lim┬(x→1)〖sin〖(4x-4)〗/(x^2-1)〗
O Does not exist
O 1
O 4
O -2
O 2
Answers
In the limit of sin(4x-4)/(x^2-1) as x approaches 1 does not exist.
Let's explain the steps to determine this.
To find the limit, we substitute x = 1 into the expression sin(4x-4)/(x^2-1). We get sin(4-4)/(1^2-1) = sin(0)/0 = 0/0.
An indeterminate form of 0/0 indicates that we need further evaluation to determine the limit.
To proceed, we can apply L'Hopital's rule by taking the derivatives of the numerator and denominator separately.
Taking the derivative of the numerator, we get 4cos(4x-4).
Taking the derivative of the denominator, we get 2x.
Now, substituting x = 1 into the derivatives, we have 4cos(4-4)/2(1) = 4cos(0)/2 = 4(1)/2 = 4/2 = 2.
Therefore, the limit of sin(4x-4)/(x^2-1) as x approaches 1 is 2.
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Related Questions
Will give another brain!!
Answers
from a collection of 50 store customers, 3 are to be chosen to receive a special gift. how many groups of 3 customers are possible?
Answers
The combination of number of ways of groups of 3 customers are 19600 .
What is permutation and combination?
Combination and permutation are two alternative strategies to divide up a collection of elements into subsets in mathematics. The components of the subset may be arranged in any order when combined.The subset's components are listed in a permutation in a certain order.The number of store customer is N = 50
The number of customer that receive a special gift is r = 3
The expression for the number of possible ways to choose 3 customers is
= ⁿCr
= ⁵⁰C₃
= 50 * 49 * 48/3 * 2 * 1
= 19600
Thus, the number of ways of groups of 3 customers are 19600.
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1) Louis is dilating triangle ABC at right. He
multiplied each x-coordinate and y-coordinate of
triangle ABC by -2.
a. What are the new coordinates of the points?
Answers
To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:
New x-coordinate = -2 * old x-coordinate
New y-coordinate = -2 * old y-coordinate
Let's apply these formulas to each point in triangle ABC:
Point A: (-3, 4)
New x-coordinate of A = -2 * (-3) = 6
New y-coordinate of A = -2 * 4 = -8
New coordinates of A: (6, -8)
Point B: (1, 1)
New x-coordinate of B = -2 * 1 = -2
New y-coordinate of B = -2 * 1 = -2
New coordinates of B: (-2, -2)
Point C: (5, -2)
New x-coordinate of C = -2 * 5 = -10
New y-coordinate of C = -2 * (-2) = 4
New coordinates of C: (-10, 4)
Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:
A: (6, -8)
B: (-2, -2)
C: (-10, 4)
Two congruent ellipses are perpendicular to each other. Squares fill the gaps between the two ellipses as shown. Show that the side of the square equals half the minor axis of the ellipse.
Answers
The side of the square equals half the minor axis of the ellipse.
To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.
Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.
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Compute the value of the discriminant and give the number of real solutions of the quadratic equation.-4x²+2x–5=0
Answers
ANSWER
\(\begin{gathered} \text{Discriminant}=-76 \\ No\text{ real solutions} \end{gathered}\)EXPLANATION
We want to find the discrimininant of the equation:
\(-4x^2+2x-5=0\)The general form of a quadratic equaion is given as:
\(ax^2+bx+c=0\)The discriminant is given as:
\(b^2-4ac\)Therefore, we need to find that.
From the given equation:
\(\begin{gathered} a=-4 \\ b=2 \\ c=-5 \end{gathered}\)Therefore, we have that the discriminant is:
\(\begin{gathered} 2^2-4(-4)(-5) \\ 4-(4\cdot20) \\ 4-80 \\ -76 \end{gathered}\)That is the discriminant.
Since the discriminant is less than 0, then there are no real solutions of the equation.
3
Solve each equation.
r - 10 = 4
Answers
Answer:
r=14
Step-by-step explanation:
14-10=4
10+4=14
14-4=10
tada
Answer:
14
Step-by-step explanation:
r - 10 = 4
r = 4 + 10
r = 14
hope this helps you!
Peach Produces pays its employees by the formula, P(b)=52b+45 P b = 5 2 b + 45 , where P(b) P b is the employee’s total daily pay and b is the number of bushels of peaches picked. According to the formula, what is the rate employees are paid per bushel of peaches picked?
A $5.00
B $2.00
C $45.00
D $2.50
Answers
Answer:
$2.50
Step-by-step explanation:
Given the daily pay formula :
P(b)=5/2b+45
P(b) = employee’s total daily pay
b = number of bushels of peaches picked
Hence from the fórmula ; rate which employees are paid per bushel. Of peach picked is the gradient of the equation :
According to the intercept slope formula:
y = mx + c ; where m = slope or gradient
From the equation :
P(b)=5/2b+45
The slope or gradient is 5/2 ; hence, employees are paid $5/2 per bushel of peaches picked.
$5/2 = $2.50
A car dealer acquires a used car for $7,000, with terms fob shipping point. compute total inventory costs assigned to the used car if additional costs include
$290 for transportation-in.
$190 for shipping insurance.
$1,000 for car import duties.
$200 for advertising.
$1,400 for sales staff salaries.
$190 for trimming shrubs.
Answers
Shipping points are independent organizational entities within which processing and monitoring of the deliveries, as well as goods issue, is carried out. A delivery is processed by one shipping point only.
"FOB shipping point" or "FOB origin" means the buyer is at risk once the seller ships the product. The purchaser pays the shipping cost from the factory and is responsible if the goods are damaged while in transit. "FOB destination" means the seller retains the risk of loss until the goods reach the buyer.
Please check the attached file for a complete answer.
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Find a point-slope form for the line with slope 1/5 and passing through the point (-2,-5)
The equation of the line in point-slope form is what?
Answers
The equation of the line in point-slope form is written as: y + 5 = 1/5(x + 2).
How to Find the Equation of a Line?We can write the equation of a line in point-slope form by substituting the value of the slope of the line, m, and the value of the coordinates of a point on the line, (a, b) into the equation y - b = m(x - a).
Given the variables below:
A point on the line (a, b) = (-2, -5)
Slope (m) = 1/5.
To write the equation of the line in point-slope form, substitute a = -2, b = -5 and m = 1/5 into y - b = m(x - a):
y - (-5) = 1/5(x - (-2))
y + 5 = 1/5(x + 2)
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1. 156÷106 Pls help and dont use a cauculator because it gives u wrong answer
Answers
156 ÷ 106 is equal to 1 remainder 50.
To divide 156 by 106, a long division can be used as shown below:
1) Put the dividend (156) inside the division bracket and the divisor (106) outside the bracket.
2) Divide the first digit of the dividend (1) by the divisor (106). Since 1 < 106, the first digit of the quotient is 0.
3) Write 0 below the dividend and multiply 0 by the divisor (106). Subtract the product (0) from the first digit of the dividend (1) to get the remainder (1). Bring down the next digit (5) to the remainder.
4) Now the new dividend is 15. Repeat steps 2 and 3 until there are no more digits to bring down. The quotient is 1 with a remainder of 50, or:
156 ÷ 106 = 1 remainder 50.
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Ellen can purchase 5 apples for $1.75. How many apples can she get for $1.00
Help!!!
Answers
Answer:
She can get 2
Step-by-step explanation:
2 multiplied by 35 equals 70 and 3 multiplied by 35 is 1.05 so Ellen can only get 2 apples
Hope it helps :)
Brainliest pls? Have a good day/night
Part A: Write an algebraic expression for 6 more than 7 times a number. (5 points)
Part B: Write a verbal expression for 3(n + 8). (5 points)
Answers
The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".
Linear ExpressionA linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.
Part AFirst, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.
The word more will be represented for the add symbol (+). Thus,
the algebraic expression is 6+7x.
Part BThe expression 3*(n+8) can be represented for the sentence:
The triple of the sum between the numbers n and 8.
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A square rug has an area of 225 square feet . How long is each side of the rug ?
Answers
Answer:
I believe it's 15
Step-by-step explanation:
15^2 is 225
What is the factored form of 8x²-36x-20?
Answers
Answer:
(4x + 2)( 2x - 10)
Step-by-step explanation:
Answer:
(8x+4) ( x-5)
Step-by-step explanation:
Well we can't factor out the 8 and solve because if we do the -20 and -36 will be decimals.
So we do this
8 * -20 = -160
We need to find 2 number that multiplies to -160 and adds to -36
-40 and 4 fit this category
they add to -36 and multiply to -160
Now we write the equation as
8x^2 - 40x + 4x -20
(8x^2-40x) (4x-20)
8x(x-5) + 4(x-5)
(8x+4) ( x-5)
A landscaper is designing a display of flowers for an area in a public park. The flower seeds will be planted at points that lie on a circle that has a diameter of 8 feet. the point where any seed is planted must be 2 feet away from the seeds on either side of it. what is the maximum number of flower seeds that can be planted using the design?
after planting the flower seeds the landscaper has 20 seeds left over. the landscaper wants to plant all of the remaining seeds in another circle so that the seeds are 2 feet apart. what is the diameter of the smallest circle that the landscaper can use to plant all of the remaining seeds?
Answers
The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.
The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.
How to find the Z score
P(Z ≤ z) = 0.60
We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.
Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.
For the second question:
We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:
P(Z ≥ z) = 0.30
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).
Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.
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Please help: State if the three numbers can be the measures of the sides of a triangle.
Answers
x2 + 2xy + y2 - m2
Factorise
Answers
Answer:
x^2 + 2xy + y^2 - m^2
= (x+y)^2-m^2
A pedestrian starts walking from town A to town B. At the same time, another pedestrian starts walking from town B to town A. They pass each other at noon and continue on their paths. One of them arrives at 4 PM, the other at 9 PM. How many hours had each walked before passing each other
Answers
The pedestrian who started in town A walked for 8 hours before the noon meeting, and the pedestrian who started in town B walked for 6 hours before the noon meeting.
Let's call the distance between town A and town B "D".
When the two pedestrians meet at noon, they have together covered a distance of D, which means they each have walked half the distance, or D/2.
Let's say the pedestrian who started in town A arrives at 4 PM, which means they have walked for 4 hours after the noon meeting. We can use the formula distance = rate x time, where rate is the pedestrian's speed, to find how far they have walked before the noon meeting:
distance = rate x time
D/2 = rate x (noon - 4)
D/2 = rate x (-4)
D/2 = -4rate
rate = -D/8
The negative sign indicates that this pedestrian is walking from town A to town B, in the opposite direction from the positive direction we defined earlier. The magnitude of the rate is D/8, meaning this pedestrian covers 1/8th of the distance every hour.
Similarly, we can use the same formula for the pedestrian who started in town B and arrived at 9 PM:
distance = rate x time
D/2 = rate x (9 - noon)
D/2 = rate x 3
D/6 = rate
rate = D/18
This pedestrian is walking from town B to town A, in the positive direction we defined earlier. The magnitude of the rate is D/18, meaning this pedestrian covers 1/18th of the distance every hour.
Now we can calculate how long each pedestrian walked before the noon meeting:
time = distance / rate
For the pedestrian who arrived in town A at 4 PM:
time = D/2 / (-D/8) = -4 hours
For the pedestrian who arrived in town B at 9 PM:
time = D/2 / (D/18) = 9 hours
The negative sign for the pedestrian who arrived in town A indicates that they started walking in the wrong direction, so they actually walked for 4 - (-4) = 8 hours in the correct direction before reaching the noon meeting point. The pedestrian who arrived in town B walked for 9 - 3 = 6 hours in the correct direction before the noon meeting.
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A point is plotted on the number line at 2 2/5 . A second point is plotted at −4 3/4 .
What is the length of a line segment joining these points?
What is the answer as a simplified mixed number?
Answers
Here, we are required to determine the length of a line segment joining the two points.
The length of the line segment is; 143/20The answer as a simplified modes number is; 7 3/4The first point is plotted on the point, 2 2/5.
i.e on point 12/5.
The second point is at -4 3/4.
i.e on point (-19/4).
The length of a line segment joining these points is given by;
12/5 - (-19/4) which yields;
(48+95)/20 = 143/20
Ultimately, the length of the line segment is;
143/20
To express the answer as a simplified modes number is; 7 3/4.
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For the following frequency distribution of quiz scores, how many individuals took the quiz (N)?
X f
5 6
4 5
3 5
2 3
1 2
ANSWERS:
A. 5
B. 15
C. Cannot determine
D. 21
Answers
The number of individuals who took the quiz is D) 21.
To determine the total number of individuals who took the quiz (N), we need to sum up the frequencies (f) in the given frequency distribution. The frequency (f) represents the number of individuals who obtained each score.
Let's add up the frequencies:
6 + 5 + 5 + 3 + 2 = 21
The total frequency is 21, which means that 21 individuals took the quiz. Each score represents a certain number of individuals who obtained that score, and by adding up all the frequencies, we get the total number of individuals.
Therefore, the correct answer is D. 21.
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what is 45/90= to
i need help
Answers
Answer:
1/2
Step-by-step explanation:
45/90 ÷ 45/45 = 1/2
Answer:
1/2
Step-by-step explanation:
divide both sides by their GCF,which is 45,and you get the most simplified fraction of 1/2
Dad is getting food ready for my birthday party! Including me, there will be 16 people at the party. Dad is baking cookies for us! He can bake 20 cookies per batch.
How many batches should I tell Dad to make so we can each have 3 cookies?
Answers
Answer:
he has to cook 3 batches of cookies
Which set of statements explains how to plot a point at the location (Negative 3 and one-half, negative 2)?
Start at the origin. Move 3 and one-half units right because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between 3 and 4. Move 2 units down because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units left because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units down because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units right because the y-coordinate is -2.
Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.
Answers
Answer:
Step-by-step explanation:
The point that you will end up at is **(-0.5, -2)**.
To see this, we start at the origin, which is the point (0, 0). We then move 3.5 units right, which brings us to the point (3.5, 0). Finally, we move 2 units down, which brings us to the point (3.5, -2).
The other points are incorrect because they do not take into account the direction of the movement. For example, the point (-2, -0.5) is incorrect because we move 3.5 units **right**, not left. Similarly, the point (-2, 2) is incorrect because we move 2 units **down**, not up.
Therefore, the only point that you will end up at is (3.5, -2).
Which of the following questions are true? Select two that apply.
Answers
Answer: A and C
Step-by-step explanation:
The other choices aren't correct because
B. \(x^{\frac{4}{5} } =\sqrt[5 ]{x^{4}}\)D. \((\sqrt{x^{3} } )^{8}=(x^{\frac{3}{2} } )^{8}=x^{\frac{24}{2} } =x^{12}\)Q4) Let x denote the time taken to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race: In less than 160 minutes? * 0.764 0.765 0.0764 0.0765 In 215 to 245 minutes? * 0.1128 O 0.1120 O 0.1125 0.1126
Answers
a. The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.
b. The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.
a. To find the probability for each scenario, we'll use the given normal distribution parameters:
Mean (μ) = 190 minutes
Standard Deviation (σ) = 21 minutes
Probability of completing the road race in less than 160 minutes:
To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.
Using the z-score formula: z = (x - μ) / σ
z = (160 - 190) / 21
z ≈ -1.4286
We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.
From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.
Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.
b. Probability of completing the road race in 215 to 245 minutes:
To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.
First, we calculate the z-scores for each endpoint:
For 215 minutes:
z1 = (215 - 190) / 21
z1 ≈ 1.1905
For 245 minutes:
z2 = (245 - 190) / 21
z2 ≈ 2.6190
Next, we find the cumulative probabilities for each z-score.
From the standard normal distribution table:
The cumulative probability for z ≈ 1.1905 is approximately 0.8820.
The cumulative probability for z ≈ 2.6190 is approximately 0.9955.
To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:
Probability = 0.9955 - 0.8820
Probability ≈ 0.1125
Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.
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which table is a linear function please help!
Answers
Which of the following could represent the interval −4 ≤ x ≤ 6?
Answers
Answer:
Step-by-step explanation:
-4 \(\leq\) x \(\leq\) 6
x = {-4,-3,-2,-1,0,1,2,3,4,5,6}
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An oil tank in the shape of a cylinder has a diameter of 40 feet and a height of 32 feet. Which expression can be used to find the volume of the oil tank? Recall the formula V = pi r squared h.
Answers
Answer:
40217.6 cubic feet
Step-by-step explanation:
Given data
Diameter= 40feet
Radius= 20feet
Height=32feet
The expression for the volume is given as
V= πr^2h
Substitute
V= 3.142*20^2*32
V= 3.142*400*32
V=40217.6 cubic feet
Hence the volume of the tank is 40217.6 cubic feet
at a gas station, suppose that 54% of the customers purchase premium grade gas. assume that these customers decide independently. find the probability that at least one of the next three customers purchases premium gas.
Answers
At a gas station, suppose that 54% of the customers purchase premium grade gas. assume that these customers decide independently. The probability that none of the next three customers purchase premium gas is 0.834
The likelihood that at least one of the following three customers will purchase premium gas is equal to the likelihood that none of the following three customers will do so. = 1 - (1-P(A))³ = 0.834
The likelihood that a customer would buy premium quality is 45%.
P(A) = 0.45 in this case.
P(B) = 0.55 is the likelihood that the consumer would buy a different grade.
Consequently, the likelihood that at least one of the following three clients will buy premium gas is
P(k=0) = (1 - P)ⁿ,
where the likelihood that at least one client will buy premium gas is complemented by the likelihood that the subsequent three customers will buy a different gas brand.
(1 - P(A))×(1 - P(A))×(1 - P(A)) = P(B)×P(B)×P(B) = 0.55³
and the complement is 1 - 0.55³ = 0.834
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The concentration of chlorine in the atmosphere serves as an indicator damage to the ozone layer. The table to the right shows the relationship of chlorine concentration in parts per billion (ppb), to the year. Using values as accurate as possible in the function, what is the predicted value of the chlorine concentration in 2060 according to the linear function? OA. 4.56 O B. 5.06 O C. 4.81
Answers
The predicted value of the chlorine concentration in 2060 according to the linear function is 5.06 ppb. So, the correct option is B.
To find the linear function that models the relationship between the year and chlorine concentration, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where y is the chlorine concentration and x is the year. We can choose any two points from the table to find the slope, m:
m = (y2 - y1)/(x2 - x1)
Let's choose the points (1985, 2.8) and (2035, 4.0):
m = (4.0 - 2.8)/(2035 - 1985) = 0.02
Now we can use the slope and one of the points to find the y-intercept:
y - y1 = m(x - x1)
y - 2.8 = 0.02(x - 1985)
y = 0.02x - 39.6
Therefore, the linear function that models the relationship between year and chlorine concentration is y = 0.02x - 39.6.
To find the predicted value of chlorine concentration in 2060, we can substitute x = 2060 into the equation:
y = 0.02(2060) - 39.6 = 5.06
Therefore, the predicted value of the chlorine by linear function is 5.06 ppb, which is option B. is correct.
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_____The given question is incomplete, the complete question is given below:
The concentration of chlorine in the atmosphere serves as an indicator damage to the ozone layer. The table to the right shows the relationship of chlorine concentration in parts per billion (ppb), to the year. Using values as accurate as possible in the function, what is the predicted value of the chlorine concentration in 2060 according to the linear function? OA. 4.56 O B. 5.06 O C. 4.81 LIN LIITUTE 1985 2.8 1995 3.6 2010 4.2 2035 4.0 Choose the graph of the function of the best fit. A. DB. Q 3 oc. D [0,60.0.6] Xscl = 10, Yscl = 1
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