Find the first derivative.
Answer: y’ = 2/3 x^1/2 - 2/ sqrt of x - 5/2x^2/3
I’m given an answer but don’t know how to get it.
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( \frac{{x}^{2} - 4x + 5) }{2 \sqrt{x} } )}{x } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ {x}^{2} - 4x + 5 }{ \sqrt{x} } [/tex]
We know, division rule of differentiation :
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{u}{v} [/tex]
then,
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{v\frac{du}{dx} - u \frac{dv}{dx} }{(v) {}^{2} } [/tex]
So, let's do the same in given equation :
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} \frac{d}{dx}(x {}^{2} - 4x + 5) - ( {x}^{2} - 4x + 5) \frac{d}{dx}( \sqrt{x} ) }{( \sqrt{x} ) {}^{2} } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( {x}^{2} - 4x + 5) \frac{1}{2 \sqrt{x} } }{x } [/tex]
[ This is the required Answer, but you can simplify it however you want according to the choices given ]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{x \bigg( \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } \bigg)}{x } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{(2x - 4)}{ \sqrt{ x}} - \frac{( {x}^{2} - 4x + 5) }{2 \sqrt{x {}^{3} } }[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Related Questions
im in a mega rush please help me fast
Answers
The equivalent expression of 2⁻³ / 2⁻⁵ will be 2².
Option A is true.
What is a mathematical expression?
Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The mathematical expression is,
⇒ 2⁻³ / 2⁻⁵
Now, The rule of exponent is;
[tex]\frac{a^{x} }{a^{y} } \\a^{x} * a^{-y} \\a^{x+ (-y)} \\a^{x-y}[/tex]
Hence, Solve the expression by rule of exponent as;
The mathematical expression is,
⇒ 2⁻³ / 2⁻⁵
⇒ 2⁻³ / 2⁻⁵
⇒ 2⁻³ × 2⁵
⇒ 2⁻³⁺⁵
⇒ 2²
So, 2⁻³ / 2⁻⁵ = 2²
Thus, The equivalent mathematical expression of 2⁻³ / 2⁻⁵ will be 2².
Option A is true.
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12. We have worked for along time
now. We're ...... ..... tired.
O O O O
A getting
B seeing
C sending
D meaning
Answers
Not seeing cause seeing is to see something.
Not sending cause you aren’t sending that you are tired.
and meaning is not it either cause you are not meaning tired.
so it would be A —> getting
Given points J(3,3), A(5.4), and R(4,2), graph ofAJAR and its reflection image across the given line.R-axis
Answers
When we reflect a point along the x-axis, the x coordinate stays the same BUT the y coordinate is negated.
A point (x,y) becomes (x, -y)
et us apply this rule to the points J, A, and R. SThis is shown below:
[tex]\begin{gathered} J(3,3)\rightarrow J^{\prime}(3,-3) \\ A(5,4)\rightarrow A^{\prime}(5,-4) \\ R(4,2)\rightarrow R^{\prime}(4,-2) \end{gathered}[/tex]The graph of the triangle will look like >>>
thank u very much to whoever do this
Answers
Answer:
C
Step-by-step explanation:
20+80 = 100
a triangle equals 180* so
1080-100=80 or just use a calculator OR with your brain
The coordinates of midpoint M and endpoint C or a segment are M(-2,-7) and C(12,-9). Find the coordinates of the other endpoint15 )
Answers
we have that the midpoint is (-2,-7)
and the endpoint is (12,-9)
We remember the midpoint formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where (x1,y1) are the coordinates of one endpoint and
(x2,y2) are the coordinates for the other endpoint.
Here, we are trying to find (x2,y2) given that
(x1, y1) ---> (12, -9)
[tex]\begin{gathered} x_1=12 \\ y_1=-9 \end{gathered}[/tex]And since we also know the midpoint M(-2, -7), making a comparison with this and the midpoint formula, we get two equations, the first one is:
[tex]\frac{x_1+x_2}{2}=-2[/tex]substituting x1 and solving for x2:
[tex]\frac{12+x_2}{2}=-2[/tex][tex]\begin{gathered} 12+x_2=4 \\ x_2=4-12 \\ x_2=-8 \end{gathered}[/tex]And now, with the second equation which is:
[tex]\frac{y_1+y_2}{2}=-7[/tex]we substitute y1 and solve for y2:
[tex]\frac{-9+y_2}{2}=-7_{}[/tex]solving for y2:
[tex]\begin{gathered} -9+y_2=-14_{} \\ y_2=-14+9 \\ y_2=-5 \end{gathered}[/tex]This the other endpoint (x2,y2) is at (-8,-5)
Ricardo can complete 4 laps around a track in 10 minutes. Create a graph that has a slope that represents the
number of laps Ricardo can run per minute.
Select two points on the coordinate grid. A line will connect the points.
HELP !!
Answers
The graph is attached below.
The number of laps completed by Ricardo in 10 minutes is 4.The number of laps completed by Ricardo in 1 minute is 4/10.Thus, slope is 0.4.We can form a linear function.The function "y" equals 0.4x.We have to graph the function.In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.y = 0.4xNow, we can get several pairs of coordinates that satisfy the above linear function.We plot the points on the graph and join them.We can see that the given function is an equation of a straight line that has a positive slope of magnitude 0.4 and passes through origin.To learn more about functions, visit :
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Solve: 18a2−30=−33a. Separate your answers, from smallest to greatest, with a comma. Enter only integer(s) or fraction(s).
Answers
The solution for the quadratic equation is -5/2, 2/3
Given,
The equation: 18a² - 30 = -33a
We have to solve this equation
We can convert this equation into a quadratic equation:
18a² + 33a - 30 = 0
Now lets solve this quadratic equation with quadratic formula:
Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
Here,
a = 18, b = 33 and c = -30
Now we can solve:
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]
= [tex]\frac{-33(+-)\sqrt{33^{2} -4(18)(-30)} }{2(18)}[/tex]
= [tex]\frac{-33(+-)\sqrt{1089-(-2160)} }{36}[/tex]
= [tex]\frac{-33(+-)\sqrt{1089+2160} }{36}[/tex]
= (- 33 ± √3249) / 36
= (- 33 ± 57) / 36
Solve for:
(- 33 + 57) / 36 = 24/36 = 2/3
Solve for:
(- 33 - 57) / 36 = - 90/36 = - 30/12 = -10/4 = -5/2
That is, the solution for the quadratic equation is -5/2, 2/3
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What number comes next in the following sequence: 8,13,18,23,28,...?
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Help me with this please
Answers
nswer : D) 1I, II and III
U.S. Customary area unit conversion with whole number values
A flower bed has the shape of a rectangle 21 feet long and 9 feet wide. What is its area in square yards?
Be sure to include the correct unit in your answer.
Answers
189cm²
Step-by-step explanation:
area is multiplication so it will be L×B
also because its a rectangle
These box plots show the prices for two different brands of shoes.65 70 75 80 85Brand AHIH1550507085Brand B0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 e 90 95 100Price (5)Which statement is the most appropriate comparison of the spreads?O A. The interquartile range (IQR) for brand A, $10, is less than the IQRfor brand B, $20.O B. The interquartile ranges (IQRS) for brands A and B are both $20.O C. The median for brand A, $75, is greater than the median for brandB. $60.O D. The interquartile range (IQR) for brand A, $20, is less than the IQRfor brand B, $70.
Answers
Given:
Given the box plots of two different brands of shoes.
Required: Most appropriate comparison of the spreads
Explanation:
From the box plot of brand A,
Minimum value = 65
First quartile, Q1 = 70
Median = 75
Third quartile, Q3 = 80
Maximum value = 85
Also, from the box plot of brand B,
Minimum value = 15
First quartile, Q1 = 50
Median = 60
Third quartile, Q3 = 70
Maximum value = 85
The interquartile range is the difference between the upper quartile and the lower quartile
The interquartile range of brand A is
[tex]\begin{gathered} Q_3-Q_1=80-70 \\ =10 \end{gathered}[/tex]The interquartile range of brand B is
[tex]\begin{gathered} Q_3-Q_1=70-50 \\ =20 \end{gathered}[/tex]Option A is correct.
The median for brand A is $75, which is less than the median of brand B, $60.
Option C is correct.
Final Answer: The most appropriate
What is the equation of a line, in slope-intercept form, that has a slope of m=4 and passes through the point (5, 12) ? Enter your answer in the box.
Answers
The equation of line is given by y-12=4(x-5).
What is equation of line with slope intercept form?
The equation of a line in point-slope form can be written as
y-y_1=m(x-x_1) where (x_1,y_1) is the points line passes through.
(y-12)=4(x-5)
Where m=4 and x_1=5,y_1=12
Hence, the equation of line is
y=4x-5+12
y=4x+7
The equation of line with the form of slope intercept form is y-12=4(x-5).
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
Answers
Consider the first equation,
[tex]y=\frac{3}{2}x-2[/tex]This equation passes through (0,-2) and (2,1).
second
[tex]y=-\frac{1}{2}x+2[/tex]This equation passes through (0,2) and (4,0).
Now we can plot the points and join them to get the corresponding lines on the graph as,
It is observed that the two lines intersect at point (2,1).
So the solution to the given equations must be x=2 and y=1.
Which of the following numbers represents the biggest risk of getting a disease? 1in 10, 1 in 1000, 1 in 100
Answers
Answer:
1 in 10
Step-by-step explanation:
Solve the problem.
Find m so that x + 4 is a factor of 5x3+ 18x² + mx + 16
Answers
The value of m such that x +4 is a factor of 5x³ + 18x² + mx + 16 is; -4.
What is the value of m for which x +4 is a factor of 5x³ + 18x² + mx + 16?It follows from the task content that the value of m for which x +4 is a factor of 5x³ + 18x² + mx + 16 is to be determined.
Hence, if x + 4 is a factor, it follows that x = -4 is a zero of the expression.
Therefore; 5(-4)³ + 18(-4)² + m(-4) + 16 = 0.
-320 + 288 - 4m + 16 = 0.
-16 - 4m = 0
4m = -16
m = -16/4
m = -4.
Ultimately, the value of m for which x+4 is a factor of 5x³ + 18x² + mx + 16 is; -4.
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The profit from the expenditure of x thousand dollars on advertising is given by P(x)=930+15x-4x^2.
Find the marginal profit when the expenditure is x = 7.
Answers
The marginal profit is -41 dollars.
In accounting, a profit is an income that is given to the owner throughout a successful market producing process (business).
Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.When one more unit is manufactured and sold, a company or individual will make a profit known as marginal profit. The additional expense or profit made when producing the following unit is referred to as marginal. While marginal cost is the additional expense for producing one extra unit, marginal product is the additional income earned.The advertising is given by P(x) = 930 + 15x -4x².
The marginal profit at x = 7 is given by
P(x) = 930 + 15x -4x²
P'(x) = 15 - 8x
Now at x = 7 the marginal profit is
P'(7) = 15 - ( 8×7 )
or, P'(7) = -41
Hence there will be marginal profit of -41 dollars.
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will give brainliest for correct answer
Answers
The correct approaches that can be used to solve the increase in area are
dr = 2Use differential to determine the change in the functionBase value of r is 42A(44) - A(42)The area of the circle has an estimated increment of 527.52 square mm
What are areas?The area of a shape is the amount of space on the shape
For all regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the correct approach to the problem?From the question, the given parameters are:
Previous radius = 42
New radius = 44
Calculate the change in the radius
dr = New radius - Previous radius
Substitute the known values in the above equation
So, we have
dr = 44 - 42
Evaluate
dr = 2
The above method leads to a differentiation problem where dr = 2
So, the correct approaches to the problem include
dr = 2Use differential to determine the change in the functionBase value of r is 42A(44) - A(42)The change in the areaThe area of a circle is
A = πr²
Differentiate
d(A) = 2πr * dr
Where
r = 42
dr = 2
So, we have
d(A) = 2 * 3.14 * 42 * 2
Evaluate
d(A) = 527.52
Hence, the estimated increase in the area is 527.52 square mm
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Enter the correct answer in the box.
Linear function g is shown in the graph. Write the slope-intercept form of the equation representing this function.
g
Answers
The equation in slope-intercept form that represents the function is: g(x) = -2x + 1.
How to Write the Slope-intercept Form of an Equation?To write the slope-intercept form of an equation that represents the linear function g, find the slope (m) of the line and determine the y-intercept (b) of the line, then substitute the values into g(x) = mx + b.
Slope of the line that represents function g = change in y/change in x = -6 units/3 units
Slope of the line (m) = -6/3
Slope of the line (m) = -2.
The line intercepts the y-axis at y = 1, therefore the y-intercept (b) of the linear function is b = 1.
To write the equation representing the function, substitute m = -2 and b = 1 into g(x) = mx + b:
g(x) = -2x + 1
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for f(x) = -2x+5, find the value of f(-1) + f(4)
Answers
Answer:
3 f
Step-by-step explanation:
(-1)+(4)
-+(4)
-+4
-f+4
-f+4
3
3
At a benefit concert, eleven bands have volunteered to perform but there is only enough time for five of the bands to play. How many lineups are possible?
Answers
The number of ways that the line up can be possible when eleven bands have volunteered to perform but there is only enough time for five of the bands to play is 462 ways.
How to illustrate the information?Eleven bands have volunteered to participate in the charity concert, but there is only enough time for five of them to do so. This involves combinations and permutations, it should be highlighted.
Therefore, the number of ways that the line up can be possible will be:
n! / (n − r)!
where n is the number of things to choose from and we choose r of them
= 11! / (11 - 5)!5!
= 11! / 6!5!
= 462
There are 462 ways.
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The line below is the function y=-x+3. Identify the equation of a perpendicular line
Answers
The equation of the perpendicular line is y = x + 3
Perpendicular line:
The perpendicular line means a straight line that makes the right angle (90 degrees) with the other line.
Given,
Here we have the equation y = -x + 3.
Now, we need to find the equation of the perpendicular line.
In order to find the equation of a perpendicular line, first we need to find the negative reciprocal of the slope given.
Through the given equation we have identified the slope of the line is -1. so the slope of the perpendicular line will be 1.
While looking at the graph we have identified the y intercept of the equation is 3.
So now we know the values of y-intercept and slope.
We just put them together, and apply it one the standard form of the equation of line, then we get,
y = 1x + 3
y = x + 3.
Therefore, the equation of perpendicular line is y = x +3.
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Which inequality describes this situation?
SPEED
LIMIT
80
MINIMUM
75
75 ≥ x ≥ 80
75 ≤ x ≤ 80
75 >x> 80
75 < x < 80
Answers
the second one
Step-by-step explanation:
if 75 is the minum speed then you need to go more than 75 and less than 80 which is what the second one is showing
The regular price of an MP3 player was $200. During a holiday sale it is marked down by $60. What is the percent discount?A.60%B.34%C.30%D.28%
Answers
Given : Regular price of MP3 player was $200. It was marked down by $60.
Required: Percent discount
Explanation:
Marked Price = $200
Discount given = $60
[tex]Percent\text{ discount = }\frac{Discount\text{ given}}{Marked\text{ price}}\ast100[/tex]So, percent discount =
[tex]\frac{60}{200}\ast100=30\%[/tex]Final answer : Percentage discount is 30%
Simplify 4 square root of 72
Answers
Simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94.
As given in the question,
Given expression,
4 square root of 72
Prime factors of 72 are as follow:
72 = 2 × 2 × 2 × 3 × 3
Rewrite them into exponent form we get
72 = 2³ × 3²
Simplification of the given expression 4 square root of 72 is
4√72
= 4 × √ 2³ ×3²
= 4 × √ 2² × 2 × 3²
Calculate the square root
= 4 ×2 ×3 √2
= 24√2
= 24 ×1.414
= 33.94
Therefore, simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94.
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The area of a rectangle is 99 m2, and the length of the rectangle is 7 m more than double the width. Find the dimensions of the rectangle.
Answers
On the Left side is just an example.
On the paper is my answer to your question with explanation.
Hope this will help:)
Lisa randomly selected 30 adult dogs from two different breeds. She gathered data about their weights and created the dot plots
shown.
Select the true statement.
Breed A
24
Breed B
24
26
26
28
28
30 32
Weight (pounds)
34
po 32
Weight (pounds)
34
36
36
30
●
38
40
40
A.
Dogs of breed B typically weigh more than dogs of breed A
B.
Dogs of breed A and breed B typically weigh the same.
C. There is too much overlap to make a generalization comparing the weights of dogs of breed A and breed B.
D. Dogs of breed A typically weigh more than dogs of breed B.
Answers
The true statement is Statement A which is dogs of breed B typically weigh more than dogs of breed A using histogram in probability concept.
What is a histogram in probability?The likelihood of each possible occurrence is displayed on the y-axis of a probability histogram. A histogram is a statistical data display that makes use of rectangles to illustrate the frequency of data items in successive numerical intervals of equal size. The dependent variable is plotted along the vertical axis in the most typical type of histogram, while the independent variable is plotted along the horizontal axis. The distribution of data is depicted graphically in a histogram. A collection of neighboring rectangles, each with a bar that represents a certain type of data, is used to illustrate a histogram. Fill L1 with the values of the random variable (remember to use the class midpoints for continuous random variables). The associated percentages should be entered into L2 with a decimal format.
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Must Find the Error in this problem
Answers
Answer:
They subtracted when they should have added
Step-by-step explanation:
You must do the opposite so if it says -17 you must add 17 to the other side the answer should be 32
Which of the following is a whole number 1. 52. 03. 104. -9.05. 19/36.-7
Answers
The whole numbers are defined as numbers that include naturals and zero. Not a fraction, decimal or negative numbers.
So in this case, the whole numbers are: 5 ; 0; 10.
Find the length of the sides of the triangle ABC if the perimeter of the triangle is 33 inches.
Answers
The length of the sides of the triangle is 11 inches.
Triangle:
Triangle is defined as the three-sided polygon that consists of three edges and three vertices
Given,
If the perimeter of the triangle is 33 inches, then we have to find the sides of the triangle.
Let x be the sides of the triangle, we know that the triangle has 3 sides.
And lest us consider this one as equilateral triangle.
So, the formula for perimeter is,
Perimeter = 3 x sides
Here we know the value of perimeter then the value of the sides are,
33 = 3 x sides
sides = 11
So, the value of the sides is 11.
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Introduction to Writing Proofs - A Geometry Performance project
Need help fast
Answers
The required expressions about the geometry figure can be proven as follows;
1. The measure of ∠2 and ∠3 are congruent by the substitution property of equality
2. ∠2 and ∠3 are congruent, (∠2≅∠3) by the property of equality
What is the property of equality?The property of equality are properties that enable the solution of algebraic equations to be found and they include, addition, subtraction, multiplication, division, reflexive, substitution, transitive and symmetric properties.
1. The required paragraph to prove that ∠2 ≅ ∠3 is as follows:
Given that ∠1 and ∠2 form a linear pair, then their sum is 180°. Given that the sum of the measure of ∠1 and ∠3 is also 180°, then the sum of ∠1 and ∠2 is equal to the sum of ∠1 and ∠3. Therefore, by the addition property of equality, ∠2 ≅ ∠3.
2. The two column proof is as follows:
Statement [tex]{}[/tex] Reasons
1. ∠ABC = ∠1 + ∠2 is ⊥ 1. Given
2. ∠ABC = 90° 2. Definition of a perpendicular line
3. ∠1 + ∠2 = 90° 3. Substitution property of equality
4. ∠1 and ∠3 are complementary 4. Given
5. ∠1 +∠3 = 90° 5. Definition of complementary
6. ∠1 + ∠2 = ∠1 +∠3 6. Substitution property of equality
7. ∠2 ≅ ∠3 7. Addition property of equality
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