Answers
Answer:
k=6
Step-by-step explanation:
For a piecewise function to be continuous, the left-side and right-side limits must be equal to each other. Therefore, the left-side limit of f(x) is 8 because the derivative of 2x^2 is 4x, and then directly substituting x=2 gives us 4(2)=8. Therefore, the right-side limit must also equal 8. Therefore, k must be 6 because 2+6=8.
Answer:
[tex]\displaystyle k = 6[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
FunctionsFunction NotationAlgebra II
Piecewise FunctionsCalculus
LimitsContinuityStep-by-step explanation:
Step 1: Define
Identify
Continuous at x = 2
[tex]\displaystyle f(x) = \left \{ {{2x^2 \ if \ x < 2} \atop {x + k \ if \ x \geq 2}} \right.[/tex]
Step 2: Solve for k
Definition of Continuity: [tex]\displaystyle \lim_{x \to 2^+} 2x^2 = \lim_{x \to 2^-} x + k[/tex]Evaluate limits: [tex]\displaystyle 2(2)^2 = 2 + k[/tex]Evaluate exponents: [tex]\displaystyle 2(4) = 2 + k[/tex]Multiply: [tex]\displaystyle 8 = 2 + k[/tex][Subtraction Property of Equality] Subtract 2 on both sides: [tex]\displaystyle 6 = k[/tex]Rewrite: [tex]\displaystyle k = 6[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Limits - Continuity
Book: College Calculus 10e
Related Questions
Write an equation for the line that is parallel to the given line and that passes through the given point. y = 1/2x - 8; (-6, -17).
Answers
Answer:
y = 1/2x - 14
Step-by-step explanation:
Parallel lines have the same gradient
So,
gradient for second line = gradient of the first line = 1/2
Also,
the line passes through (-6,-17)
So, we can find the y-intercept by substitution
y = mx + c
-17 = (1/2 * -6) + c
-17 = -3 + c
c = -14
So,
the equation is y = 1/2x - 14
Write an exponential function in the form y = ab" that goes through points (0,7)
and (9,3584).
Answers
Answer:
Step-by-step explanation:
I'm going to assume you meant y = ab^x. If this is not correct, leave a comment.
x = 0
y = 7
7 = a * b^0
anything to the zero power is 1
y = a*b^0
y = a*1
7 = a
So far what you have is
y = 7 * b^x
Now let
x = 9
y = 3584
3584 = 7 * b^9 Divide by 7
3584/7 = b^9
512 = b^9
If you knew how to use logs, that would be the surest way to do this question. However I'm going to make an assumption again and assume that you have not taken those yet.
So the easiest way is to find out what raised to the 9th power will equal 512
Could b = 5?
5^9 = 1 million 9 hundred thousand something. 5 is far too big. Make sure you understand why. 1 million is far greater than 512
So let's try b = 3
3^9 = 19 thousand which is still far too big. 19 thousand something is far larger than 512.
We have just one more number that we can try.
2^9 = 512 and we have it
Answer y = 7*2^x
Write 8 as a percentage of 32
Plssss helppp
Answers
Answer:
25% of 32 is 8
Step-by-step explanation:
[tex]\frac{x}{100} * 32 = 8\\\\x = 25%[/tex]
Therefore, 25% of 32 is 8.
8 is 25% of 32.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
We know that, 8/32=1/4
in percentage form, 8 of 32= 1/4×100
=25%
Hence, 8 if 25% of 32.
To learn more on percentage click:
https://brainly.com/question/13450942
#SPJ2
On a coordinate plane, a curved line with minimum values of (negative 1.5, negative 2) and (1.5, 2), and a maximum value of (0, 4), crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 4).
Which is an x-intercept of the graphed function?
(0, 4)
(–1, 0)
(4, 0)
(0, –1)
Answers
Answer:
It's (-1,0)
Step-by-step explanation:
Just did the question.
Answer:(-1,0)
Step-by-step explanation:
Please help me with this please
Answers
Answer:
option 2 : y-7 = 2(x-1)
Step-by-step explanation:
the fastest way is to simply put the x- and y-values of both points into the equations, and see, which one is true for both points.
the first option is only true for the second point
7-7 = 4(1-1)
0 = 4×0 = 0
but for the first point
3-7 = 4(-1 - 1)
-4 = 4×-2 = -8
-4 = -8 is false
the second option then is true for both points
7-7 = 2(1-1)
0 = 0
3-7 = 2(-1 - 1)
-4 = 2×-2 = -4
Helppp please and thank you!!
Answers
Answer:
Step-by-step explanation:
3,-3
can anyone help me plz
Answers
224 in ^2
Explanation:
Surface Area = 2x(12x4 + 12x11 + 4x11)= 448in^2
I hope this helps you. If available please give me a Branliest. It would be much appreciated. It would also help me answer more questions! Goodluck.
- Mathhotdog •~•
Two-thirds of a number is 5 more than half of it . What is the number ?
Answers
Answer:
2.50 is the answer of the question
Question 17 of 33
Which of the following terms best describes a group of equations in which at
least one equation is nonlinear, all of the equations have the same variables,
and all of the equations are used together to solve a problem?
A. System of linear inequalities
B. System of nonlinear equations
C. System of linear equations
D. System of nonlinear inequalities
Answers
Answer:
C
Step-by-step explanation:
i took the test
A jar of marbles has three blue marbles, four red marbles, and two green marbles, what is the possibility of drawing a marble that is green or not red?
1/3
4/9
5/9
2/3
Answers
Answer:
5/9
Step-by-step explanation:
There are 9 marbles total (3+4+2). There are 2 green marbles and 3 blue marbles (not red). The total fraction will be 5/9.
In a survey of 3,500 people who owned a certain type of car, 1,225 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answers
So move the decimal to the right 2 places & that gives you 35% of the people were satisfied with the car.
I would not buy that car!
Which equation gives the volume of the sphere?
O V=2/3(27ń)
O V=4/3(27)
O V= 2/3 (27)
O V= 4/3 (27ń)
Answers
Answer:
The correct option is (b).
Step-by-step explanation:
A sphere and a cylinder have the same radius and height,
The volume of cylinder is,
[tex]V=\pi r^2 h\\\\V=\pi r^3[/tex]
ATQ,
The volume of cylinder is 27 cubic units.
[tex]\pi r^3 = 27[/tex]
The formula for the volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\times 27[/tex]
So, the correct option is (b).
Graph the function.
y = 2x^2 + 4x
Answers
Answer:
Step-by-step explanation:
The function y = 2x^2 + 4x has a parabolic graph that opens up.
*In factored form we have y = 2x(x + 2); if we set this equal to zero and solve for x, we obtain {-2, 0}, the roots of this function.
*The axis of symmetry is halfway between these roots: x = -1. The y-value of the vertex is the value of the function at x = -1: f(-1) = 2(-1)^2 + 4(-2) = -6. Thus, the vertex is (-1, -6).
* The y-intercept is (0, 0), since y = 0 when x = 0.
Graph the points shown and draw a smooth curve through them, remembering that this parabola opens up.
Round to the nearest cent or whole number as needed.
The price of a bracelet is $1.29. If the tax rate is 5%, find the total cost of the bracelet
Answers
Answer:
Cost of bracelet = $1 and 35 cents
Step-by-step explanation:
Price before tax = $ 1.29
Tax Price = 5% of 1.29
[tex]=\frac{5}{100} \times 1.29\\\\= 6.45 \times \frac{1}{100} \\\\= 0.0645[/tex]
Therefore price after tax = 1.29 + 0.06245 = 1.3545
Ans : cost of bracelet = $1 and 35 cents
One of the angles formed by two intersecting lines is 40°. What is the measure of the other three angles?
Answers
Answer:
Hello! answer:
140, 140 and 40
Step-by-step explanation:
140 + 140 + 40 + 40 = 360
The other three angles would measure to 140, 140 and 40 Hope that helps!
In the expansion of (3x^3 + 4x) (2x^2 5), what is the coefficient of x^3?
Answers
Answer: 30x^5+40x^3
Step-by-step explanation:
I have a calculator so I put the whole thing in. This might not be much of a help and sorry there is no explanation for this question from me.
Solve the inequality.
1
x+5 < 6
2
Help me please
Answers
Answer:
If we are solving x + 5< 6 the inequality is x< 1
Step-by-step explanation:
If helps mark as brainllest please!!!
geometric probability
PLEASE HELP!
Answers
Answer:
Step-by-step explanation:
The red sections are sectors of the circle. We need that area. We'll find one then multiply it by 2, since they're both the same.
[tex]A_s=\frac{60}{360}\pi (4)^2\\A_s=\frac{1}{6}\pi (16)\\A_s=8.377[/tex]and now we multiply it by 2 to get the red area:
[tex]A_s=16.754[/tex]
And now the area of the circle:
[tex]A_c=\pi (4)^2\\A_c=16\pi\\A_c=50.265[/tex] and now divide to get the percentage:
[tex]\frac{16.754}{50.265}*100=[/tex] 33.3%
The distance from the Earth to the Sun is 92,640 miles Write the distance between the Earth and the Sun, rounded to two significant figures
Answers
Step-by-step explanation:
In scientific notation, we can write the distance as
92,640 mi = 9.264×10^4 mi
Reducing this to 2 signficant figures, we get
9.3×10^4 mi
with proper rounding off of the. numbers.
What is the pre image vertices?
Answers
Answer:
you divide all the numbers so the triangle will be at -2.5x, 1x and 2y and the rectangle is multiplied by 2 so 5x and 4y
Step-by-step explanation:
Question
The average of 10 numbers in a list is 16. If two of the numbers in the list are each increased by 5, by how much will the average of the 10 numbers in the list be increased?
[please help]
Answers
Answer:
Step-by-step explanation:
Lets understand what the question says:-
Mean or average in a list=16
Total sum of observations= x
Equation:-
x/10=16
x=160
If 2 numbers are increased by 5 that means
New sum of observations=160+10=170
Therefore,
New average or new mean=170/10=17
Therefore the average gets increased by 1
Which?
A
B
C
D
Help me for 20 points!!!
Answers
Answer:
8/5
Step-by-step explanation:
7 3/10-5 7/10=8/5
Find the equation of the line that passes through the points A (2, 3) and B (5, -7)
Answers
Answer:
10x+3y=29
Step-by-step explanation:
Given points:(x1,y1)=(2,3)
(x2,y2)=(5,-7)
We know, the equation of line passing through two points is given by,
y-y1={(y2-y1)/(x2-x1)}*(x-x1)
Hence,y-3={(-7-3)/(5-2)}*(x-2)
or,y-3=(-10/3)*(x-2)
or,3y-9= -10x+20
or,3y+10x=20+9
or,10x+3y=29 is the required equation.
Which of the following is the best approximation of the volume of the cylinder below?
Use 3.14 for π
Answers
Answer:
sana Po nakatulong
stay safe po
help with the question
Answers
10. How many solutions does this system of equations have? Explain how you know.
y = -4x + 3
2x + 8y = 10
Answers
18 divided by under root 18
Answers
Answer:
18
√18
=3√2(Decimal: 4.242641)
Frog Kayaks LLC charges $50 to rent a kayak
and an additiona $10 per hour for a quided
river trip. I Tonya's trip lasts 7 hours, what is
the total cost to kayak?
Answers
Answer:
120$
Step-by-step explanation:
Equation
$= 10x + 50
x is the amount of hours.
Plug in for x
$ = 10(7) + 50
$ = 70 + 50
$ = 120
ellus
Find the total surface area of the
following cylinder:
r= 3 cm
3 cm
SA = [ ? ]cm2
Leave your answer in terms of t.
Enter the number that goes in the green box.
Enter
Answers
Answer:
36pi ( 113.1 if you want in decimal )
Step-by-step explanation:
A=2πrh+2πr2=2·π·3·3+2·π·32≈113.09734 = 36 pi
Calcula el perímetro y el área de un hexágono de 4 metros de lado y 3.46 m de apotema
Answers
Answer:
[tex]P=24\: m[/tex]
[tex]A=41.52 \m^{2}[/tex]
Step-by-step explanation:
El perímetro de un hexágono se calcula de la siguiente manera:
[tex]P=6*l[/tex]
l es el lado del hexágono l = 4 m
Entonces P es:
[tex]P=6*4=24\: m[/tex]
El área del hexágono puede calcularse de la siguiente manera:
[tex]A=\frac{P*Ap}{2}[/tex]
P es el perímetro = 24 m
Ap es la apotema = 3.46 m
El Area sera:
[tex]A=\frac{24*3.46}{2}[/tex]
[tex]A=41.52 \m^{2}[/tex]
Espero te haya sido de ayuda!
