Answers
Since [tex]x[/tex] is approaching 1 from the left/below, we take the part of [tex]f(x)[/tex] that is defined over [tex]x<1[/tex], for which we have
[tex]f(x) = \dfrac{x-1}{\sqrt{x-1}}[/tex]
Since [tex]x\neq1[/tex], we can simplify this to
[tex]f(x) = \dfrac{x-1}{(x-1)^{1/2}} = (x-1)^{1/2} = \sqrt{x-1}[/tex]
and this is continuous at [tex]x=1[/tex], so we can evaluate the limit by directly substituting [tex]x[/tex].
To summarize:
[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} \frac{x-1}{\sqrt{x-1}} = \lim_{x\to1} \sqrt{x-1} = \sqrt{1-1} = \boxed{0}[/tex]
Related Questions
Select the correct answer.
How many solutions for x does the following equation have?
2(x+4) -1 = 2x + 7
O A. 1
О в. о
OC. 7
OD. infinite
Answers
Answer:
D. infinite
Step-by-step explanation:
2(x+4) -1 = 2x + 7
To solve for x
Distribute
2x+8 -1 = 2x+7
Combine like terms
2x +7 = 2x + 7
Subtract 2x from each side
2x+7-2x = 2x+7-2x
7 = 7
This is always true, so there are infinite solutions
In a class there are
10 students who play football and cricket
7 students who do not play football or cricket
14 students who play football
21 students who play cricket
Find the probability that a student chosen at random plays football and cricket.
Answers
Answer: 31.25%
Step-by-step explanation:
Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%
Where is the least common denominator of two fractions to product of the denominator?
Answers
When two or more fractions are provided, the least common denominator is defined as the smallest common multiple of all the common multiples of the denominators.
What is the least common denominator?The smallest number that is a common denominator for a particular set of fractions is referred to as the least common denominator (LCD). For fraction addition and subtraction, as well as comparing two or more fractions, the given fractions must have common denominators.Let's assume we have to add the fractions: (2/9)+(3/4)
We need to determine a common integer that is a multiple of both denominators, which are 9 and 4.
This common multiple will aid in the solution of the problem. As a result, the least frequent multiple for 9 and 4 is 36. As a result, the expression can be written as follows:
(2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36
To know more about least common denominator visit:
https://brainly.com/question/13767255
#SPJ13
The rooftop of a 5-story building is 50 feet above the ground.
How long does it take the water balloon dropped from the
rooftop to pass by a third-story window at 24 feet?
Using the model h(t) = h, 16², solve the equation
h(t) = 24. (When you reach the step at which you divide
both sides by -16, leave 16 in the denominator rather than
simplifying the fraction because you'll get a rational
denominator when you later use the quotient property.)
Answers
With the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.
What do we mean by Quotient?In this example, the number divided by (15) is known as the dividend, and the number divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.The quotient is the result of dividing two numbers by each other. As in the case of 8 ÷ 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4. The quotient and divisor are always less than their dividend, as you can see.So, h(t) = 24:
= 50Then, calculate as follows:
h(t) = - 1624 = 50 - 1616 = 50 - 2416 = 26 = 26/16t = √26/16t = 1.3secTherefore, with the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.
To learn more about Quotient click on the link
brainly.com/question/2053526
#SPJ9
A college professor hands out a list of 16 questions, 8 of which will appear on the final examination for the course. One of the students taking the course is pressed for time and can prepare for only 9 of the 16 questions on the list. Suppose the professor chooses the 8 questions at random from the 16. What is the probability that the student will be prepared for exactly 4 questions?
Answers
The probability that the student will be prepared for exactly 4 questions is; 0.3427
How to solve Hypergeometric Probability distribution?
Hypergeometric distribution is defined as a discrete probability distribution that expresses the probability of k successes in n draws, done without replacement, from a finite population of size N that contains exactly K objects with that feature. In this disdtribution, each draw is either a success or a failure.
The probability mass function of Hypergeometric distribution is given by the formula;
P(K = k) = KCk * N-KCn-k ]/NCn
Now, the probability that the student will be prepared for exactly 4 questions will be;
P(K = 4) where;
N = 16
K = 9
n = 8
Solving P(K = 4) = 9C4* 16-9C8-4 ]/16C8 = 0.3427
Read more about Binomial Probability Distribution at; https://brainly.com/question/24670062
#SPJ1
PLEASE ANSWER QUICK ILL GIVE BRAINLIEST IF CORRECT
Answers
Answer:
domain: [-1,4]
range: [-2,4]
the graph is not a function, this is proven by using the vertical line test.
hope this helps :)
The original price of a DVD is $12 the sale Price is 35% of the original price final total cost of the DVD
Answers
Answer: $4.20
Step-by-step explanation:
The sale price is $12 * .35 = 4.2
f(x) = -x² + 8x - 12; Find ƒ(3)
Answers
The result of the function f(3) is 3.
What does it mean to evaluate function?The process of evaluating a function is typically straightforward when we have the function in the form of a formula. When a function is evaluated, a variable is replaced with its provided value or expression. Example. For x = 5, evaluate f(x) = 2x + 4. This implies to simplify and change x to 5. It is advised to enclose the value being substituted in parentheses.Given:
f(x) = -x² + 8x - 12
x = 3
Putting the value of x in the given function to obtain the outcome of the function,
f(3) = -(3)² + 8 × 3 - 12
= -9 + 24 - 12
= 24 - 21
= 3
To learn more about evaluating functions visit:
https://brainly.com/question/24477011
#SPJ9
A particle moves along the r-axis so that its velocity vat any given time t, for 0 St $ 16, is given byW(0) =e»-1. At time r=0, the particle is at the origin. At what time does the particle's accelerationequal zero for the first time?Round to the nearest thousandth or write as a fraction
Answers
Given: The velocity function of a moving particle as
[tex]V(t)=e^{2sint}-1[/tex]To Determine: The time at which the acceleration equals to zero
Solution
Note that at time t=0, the particle is at origin, so
[tex]\begin{gathered} V(0)=e^{2sin0}-1 \\ V(0)=e^{2\times0}-1 \\ V(0)=e^0-1 \\ V(0)=1-1 \\ V(0)=0 \end{gathered}[/tex]Determine the acceleration function
The acceleration of a particle is the rate of change of velocity or the derivative of the velocity function. Therefore,
[tex]A(t)=\frac{dV(t)}{dt},or,A(t)=V^{\prime}(t)[/tex][tex]\begin{gathered} V(t)=e^{2sint}-1 \\ let:u=2sint:\frac{du}{dt}=2cost \\ V(t)=e^u \\ \frac{dV(t)}{du}=e^u=e^{2sint} \\ A(t)=\frac{dV(t)}{dt}=\frac{dV}{du}\times\frac{du}{dt} \\ A(t)=e^{2sint}\times2cost \\ A(t)=2e^{2sint}cost \end{gathered}[/tex]When the acceleration is equal to zero, then we have
[tex]\begin{gathered} A(t)=0 \\ 2e^{2sint}cost=0 \end{gathered}[/tex]Let us plot the graph of the acceleration function
The time for given interval for which the acceleration is zero are
[tex]t=\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},\frac{7\pi}{2},\frac{9\pi}{2}[/tex]ence, thre first time the acceleration is zero is π/2 or 1.571
Needing help for this
Answers
The pairs of angles that are linear pairs involving point F are:
A. ∠DFC and ∠CFG
D. ∠HFD and ∠CFD
E. ∠GFH and ∠GFC
F. ∠HFG and ∠DFH
What is a Linear Pair?When two angles that are adjacent to each other, (that is, they share the same vertex and the same side), are located on a straight line, these angles are linear pairs and are also supplementary angles.
Making reference to the image given, angles DFC and CFG share a common vertex F and a common side CF. Also, they lie on a straight line. Therefore, angle DFC and angle CFG are a linear pair.
Angles HFD and CFD share a common vertex F and a common side FD. They lie on a straight line. Thus, angle HFD and angle CFD are also a linear pair.
The same thing applies to angle GFH and angle GFC, as well as angle HFG and angle DFH.
The linear pairs are:
A. angle DFC and angle CFG
D. angle HFD and angle CFD
E. angle GFH and angle GFC
F. angle HFG and angle DFH
Learn more about linear pair on:
https://brainly.com/question/13218054
#SPJ1
how many 14 goes into 78
Answers
The amount of times that 14 goes into 78 is; 5 times
How to carry out division of numbers?
We want to find how many 14 goes into 78.
Now, it is pertinent to note that this expression is used in our common daily lives for basic things of life. For example, if i want to know how many 10 dollars can go into 100 dollars, i will just divide 100 by 10.
Similarly another example is if i want to know how many 5 liters container of fuel would go into a 60 liters tank, i will just divide 60 by 5 to get the number.
In a similar vein, we can solve this question by dividing 78 by 14 to get;
78/14 = 5 ⁸/₁₄
This means 14 can only go in 5 full times as we will not count the fraction.
Read more about division of numbers at; https://brainly.com/question/1622425
#SPJ1
Each letter is three. 5 m away from the base of the building. How high is window A?
Answers
Solution
A
Using pythagorean theorem
[tex]\begin{gathered} 5.5^2=3.5^2+A^2 \\ 30.25=12.25+A^2 \\ Re-arrange \\ A^2=30.25-12.25 \\ A^2=18 \\ Take\text{ the square root of both sides} \\ A=\sqrt{18} \\ A=4.2426 \end{gathered}[/tex]The final answer
The height of window A is
[tex]4.24meters[/tex]
1.
find a
a =
21°
explain why using one of these
words: adjacent,
complementary, supplementary,
vertical
explanation goes here
add a pic of your work
(or just type it here)
to show HOW you got your
answer
pic (or typing) goes Hereford
Answers
[tex]21+a=90 \implies a=69^{\circ} [/tex]
This is because the angles are complementary.
Suppose that the mean cranial capacity for men is 1160 cc (cubic centimeters) and that the standard deviation is 200 cc. Assuming that men's cranial capacities are normally distributed, complete the following statements.
Answers
Solution:
Given;
[tex]\mu=1160,\sigma=200[/tex]The z-score is calculated using;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{760-1160}{200}\text{ at }x=760 \\ \\ z=-2 \\ \\ z=\frac{1560-1160}{200}\text{ at }x=1560 \\ \\ z=2 \end{gathered}[/tex]Thus;
[tex]P(-2ANSWER: 95%(b) The z-score of 99.7 probability is between -3 and 3. Thus;
[tex]\begin{gathered} -3=\frac{x_1-1160}{200} \\ \\ x_1=560 \\ \\ 3=\frac{x_2-1,160}{200} \\ \\ x_2=1760 \end{gathered}[/tex]ANSWER: Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc
Consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. All angles are right angles. Which plane(s) contain point B and appear to be parallel to plane CDH?
Answers
The plane containing point B and parallel to the plane CDH is plane ABF.
What is defined as the parallel plane?Parallel planes are spatial planes that never intersect. The length about any line segment perpendicular both to planes connecting two parallel planes is indeed the distance between them. There are an infinite number of perpendicular line segments between two parallel planes. Two of the perpendicular segments the above are line segments AB and CD. Any line segment that is perpendicular to both planes also has the shortest distance between them.As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.
But plane ABC is intersecting the given plane CDH, while plane ABF is not.
Thus, plane ABF is parallel to the plane CDH.
To know more about the parallel plane, here
https://brainly.com/question/1578741
#SPJ10
Kaj earns $35 for 2 hours of work. If she makes a constant hourly wage, which table
represents the relationship between the number of hours she works and her total
earnings?
Answers
The table of values of the relationship between time and earnings is a linear relation
How to determine the table of values that represents the earnings?From the question, we have the following parameters:
Number of hours = 2 hours
Total earnings in this time = $35
Also from the question, we understand that:
She makes a constant hourly wage
A constant hourly wage implies that the table of values has a linear relationship
In this case, the linear relationship is represented as
A(t) = constant hourly wage * t
Where
A(t) represents the earnings
t represents the number of hours
So, we have
constant hourly wage * 2 = 35
Divide both sides of the equation by 2
So, we have
constant hourly wage = 17.5
Substitute constant hourly wage = 17.5 in A(t) = constant hourly wage * t
A(t) = 17.5 * t
Evaluate
A(t) = 17.5t
Using the values of t as:
t = 0, 2, 4, 6
We have the following table of values
Number of hours (t) || Amount earned
0 0
2 35
4 70
6 105
Read more about linear relationship at
https://brainly.com/question/10209928
#SPJ1
The actual lengths of Wall A, Wall B, and Wall D are 2.5 m, 2.75 m, and 3.75 m. If 1 m = 4 cm then determine how long these walls will be on Noah’s scale drawing. Be sure to include your units; use 'cm' for centimeters.
Answers
Step-by-step explanation:
1 m = 4 cm
therefore,
A = 2.5 m = 2.5×1 m = 2.5×4 cm = 10 cm
B = 2.75 m = 2.75×1 m = 2.75×4 cm = 11 cm
D = 3.75 m = 3.75×1 m = 3.75×4 cm = 15 cm
1/4(n-6)=1/4n-3/2
Hint: undo the fraction
Answers
The solution to 1/4(n - 6) = 1/4n - 3/2 is infinite many solutions
How to solve the equation?The equation is given as
1/4(n - 6) = 1/4n - 3/2
Multiply through the fraction equation by 4
So, we have the following equation
4 x 1/4(n - 6) = 4 x 1/4n - 4 x 3/2
Evaluate the products in the equation
So, we have the following equation
n - 6 = n - 6
Evaluate the like terms
0 = 0
The equation cannot be solved further
If the solution to an equation is 0 = 0, then the equation has infinite many solutions
Read more about equations at
https://brainly.com/question/2972832
#SPJ1
Answer: infinite many answers
Step-by-step explanation:
Can I get help please ?
Answers
SOLUTION:
Case: Pythagoras Triple
Method:
The Pythagorean triple:
(8, 15, 17) can be formed with factor integers
8----> 4
15---->3.
Final answer:
x=4, y= 3
1. A triangle is rotated 90° about the origin. What is true about the relationship between the image and the
pre-image?
(1 point)
The lengths of the sides and the measures of the angles are preserved, so the triangles are congruent.
The lengths of the sides are enlarged and measures of the angles are preserved, so the triangles are similar.
The lengths of the sides change and the measures of the angles change as well, so the triangles look nothing alike.
The lengths of the sides are reduced and measures of the angles are preserved, so one triangle is a reduction of the other.
Answers
Answer:
the first answer option : all lengths and angles stay the same.
Step-by-step explanation:
imagine you have a piece of plastic or glass of a triangular shape on your table.
now, lower your hand on the table, so that your thumb touches the table and one of your other fingers touches the triangle on the top.
and now twist your hand that your thumb stays at the same point, and your finger holding the triangle starts making a circular motion.
that finger is dragging the triangle along.
what happens to the triangle ? it keeps its original shape, and changes only its location and orientation.
that is what a rotation is.
x ÷ 5 - 13 = 2
What is x?
Answers
Answer:
75
Step-by-step explanation:
Answer:
75. ..... ............................
Amy is experimenting with three different strawberry smoothie recipes. She makes all three smoothies for each of her x friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6. Pick all the expressions that represent how many strawberries Amy needs for all the smoothies.
Answers
The total number of strawberries needed for making all the smoothies can be represented by the expression -
y = 15x
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is Amy who is making all three smoothies for each of her x number friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6.
Number of friends [n] = x
Each of the three friends will get smoothies made from recipe 1, recipe 2 and recipe 3.
Then -
Number of strawberries needed for smoothie made from recipe 1 for x friends = n[1] = 4x
Similarly, for smoothies made from recipe 2 and 3 will need -
n[2] = 5x and n[3] = 6x number of strawberries.
Assume that total number of strawberries needed for making all the smoothies are y. Then, we can write -
y = 4x + 5x + 6x
y = 15x
Therefore, the total number of strawberries needed for making all the smoothies can be represented by the expression -
y = 15x
To solve more questions on Equation modelling, visit the link below-
https://brainly.com/question/14362668
#SPJ1
solve the system of equations using the elimation menthod. show your work. make sure to express your solution as an ordered pair
Answers
-3x - 4y = -5
12x - 3y = -18
Multiply the first equation by 4, and add both
-12x - 16y = -20
+
12x - 3y = -18
___________
-19y = -38
Solve for y:
y = -38/-19
y= 2
Replace y on any equation and solve for x
-3x - 4(2)=-5
-3x -8 = -5
-3x = -5+8
-3x = 3
x=3/-3
x=-1
Solution = (-1,2)
If x=8, y=4 z=2 then what is 3z(x-z)-y(x/2)
Answers
3(2)(8-2)-4(8/2)
6(6)-4(4)
36-16=20
I think
3(2)(6)-4(4)
3(12)-16
36-16 = 20
State the postulatr ir theorem for no. 6 and 9
Answers
Solution
Number 6
for this case we can see that we have two common angles and one equal side. By the way we have also a common side and then since we have right triangles the correct postulate would be:
SSS
Number 9
Find a function f whose graph is a parabola with the given vertex and that passes through the given point.
vertex (−1, 9); point (−2, −8)
Answers
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=9 \end{cases}\implies y=a(~~x(-1)~~)^2 +9\implies y=a(x+1)^2 + 9 \\\\\\ \textit{we also know that} \begin{cases} x=-2\\ y=-8 \end{cases}\implies -8=a(-2+1)^2 + 9 \\\\\\ -17=a(-1)^2\implies -17=a\hspace{9em}\boxed{y=-17(x+1)^2 + 9}[/tex]
What is the value of 2x + 11y when x = 4 and y = 2? 303848136
Answers
We want to find the value of the expression;
[tex]2x+11y[/tex]When x = 4 and y = 2.
All we have to do is substitute these values; when we do that, we have;
[tex]\begin{gathered} 2(4)+11(2) \\ =8+22 \\ =30 \end{gathered}[/tex]Therefore, the answer is 30.
Tammy has 4 more then five times the amount of dimes than nickels in her pocket. She has total of $1.50 in her pocket. Write an equation that could be used to determine the number of nickels(x) she has in her pocket.
Answers
In a case whereby Tammy has 4 more then five times the amount of dimes than nickels in her pocket and have total of $1.50 in her pocket the equation that could be used to determine the number of nickels(x) she has in her pocket is (0.05)(X+3) = 1.50.
How can the number of nickels(x) she has in her pocket been determined?The number of nickels(x) that can be found her pocket be determined by adding the the number of times the amount of dimes is than nickels, which can be expressed as :
let x will be number of dimes
let x+4 will be number of nickels
Therefore the number of nickels(x) that is required will be (0.10)X + (0.05)(X+3) = 1.50
Read more about equation here:
https://brainly.com/question/2972832
#SPJ1
Does the table show a proportional relationship? If so, what is the value of y when x is 11?
x 4 5 6 10
y 64 125 216 1,000
Answers
Help Me Pleaseeeeeee.
Answers
Based on the dimensions of the right triangle, the equation to be used to find the missing lengths is hypotenuse² = Known leg² + Unknown leg².
How to find a missing length on a right angled triangle?To find the missing length of a right-angled triangle, you should use Pythagoras theorem.
This theorem allows you to find the dimensions of missing leg as:
hypotenuse² = Known leg² + Unknown leg²
When you solve for the missing length, the length is:
9² = 6² + Unknown leg²
81 = 36 + Unknown leg²
Unknown leg² = 81 - 36
Unknown leg = √(81 - 36)
Unknown leg = 6.7
Find out more on right triangles at https://brainly.com/question/25016594
#SPJ1