For what value of the constant c is the function f continuous on (-infinity, infinity) for the equation f(x) = cx^2 + 2x if x < 2 and x^3 - cx if x> or = 2
To find the constant c that makes the given piecewise function continuous for all real numbers, the two parts of the piecewise function need to be equal at x = 2. By setting these two equal and solving for c, you will find the value that makes the function continuous.
Explanation:The question presents a piecewise function and asks for which value of the variable c does it become continuous for all real numbers. To make a function continuous at a certain point, both parts of the function must be equal at that point. In this case, the two parts meet at x = 2. We need to set the two parts equal to each other at x = 2 and then solve for c.
For the first part of the piecewise function,
[tex]f(x) = cx^2 + 2x[/tex], when we substitute x = 2, it becomes f(2) = 4c + 4.
For the second part of the piecewise function,
[tex]f(x) = x^3 - cx[/tex], substituting x = 2 again gives us f(2) = 8 - 2c.
In order for the function to be continuous, these two results must be equal. We set 4c + 4 = 8 - 2c and solve it for c. Solving this equation will provide the value of c for which the function is continuous for all x .
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What is the difference between a buffalo and a birthday cake?
Answer:
The buffalo is an animal and the birthday cake is a food.
Step-by-step explanation:
Hi, Buffaloes are heavily built oxen, with sparsely haired skin, large ears, long, tufted tails, broad muzzles and massive angulated horns. In having only 13 pairs of ribs they resemble the typical oxen. African buffaloes all have the hair of the back directed backwards.
A birthday cake is like a normal cake but made for the special celebration of birthdays.
A circle with a radius of inches has a central angle of 0.25 radians that intercepts an arc of inches.
Answer:
Step-by-step explanation:
Given that there is a circle of .... inches with central angle 0.25 inches
by formula we have arc = radius *central angle in radians
The radii are given three options as 10,20,4 and corresponding arcs as
25,5, 16 inches.
By matching we find that 10(0.25) not equals 25
But 20(0.25) = 5 inches
Also 4(0.25) not equals 16 inches
Hence correct answer is radius = 20 and central arc = 5 inches
Which numbers are a distance of 3 units from 12 on a number line?
Answer:
Probably 15 and 9
Hank delivers packages in his office building on Tuesday he delivers four more packages then on Monday and on Wednesday he delivered six more packages then on Monday if he delivers 28 packages all together how many did he deliver on Monday??
A)6
B)10
C)18
D)22
6 i hope this helps you
The distance between P and T on the coordinate grid is ___ units. (Input whole numbers only.) Image of a coordinate grid with point P located at negative 10, 15 and point T located at 15, 15.
Answer:
The distance between P and T on the coordinate grid is 25 units.
Step-by-step explanation:
Coordinate of P = (-10,15)
Coordinate of T = (15,15)
By distance formula we have distance between ( a,b) and (c,d) is
[tex]\sqrt{(c-a)^2)+(d-b)^2}[/tex]
Here (a,b) = Coordinate of P = (-10,15) and (c,d) = Coordinate of T = (15,15)
Substituting
[tex]\texttt{Distance =}\sqrt{(c-a)^2)+(d-b)^2}=\sqrt{(15-(-10)^2)+(15-15)^2}=\sqrt{25^2}=25units[/tex]
The distance between P and T on the coordinate grid is 25 units.
Need help asap please!
4v=64 how do I solve this and what’s the answer
The cube will be enlarged by a scale factor of 8.
What will be the volume of the new cube?
8 cubic units
64 cubic units
192 cubic units
4,096 cubic units
lincoln high school has 98 teachers. of them 48 teachers, 9 of them teach math. one-fifth of them teachers teach math
Kelsey is asked to find the probability of rolling a composite number on a die. She states that this is a simple event. True or false
In the Founder's Day Parade in Happy, USA, many organizations participate by building floats. The Float Committee has issued a decree that each float can only have 300,000 flowers on it this year. The Happy Campers have already attached 15,625 flowers to their float. If the flowers come in containers which hold 125 flowers, which equation represents how many more containers they can use on their float?
A. 125x + 15,625 = 300,000
B. 125x = 300,000 + 15,625
C. 0x = 300,000 + 125
D. 0x + 125 = 300,000
In a normal distribution, what percentage of scores fall between –1 and +1 standard deviation units of the mean?
A store is having a sale on almonds and jelly beans. For 8 pounds of almonds and 3 pounds of jelly beans, the total cost is $18 . For 2 pounds of almonds and 5 pounds of jelly beans, the total cost is $13 . Find the cost for each pound of almonds and each pound of jelly beans.
By setting up a system of equations and solving them, we find that the cost per pound of almonds is $1.50, and the cost per pound of jelly beans is $2.00.
To find the cost for each pound of almonds and each pound of jelly beans, we can set up two equations to solve the problem algebraically. Let's denote the cost per pound of almonds as a and the cost per pound of jelly beans as b. We have two scenarios provided:
8 pounds of almonds and 3 pounds of jelly beans cost a total of $18.
2 pounds of almonds and 5 pounds of jelly beans cost a total of $13.
We can translate these scenarios into two algebraic equations:
8a + 3b = 18
2a + 5b = 13
Now, we will solve this system of equations to find the values of a and b.
Step 1: Multiply Equation (2) by 4
8a + 20b = 52 (We multiplied all terms by 4 to match the coefficient of a in Equation (1))
Step 2: Subtract Equation (1) from the new equation
8a + 20b - (8a + 3b) = 52 - 18
17b = 34
Step 3: Solve for b
b = 34 / 17
b = 2
Now we know each pound of jelly beans costs $2.
Step 4: Substitute b back into Equation (1) to solve for a
8a + 3(2) = 18
8a + 6 = 18
8a = 12
a = 12 / 8
a = 1.5
So, each pound of almonds costs $1.50.
Therefore, the cost per pound of almonds is $1.50, and the cost per pound of jelly beans is $2.00.
Which angle pairs are supplementary ?
Answer:
4,5
Step-by-step explanation:
Daniel got a life insurance check of $5875 after the death of a close relative. He deposited it into a savings account at 1.7 percent interest for five years. What was the total amount of money in the account after five years?
A. $6462.50
B. $6433.13
C. $6374.38
D. $6315.63
a rectangle has perimeter 182 inches and length 52 inches what is the width
Which normal distribution has a wider spread: the one with mean 3 and standard deviation 4 or the one with mean 4 and standard deviation 3 ? the normal distribution with mean 4 and standard deviation 3 has the wider spread?
Answer:
The correct option is 1. The normal distribution with mean 3 and standard deviation 4 has a wider spread.
Step-by-step explanation:
Normal distribution is defined by two variables, mean and standard deviation.
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The spread of a normal distribution is not dependent on mean, it is completely dependent of standard deviation. Larger standard deviation means wider spread.
It is given that first normal distribution has
[tex]\mu_1=3[/tex]
[tex]\sigma_1=4[/tex]
Second normal distribution has
[tex]\mu_2=4[/tex]
[tex]\sigma_2=3[/tex]
Since [tex]\sigma_1>\sigma_2[/tex], therefore the normal distribution with mean 3 and standard deviation 4 has a wider spread.
Hence the correct option is 1.
Final answer:
The normal distribution with a mean of 3 and a standard deviation of 4 has a wider spread than a normal distribution with a mean of 4 and a standard deviation of 3, as the spread is determined by the standard deviation.
Explanation:
The question is asking which of the two normal distributions has a wider spread. The spread of a normal distribution is determined by its standard deviation. A normal distribution with a higher standard deviation will have a wider spread. In this case, the normal distribution with a mean of 3 and a standard deviation of 4 will have a wider spread compared to the normal distribution with a mean of 4 and a standard deviation of 3. Thus, the statement 'the normal distribution with mean 4 and standard deviation 3 has the wider spread' is incorrect.
In a normal distribution, as the standard deviation increases, the distribution curves become wider and shorter, reflecting a greater spread in the data. Because both distributions are normally distributed, we can compare the standard deviations directly to determine the spread: a standard deviation of 4 indicates a wider spread than a standard deviation of 3.
The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?
Answer: the answer is D
Step-by-step explanation:
By what transformation can the set representing the inverse of a function be found? 1) reflection in the origin 2) reflection in the line y = x 3) rotation of 90o about the origin
Answer:
2) reflection in the line y = x
Step-by-step explanation:
A function is transformed to its inverse by swapping the independent and dependent variables. Reflection in the line y = x does that.
One fourth of a number q is 3 more than three times a number w. Solve for q.
To solve for q, multiply both sides of the equation 1/4q = 3 + 3w by 4. This eliminates the fraction and gives us q = 12 + 12w.
Explanation:To solve for q, we need to translate the given information into an equation. The problem states that one fourth of q is 3 more than three times a number w. Written as an equation, this is represented as:
1/4 q = 3 + 3w
To solve for q, we can multiply both sides of the equation by 4 to eliminate the fraction:
q = 12 + 12w
This gives us the solution for q in terms of w.
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Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p.m. and walks at 90 steps per minute. At what time will Malory's steps catch up to Dori's steps?
The altitude of an equilateral triangle is 9 inches. Find the perimeter of the triangle in inches.
The perimeter of the triangle will be 31.18 inches.
what is perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.
If we draw a perpendicular line from one of the vertices of the triangle we get 2 right angled triangles each with altitude 9 ins and vertex angle = 30 degrees. So:-
[tex]Cos 30 =\dfrac{ 9} {h}[/tex]
where h = one of the sides of the equilateral triangle
[tex]h = \dfrac{9 }{ cos 30} = 10.392 \ inches[/tex]
Therefore the perimeter of the triangle =
[tex]3 \times 10.392 = 31.1769 \ inches[/tex]
Answer is 31.18 inches to the nearest hundredth.
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For the questions, imagine a segment in a plane. Use that information to help you answer the questions.
1. How many midpoints does the segment have?
a. one
b. two
c. indfinitely many
d. none
2. How many bisectors does the segment have?
a. one
b. two
c. indfinitely many
d. none
3. How many lines in the plane are perpendicular bisectors of the segment?
a. one
b. two
c. indfinitely many
d. none
how to write this number 2,015,473 in expanded form
If the equation of a line has a slope of zero and passes through the point (3,3) which form would be used to write the question of the line
What is the measure of angle S?
132 + 56 + 79 = 267
360 - 267 = 93
answer is 93 degrees
What is 30 1/4% as a fraction in simplest form
The simplest form is 3/40
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
Given:
30 * 1/4%
= 30* 1/400
= 30/400
=3/40
=0.075
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Find the midpoint of the line segment whose endpoints are (0,1/2 ) and (0,3/4 ).
Answer:
(0, 5/8)
Step-by-step explanation:
Write a compound inequality that represents the situation. On a road in the city of Rochester, the maximum speed is 50 miles per hour, and the minimum speed is 20 miles per hour.
A. 20 ≥ x ≥ 50
B. 20 > x > 50
C. 20 < x < 50
D. 20 ≤ x ≤ 50