Use the definition of the derivative as a limit to find the
derivative f′ where f(x)= √ x+2.
Step-by-step explanation:
If the equation is
[tex] \sqrt{x + 2} [/tex]
Then, here is the answer.
The definition of a derivative is
[tex] \frac{f(x + h) - f(x)}{h} [/tex]
Also note that we want h to be a small, negligible value so we let h be a value that is infinitesimal small.
So we get
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} [/tex]
Multiply both equations by the conjugate.
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \times \frac{ \sqrt{x + h + 2} + \sqrt{x + 2} }{ \sqrt{x + h + 2} + \sqrt{x + 2} } = \frac{x + h + 2 - (x + 2)}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{h}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{ \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
Since h is very small, get rid of h.
[tex] \frac{1}{ \sqrt{x + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{2 \sqrt{x + 2} } [/tex]
So the derivative of
[tex] \frac{d}{dx} ( \sqrt{x + 2} ) = \frac{1}{2 \sqrt{x + 2} } [/tex]
Part 2: If your function is
[tex] \sqrt{x} + 2[/tex]
Then we get
[tex] \frac{ \sqrt{x + h} + 2 - ( \sqrt{x} + 2) }{h} [/tex]
[tex] \frac{ \sqrt{x + h} - \sqrt{x} }{h} [/tex]
[tex] \frac{x + h - x}{h( \sqrt{x + h} + \sqrt{x}) } [/tex]
[tex] \frac{h}{h( \sqrt{x + h} + \sqrt{x} ) } [/tex]
[tex] \frac{1}{ \sqrt{x + h} + \sqrt{x} } [/tex]
[tex] \frac{1}{2 \sqrt{x} } [/tex]
So
[tex] \frac{d}{dx} ( \sqrt{x} + 2) = \frac{1}{2 \sqrt{x} } [/tex]
2 points
Daria earns h dollars per hour at the grocery store. She works 9 hours per week. She writes the expression 9 • h • 4 to represent how much
money she earns in a four-week month. Daria's boss writes the expression 36h. Which person's expression tells you how many hours Daria
works per four-week month? EXPLAIN YOUR REASONING.
Answer:
Daria's boss expression
Step-by-step explanation:
Her boss expression because it's asking about the hours worked per four week month. Daria's expression represents the 9 hours she works per week for the 4 weeks in the month.
Her boss expression represents the total number of hours she works altogether in all the four weeks in the month.
A researcher is interested in determining whether teens who transfer schools after their freshman year in high school demonstrate
more behavior problems on the Achenbach Youth Self Report test with a population mean of 50 and a population standard deviation of
10. The researcher has a sample of 100 teens with a mean score of 59. What is your obtained z?
The z-score of the number of teens that transfered schools is the standard score
The obtained value of z is 5
How to determine the value of z?The given parameters are:
Population mean, μ = 50Population standard deviation, σ = 10Sample, x = 100Sample mean = 59The z-value is calculated using:
z = (x - μ)/σ
Substitute known values in the above formula
z = (100 - 50)/10
Evaluate the difference
z = 50/10
Evaluate the quotient
z = 5
Hence, the obtained value of z is 5
Read more about z-scores at:
https://brainly.com/question/25638875
Help! 10 Points !!
A line passes through the point (-8. 5) and has a slope of -5/4
-3/5m + 8 = 20
what is the answer of m
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m + 8 = 20[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m = 20 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m =12[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ }{} m =12 \times \frac{5}{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: - m = 4 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:m = - 20[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
What is the solution to the system of equation s x+y=4. X=y-1
Answer:
x = 3/2
y = 5/2
Step-by-step explanation:
x + y = 4
x = y - 1
substitute y - 1 in for x in the first equation, to find y
y - 1 + y = 4
2y - 1 = 4
add 1 on both sides
2y - 1 = 4
+1 +1
2y = 5
divide by 2 on both sides
2y/2 = 5/2
y = 5/2
subtitute y in for the second equation, to find x
x = 5/2 - 1
x = 5/2 - 2/2
x = 3/2
so x = 3/2 and y = 5/2
to double check, plug x and y in the first equation
3/2 + 5/2 = 4
8/2 = 4
4 = 4
Find the equation of a line that passes through the point (0,-4) and has a gradient of 2. Leave your answer in the form y=mx+c
Answer:
y=2x-4
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=2(x-0)
y+4=2x-0
y=2x-0-4
y=2x-4
Someone pls
.
A
A
A
A
A
A
S
Answer:
7
Step-by-step explanation:
Degree of a polynomial is a variable's highest exponent
In this expression the degree is 7
Answer:
7
Step-by-step explanation:
If you used
P.E.M.D.A.S
Brainly please I worked so hard for this answer
In the electric field [tex]{\vec{E}=3x\hat{i}-2y\hat{j}+5z\hat{k}}[/tex], find the potential difference between the points A(1,3,5) and B(3,2,7)
Let's recall that, the potential difference between any two points X(x,y,z) and Y(a,b,c) is given by ;
[tex]{\boxed{\bf{V_{Y}-V_{X}=\displaystyle \bf -\int_{X}^{Y}\overrightarrow{E}\cdot \overrightarrow{dr}}}}[/tex]So, here ;
[tex]{:\implies \quad \sf \overrightarrow{E}=3x\hat{i}-2y\hat{j}+5z\hat{k}}[/tex]
So, now our second component of the Integrand will just be ;
[tex]{:\implies \quad \sf \overrightarrow{dr}=dx\hat{i}+dy\hat{j}+dz\hat{k}}[/tex]
So, now the whole integrand will just be ;
[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=(3x\hat{i}-2y\hat{j}+5z\hat{k})(dx\hat{i}+dy\hat{j}+dz\hat{k})}[/tex]
[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=3xdx-2ydy+5zdz}[/tex]
Now, Let's move to the final answer ;
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\int_{X}^{Y}3xdx-2ydy+5zdz}[/tex]
As,X is the point (1,3,5) and Y being (3,2,7) , so seperate the integral into three integrals with limits as follows respectively;
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(\int_{1}^{3}3xdx-\int_{3}^{2}ydy+\int_{5}^{7}zdz\bigg)}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(3\int_{1}^{3}xdx-2\int_{3}^{2}ydy+5\int_{5}^{7}zdz\bigg)}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{3\bigg(\dfrac{x^2}{2}\bigg)\bigg|_{1}^{3}-2\bigg(\dfrac{y^2}{2}\bigg)\bigg|_{3}^{2}+5\bigg(\dfrac{z^2}{2}\bigg)\bigg|_{5}^{7}\bigg\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{2\bigg(\dfrac{9}{2}-\dfrac12\bigg)-2\bigg(\dfrac{4}{2}-\dfrac92\bigg)+5\bigg(\dfrac{49}{2}-\dfrac{25}{2}\bigg)\bigg\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{3(4)-(-5)+5(12)\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{12+5+60\}}[/tex]
[tex]{:\implies \quad \displaystyle \boxed{\bf{V_{Y}-V_{X}=-77\:\: Volt}}}[/tex]
Hence, this is the required answer
Four friends are order pizza from a take away.
The amount of pizza each person eats is shown as a fraction below
Matthew eats 0.8of a pizza
Lily eats 3/4of a pizza
George eats 77%opizzas f a pizza
Sam eats 82%of a pizza
Which person eats the most pizza?
You must show your workings
Answer:
Sam ate the most pizza.
Step-by-step explanation:
Mathew: 0.8 is equal to 80%
To get a percentage, you need to move the decimal two places to the right.
Lily: 3/4 = 75%
George: 77%
Sam: 82%
The population of a city increased from 21,400 to 27,700 between 2007 and 2016. Find the change
of population per year if we assume the change was constant from 2007 and 2016.
Answer:
700
Step-by-step explanation:
2016 - 2007 = 9
27,700 - 21,400 = 6300
6300 / 9 = 700.
f(x) = x^2-3
What is the average rate of change on the interval [-5, 2] ?
Answer:
[tex](-3)[/tex].
Step-by-step explanation:
Over this interval, the change in the value of this function is:
[tex]f(-5) - f(2) = 22 - 1 = 21[/tex].
The corresponding change in the value of [tex]x[/tex]:
[tex](-5) - 2 = -7[/tex].
The average rate of change of function [tex]f[/tex] over this interval is equal to the change in the function value divided by the corresponding change in [tex]x[/tex]:
[tex]\begin{aligned}& (\text{average rate of change}) \\ =\; & \frac{(\text{change in function value})}{(\text{change in $x$})} \\ =\; & \frac{f(-5) - f(2)}{(-5) - 2} \\ =\; & \frac{22 - 1}{-7} \\ =\; & \frac{21}{-7} \\ =\; & -3\end{aligned}[/tex].
Thus, the average rate of change of [tex]f(x) = x^{2} - 3[/tex] over the interval [tex][-5,\, 2][/tex] would be [tex](-3)[/tex].
A bag contains 2 red marbles, 7 blue marbles and 5 green marbles. If two marbles are
drawn out of the bag, what is the exact probability that both marbles drawn will be
blue?
Answer:
1/2
Step-by-step explanation:
There are :-
⇒ 2 red marbles
⇒ 7 blue marbles
⇒ 5 green marbles
Probability (Blue)
= No. of blue marbles / No. of total marbles= 7 / (2 + 7 + 5)= 7/14= 1/2True or False: In an exponential regression, the data points tend to increase in one direction and flatten out in the other direction.
Answer:
T
Step-by-step explanation:
The regression line is flat when there is no ability to predict whatsoever. The regression line is sloped at an angle when there is a relationship. The extent to which the regression line is sloped, however, represents the degree to which we are able to predict the y scores with the x scores
help me please. either one is fine.
PLEASE HELP PLEASE HELP
Consider the graph of the quadratic function. Which
interval on the x-axis has a negative rate of change?
-2 to -1
-1.5 to 0
0 to 1
1 to 2.5
The only interval with a negative rate of change is the last one:
[1, 2.5]
When the rate of change is negative?
For an interval (a, b) and a function f(x), the rate of change is defined as:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
So the rate of change is only negative when the function evaluated on the first value of the interval is larger than the function evaluated in the second one.
For example, on the interval [1, 2.5} we can see that:
f(1) = 3
f(2.5) = -1
Then on this interval, the rate of change will be negative, meaning that this is the correct option.
If you want to learn more about rates of change, you can read:
https://brainly.com/question/8728504
Answer:
It's D: 1 to 2.5
Step-by-step explanation:
It's D: 1 to 2.5
Help picture below problem 16
Concept :-
⠀
We have studied the law which states that the sum of all angles in a triangle is 180°, this is known as angle sum property of a triangle. We can solve this question based on that property.
Solution :-
⠀
Let us assume the missing angle to be x,
Therefore,
→ 66° + 71° + x = 180° ( Angle sum property of a triangle )
→ 137° + x = 180°
→ x = 180° - 137°
→ x = 43°
Thus, the measure of the missing angle is 43°.
Hope that helps :)
Find angles B, E, C, and D, given that angle m A=140° and m F=130°.
*Picture is not drawn to scale*
Answer:
Angle B=40 degrees
Angle C= 90 degrees
Angle E=50 degrees
Please Mark Brainliest
these answer- I am sure they ar correct
A large set of data was collected and analyzed for the majors of college seniors in the U.S. From the scatter plots produced the following associations were observed. The linear model P(t) 2,376 + 73,219 can be used to estimate the number of college seniors who graduated with a bachelor's degree in psychology, tyears after 2000 - The linear model B(t) = 2, 414t + 56, 545 can be used to estimate the number of college ( seniors who graduated with a bachelor's degree in biology, tyears after 2000. Which of the following statements are true? The number of psychology degrees increases by about 73,219 each year after 2000. The number of biology degrees increases by about 2.414 each year after 2000. About 73.000 students graduated with degrees in psychology in 2000. About 2.400 students graduated with degrees in biology in 2000. in 2000, more students graduated with psychology degrees than biology degrees
Using linear function concepts, it is found that the true statements are as follows:
The number of biology degrees increases by about 2.414 each year after 2000. About 73.000 students graduated with degrees in psychology in 2000.In 2000, more students graduated with psychology degrees than biology degrees.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.In this problem, for psychology, the model for the number of graduated students in t years after 2000 is:
P(t) = 2,376t + 73,219.
For biology, it is given by:
B(t) = 2,414t + 56, 545
Hence, the correct statements are:
The number of biology degrees increases by about 2.414 each year after 2000. About 73.000 students graduated with degrees in psychology in 2000.In 2000, more students graduated with psychology degrees than biology degrees.More can be learned about linear function concepts at https://brainly.com/question/24808124
A bedroom door in the house has the same dimension as the front door but the length is 30 inches rather than 36 inches how much greater is the volume of the front door than than the bedroom door
Answer:
6/5
Step-by-step explanation:
Calculate the volume by multiplying the measured length and width of the space together, then multiply the result by the height of the room. From the example, 10 * 25 feet = 250 square feet, and 5 * 10 feet = 50 square feet.
The area of South America is approximately 1.78 × 107 square kilometers. Its population is approximately 3.50 × 108 people. What is the approximate population density (people per square kilometer) of South America? Write your answer in standard form. If necessary, round your answer to the nearest hundredth.
A: 19.66 people/km^2
B: 1.97 × 10^15 people/km2
C: 5.09 people/km^2
D: 1.97 × 10^1 people/km^2
Answer: 19.66 people/km^2, A
Step-by-step explanation:
The population density will be equal to 82.96 people/km2.
The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
here, we have,
Given that the area is 1.78 × 10⁷ km² with 3.50 × 10^8 people.
The population density will be calculated as below:-
Density = people / km² = ( 3.50 × 10^8 ) / ( 1.78 x 10⁷ )
Density =19.66
Density = 19.66 people/km²
Therefore, the population density will be equal to 82.96 people/km2. The correct option is A.
To know more about an expression follow:
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Can you be serious and more understanding about the home work
Answer:
yes
Step-by-step explanation:
is there a specific question?
Answer: All children should be doing homework. But the amount and quality should change." His basic prescription.
Step-by-step explanation:
When do you say that a given quadrilateral is a parallelogram?
Answer:
Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D. We know that the sum of the angles of a quadrilateral is 360o.
Step-by-step explanation:
hope that helps
the figure represent 7/9 0f a full circle Find the measure of the marked central angle
Step-by-step explanation:
tbh I don't know I need help with that too please like this comment
The measure of the marked central angle of the sector will be 280°.
What is the arc length of the sector?Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be
Arc = (θ/2π) 2πr
The figure addresses 7/9 of a complete circle. Then the arc length of the circle will be given as,
Arc / P = 7/9
Simplify the equation, then we have
(θ/2π) 2πr / 2πr = 7/9
θ/2π = 7/9
θ = 14π / 9
θ = 280°
The central angle of the sector will be 280°.
More about the arc length of the sector link is given below.
https://brainly.com/question/15955580
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The value of x is 6. What is the value of y ?
Answer: y = 4.5
scale factor = 4/3
Change 75m to decimeters
Answer:
750 decimeters
Step-by-step explanation:
1 meter is equal to 10 decimeters.
so 75 times 10 equals your answer: 750 decimeters
Hope that helps!
write THREE equivalent fractions for the following fractions:
25/50 = ___ = ___ =____
Answer:
25/50 = 5/10 = 1/2
Step-by-step explanation:
I hope it will be helpful
Answer:
25/50 = 5/10 = 1/2Hooe this helps you :)PLEASE HELP!!!!
Earth is about 1.5 x 10^8 kilometers away from the sun. Saturn is about 1.4 x 10^9 kilometers away from the sun. How many times closer to the sun is Earth than Saturn? Give answer is standard form and round to the nearest tenth.
If you can, please explain, or just show what you did
Answer:
8.33
Step-by-step explanation:
Answer: 8.33 minutes will it take to travel from the sun to the earth. Step-by-step explanation: Distance of the Earth from the Sun = d = 1 km = 1000 m.
Answer: 9.33
Step-by-step explanation: you divide Saturn by earth
what is the formula for the volume of a sphere with radius r = 5?
Answer:
V = (4/3)π·5³ = 500π/3
Step-by-step explanation:
The formula for the volume of any sphere as a function of its radius is ...
V = (4/3)π·r³
When the sphere has a radius of 5, we replace r in the formula with 5. The formula for the volume of a sphere with radius 5 is ...
V = (4/3)π·5³
__
When that is evaluated, the volume is found to be ...
V = 500π/3 ≈ 523.599 . . . cubic units