-by-step explanation:
Ok, so it goes 1.75 (1 3/4) miles in 2 minutes and 20 seconds, or 140 seconds. Divide 1.75 miles by 140 and you get 0.0125 miles per second, or 0.75 (3/4) miles per minute. Multiply 0.75 by 60 minutes and you get 45 miles.
What is the area of rectangle WXYZ?
A. 4 square units
B. 7.5 square units
C. 10 square units
D.15 square units
A sequence of digits has the property that each pair of successive digits, taken in the order written, forms a decimal numeral representing a multiple of either 1717 or 2323. If the first digit is 99 and the sequence is finite, what is its last (possible) digit
Answer:
Concept: Mathematical Sequences
Let An be 99 a double digit multiple The sequence is finite. Finite= restricted and not bounded to positive infinity By that logic the last possible digit is 999999999999999999999999999999999999999999999Dylan and Abigail are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Dylan is 269 miles away from the stadium and Abigail is 329 miles away from the stadium. Dylan is driving along the highway at a speed of 45 miles per hour and Abigail is driving at speed of 57 miles per hour. Let DD represent Dylan's distance, in miles, away from the stadium tt hours after noon. Let AA represent Abigail's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t,t, and determine the number hours after noon, t,t, when Dylan and Abigail are the same distance from the stadium.
Answer:
D= 269-45t A=329-57t
5 hours
After jeeves lost 7 pounds, he weighed 124 pounds. How
much did he weigh originally?
Answer:
He now weighs 131 pounds.
Step-by-step explanation:
You can work backwards.
Past weight - 7 = 124
Past weight = 124 + 7
Past weight= 131
Is the discriminant of g positive, zero, or negative?
Answer:
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.
Step-by-step explanation:
The discriminant of the quadratic equation g is negative.
In algebra, the discriminant of a quadratic equation plays a crucial role in determining the nature of its roots. For a quadratic equation of the form ax² + bx + c = 0, the discriminant is given by Δ = b² - 4ac. Depending on whether the discriminant is positive, zero, or negative, we can determine the types of roots the equation possesses.
When the discriminant is negative, it implies that the quadratic equation has no real roots. In this case, the graph of the quadratic equation does not intersect the x-axis at all, indicating that it has complex roots. These complex roots are a pair of complex conjugates of the form (p + qi) and (p - qi), where p and q are real numbers and i is the imaginary unit (√(-1)).
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mrs aleaze tells her stuents there will be 50 questions on their test and 20 percent of them will be word problems how much problems are on the test
sience 20% of 50 is equal to _ there will be_ word problems
the value of a second-hand car is £8000
Each year it loses 20% of it value at the start of this year. work out its value in 5 years time.
pls show working out
I will mark brainest and rate 5 stars
Answer:
£2,621.44
Step-by-step explanation:
Original cost of car = £8000
If it looses 20% of its value yearly
Value at the end of first year
80% * 8000
= 0.8 * 8000
= 6400
Value at the end of second year
80% * 6400
= 0.8 * 6400
= 5120
Value at the end of third year
80% * 5120
= 0.8 * 5120
= 4096
Value at the end of fourth year
80% * 4096
= 0.8 * 4096
= 3,276.8
Value at the end of fifth year
80% * 3,276.8
= 0.8 * 3,276.8
= 2,621.44
Hence the value in 5 years time will be £2,621.44
Need help on this, please
Answer: 30 something?
Step-by-step explanation:
What is 14 x7/8
PLEAAAAASSSSSEEEEEEE HELP.
Answer:
49/4
Step-by-step explanation:
Answer: 12 1/4
Step-by-step explanation:
Which of these is the algebraic expression for "4 times the sum of 2 and y?"
4. 2 + y
4(2 + y)
2 +4.7
2(4 + y)
Fill in the blank 8(? +3) =48+24
Answer:
6
Step-by-step explanation:
treat the ? as an x. you need to get it by itself. but first you should distribute the 8.
8x + 24 = 48 +24
8x+24 = 72
take the 24 and subtract it from 72
8x= 48
now divide both sides by 8
x= 6
Answer:
6
Step-by-step explanation:
8(6 + 3) =48+24
8(9) = 48+24
72 = 48 + 24
72 = 72
Which point is a reflection of M(-5, -6) across the y-axis?
Y
8
7
6
5
4
3
2
0
-6 -5 -4 -3 -2
0 1
3
4
5
6
- 2
-3
-4
-5
-6
-8
-9
Answer:
point R
Step-by-step explanation:
reflection rule for the y-axis
p(x, y)->p'(-x, y)
therefore:
M(-5, -6)->R(5, -6)
The cost of 5 litres of milk is Rs. 55. Tabulate the cost of 2, 4 and 10 litres of milk
please help me complete the table
Answer:
The answer would be
22 Rs
44 Rs
110 Rs
Step-by-step explanation:
5 litres : 55 Rs
2 litres : y1
y1=2*55/5=22 Rs
4liters : y2
y2=4*55/5=44 Rs
10 litres : y3
y3=10*55/5 =110Rs
The area of the September is 336cm is all this model rectangles are exactly the same what is the perimeter of rectangle if the length of one rectangle is 12 CM
Answer:
Perimeter is 80cm
Step-by-step explanation:
A rectangle's area is calculated by multiplying the length by the width. If we are given the area of the rectangle and the length then we would simply need to solve for the width of the rectangle using the area formula we just mentioned...
A = l * w
336[tex]cm^{2}[/tex] = 12cm * w ... divide both sides by 12cm
28cm = w
Now we can see that the width of this rectangle is 28cm. To find the perimeter we need to add all four sides together, since we know that a rectangle's opposite sides are the same then we add the length and the width twice to calculate the perimeter (P)
P = 12cm + 12cm + 28cm + 28cm
P = 80cm
determine weather the line is parallel perpendicular or neither
4x – 3y = 8 and 4y + 3x= 12
Can someone explain to me how to get the answer:
-3 |2d| = 12
Answer:
d= -2Step-by-step explanation:
-3×2d=12 -6d= 12 d= 12/(-6) d= -2Hope it helps you......Pls Mark this answer as brainliest.
If it takes 5 gallons of gas to drive 125 miles, how many miles can be driven using 8 gallons of gas? (GIVE ONLY NUMERICAL ANSWER)
What is the b value of the equation
y= -4x - 10?
Answer: -10
Step-by-step explanation: In slope-intercept form, the formula is y = mx + b with m = slope and b = y-intercept. In the expression, the "b" is -10. Therefore, the b value of this equation is -10.
can someone help me with my math, i am really struggling rn with life and i need help, please dont post random stuff, and i will give brainliest :(
^
https://brainly.com/question/20134003
Answer:
Step-by-step explanation:
Ummmmmmmmm what do u need help with u got to put down a question
Noah invested $2,500 in an account paying 4.5% simple interest. How much was his account worth after 5 years?
Answer:
$3,062.50 after 5 years.
Step-by-step explanation:
The answer is 3,062.50 because 4.5% of 2,500 is 112.5 and 112.5 multiplied by 5 is 562.5 and 2,500 plus 562.5 is 3,062.50.
P.S Can I have brainliest?
A density curve for all the possible temperatures between 0 degrees F and 40 degrees F is a rectangle. What is the height of the rectangle in this density curve?
A. 0.025
B. 0.00025
C. 0.0025
D. 0.25
Answer:
Concept: Higher Level Mathematics
You have a density curve, aka probability You are asked to find the height Hence 0-40F has 40 total integers or values of X(probability) Hence you have a total Area of [tex] \binom{40}{0} [/tex]Integrate f(x) to get 0.025. Hence the answer is A Rate positively and give brainlistA demon possessed woody and turned him into a monster!
He now hunts children aged 7-16 because he likes his meals chewy.
His head turns 360 degrees to spot prey.
If you look at the picture he will rise out of your sheets and put snakes in your shoes.
And he's right behind you.
Answer:
Ë
Step-by-step explanation:
Im literally going to poop my pants that is SO scawwwy. I deserve compensation for this. My lawyers are coming after you
Answer:
i looked behind me and yes i did see a monster, my brother
Step-by-step explanation:
5/8 divided by 1 1/3? In fraction form
Answer:
15/32
Step-by-step explanation:
15/32 is the fraction form of the statement 5/8 divided by 1 1/3.
To divide 5/8 by 1 1/3, we first need to convert the mixed number 1 1/3 to an improper fraction.
1 1/3 can be written as (3/3 + 1/3), which simplifies to 4/3.
Now, we can rewrite the division as the multiplication of the dividend by the reciprocal of the divisor:
(5/8) * (3/4)
Multiplying the numerators and denominators:
(5 * 3) / (8 * 4) = 15/32
Therefore, 5/8 divided by 1 1/3 in fraction form is equal to 15/32.
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what is the slope of a line parallel to each given line y = 4x - 5
Answer:
20???
Step-by-step explanation:
Answer:
4x
Step-by-step explanation:
At angle θ lies in Quadrant III. If cosθ=-0.487, what is tanθ rounded to the nearest thousandth??
Answer:
TanФ=-1.793
Step-by-step explanation:
[tex]Sin^{2} (A) + Cos^{2} (A) = 1[/tex]
[tex]Sin(A)=\sqrt{1-Cos^{2} (A)}[/tex]
[tex]Tan(A) = \frac{Sin(A)}{Cos(A)}[/tex]
[tex]Tan(A) =\frac{\sqrt{1-Cos^{2}(A) } }{Cos(A)} \\Tan(A) =\frac{\sqrt{1-(-.487)^{2} } }{-.487}=-1.793433202[/tex]
Write an inequality for the graph below.
Answer:
(1,-2) They are only asking for one inequality which is like (-3,0) which is the other point.
Step-by-step explanation:
in each one section there are 27 student and there are 17 section how many students are in total
Answer:
459 students.
Explanation:
Since you are given the number of how many students are in each section, simply multiply to find the total answer.
27 x 17 = 459
There are 459 students.
Answer:
459 students
Step-by-step explanation:
Since there are 27 students, and 17 sections, multiply the two numbers:
27 × 17 = 459