Answers
Answer:
[tex]\textrm {D. The derivative is }\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \dfrac{u(x)}{v(x)}[/tex]
the derivative of f(x) wrt x is
[tex]f'(x) = \dfrac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}[/tex]
[tex]u(x) =x^9 \;so \; u'(x) = 9x^8[/tex]
[tex]v(x) = x^3 , v'(x) = 3x^2\\\\\[v(x)\]^2 = [x^3]^2 = x^6[/tex]
Putting all these together we get
[tex]f'(x)=y'=\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}[/tex]
Missing entries are in bold
Related Questions
Help to count area, i’am too bad for this, thank’s
Answers
Answer:
a) 93 cm²
b) 98 cm²
Step-by-step explanation:
You want the areas of the squares shown in each of the figures.
Pythagorean theoremThe Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the other two sides of a right triangle.
a)The square of the hypotenuse is 17² = 289.
The sum of the squares of the other two sides is ...
shaded square + (14)² = 17²
shaded square + 196 = 289
shaded square = 289 -196 = 93 . . . . cm²
Sabcd = 93 cm².
b)The square of the diagonal is the sum of the squares of the sides. Each of those squares is the area of interest:
14² = (shaded square) + (shaded square)
196 = 2(shaded square)
98 = shaded square
Sabcd = 98 cm².
__
Additional comment
Perhaps you have seen the attached figure. It is intended to show the squares on each of the legs of the right triangle, and to illustrate that the sum of the areas of the green and purple squares is the area of the red square. This figure compares to the one for part (a) of the problem.
a² +b² = c² ⇒ a² = c² -b²
brooke has a square yard with grass and gravel parts as shown. The perimeter of the part covered in gravel is 22 meters. what is the area of the grass section of Brookes yard
Answers
Brooke's yard is a square with a side length of 22 meters.
What is perimeter?Perimeter is the total distance around the outside edge of a two-dimensional shape. Perimeter is a measure of the length of the boundary of a shape and is typically expressed in units of length, such as feet or meters. Calculating the perimeter of a shape can help you measure the size of a yard, garden, or other outdoor area.
Since the perimeter of the part covered in gravel is 22 meters, we can use the formula for the perimeter of a square (4s) to find the length of one side of the square. Therefore, the side length of the part covered in grass is 4s = 22, or s = 5.5 meters.
Using the formula for the area of a square (A = s²), we can calculate the area of the grass section of Brooke's yard. The area of the grass section of Brooke's yard is A = s²= 5.5²= 30.25 square meters.
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18. True or False. If a function has a real sero of 4 with a multiplicity of three and an imaginary
zero of 41, then it has a degree of four.
19. True or False. The imaginary number 27 is a nero of ƒ(x) = x² −x² + 4x − 4.
20. True or False. The quotient of (x²-x² − 16x + 16) + (x − 1) is an irreducible quadratic.
For problems 21-26, use the limits of a polynomial to determine the end behavior.
Find the zeros of the function and indicate multiplicity. Then write the polynomial as a
product of linear factors. Sketch the graph, showing all intercepts.
/(x)=x² + 3x²-4
21. lim f(x) =
22. lim f(x) =
23. Zeros of f(x):
24. y-intercept of f(x):
25. Product of linear and irreducible quadratic factors of fix)
26. Sketch of f(x) using end behavior and intercepts. NO Desmos graphs.
Answers
The polynomial's zeros must be located using a method of your choice, and the linear expressions that produce those zeros must then be combined in order to describe the polynomial as a product of linear factors.
What is a linear factor of a polynomial?The term "triple zero" or "zero with multiplicity 3" is used to describe this. The power p governs the behaviour close to the x-intercept if a polynomial has a factor of the type (xh)p. A zero of multiplicity p is defined as x=h. The x-axis will be touched at zeros with even multiplicities on a polynomial function's graph.
A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.
You must first determine the polynomial's zeros using the method of your choice, and then combine the linear equations that result in those zeros. If you factor, you will arrive at the third degree polynomial, which must then be sorted through.
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Sam weighed 105 lbs. before the holidays. She now weighs 110 lbs. Find the Percent of Change.
Answers
Answer:
5%
Step-by-step explanation:
105=100
110=x
*cross multiply*
=100x110/105
=104.76
=100-105
=5%
subtract the answer gotten with the 100 %
(Brainliest)(7th grade)Find x and y of this obtuse triangle.
Answers
In ΔXYZ, x = 830 cm,
m
m∠Y=141° and
m
m∠Z=25°. Find the length of z, to the nearest 10th of a centimeter.
Answers
=======================================================
Explanation:
Use the two given angle measures (Y and Z) to find angle X.
X+Y+Z = 180
X+141+25 = 180
X+166 = 180
X = 180-166
X = 14
Angle X is 14 degrees.
-----------
Now use the law of sines to determine side length z.
Make sure your calculator is in degree mode.
z/sin(Z) = x/sin(X)
z/sin(25) = 830/sin(14)
z = sin(25)*830/sin(14)
z = 1449.9438
z = 1449.9 cm is the final answer.
The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Explanation:
Use the two given angle measures (Y and Z) to find angle X.
X+Y+Z = 180
X+141+25 = 180
X+166 = 180
X = 180-166
X = 14
Angle X is 14 degrees.
Now use the law of sines to determine side length z.
z/sin(Z) = x/sin(X)
z/sin(25) = 830/sin(14)
z = sin(25)*830/sin(14)
z = 1449.9438
z = 1449.9 cm is the final answer.
Hence, The solution is : the length of z, to the nearest 10th of a centimeter is, 1449.9 cm.
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Examine the triangle below, solve for x and y, rounded to two decimal places.
X=
y=
30°
16
X
y
Answers
Which of the following is true of z scores that fall below the mean?
O Group of answer choices
O They are negative.
O They are equal to the mode.
O They are positive.
O They are in the upper half of the distribution.
Answers
The truth of z scores that fall below the mean is - they are negative. Option(b) is the correct answer.
A z-score called a standard score gives an idea of how far from the mean a data point is. But technically it is a calculation of how many standard deviations below or above the population mean a raw score is.
A z-score can place on a normal distribution curve. Z-score ranges from -3 standard deviations up to +3 standard deviations.
A z-score is equal to 0 means that it is on the mean. A positive z-score shows the score is higher than the mean average.
A negative z-score reveals the score is below the mean average.
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an expression is shown. 8x^3-12x^2-2x+3
Answers
Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.
what is an expression means?Verifying an algebraic expression requires substituting a number for each variable and performing arithmetic operations. Given that 6 + 6 equals 12, the answer variable in the example above is equivalent to 6. If we are aware of the values of the variables, we can substitute those values for the original ones, which will allow us to evaluate the expression.
Here,
It is important to note that now the ratio of a coefficient of the terms
The coefficient ratio of the words
8x³ and 2x is 8:2 = 4:1, and the coefficient ratio of the phrases 12x² and 3 is 12:3 = 4:1.
This suggests that we should categorize the original statement as follows:
This suggests that we should combine the original expression, which is written as
=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),
before determining the common component (4x2+1)=(2x³)(4x2+1).
The fact that 4x²≥0 for x ∈ R means that
4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.
Therefore , the solution of the given problem of expression comes out to be 4x² +1 cannot equal 0 and thus (4x²≥0+1) has no Real factors.
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Express the absolute value function f(x) = -7|x| as a piecewise-defined function.
Answers
Answer:1111
Step-by-step explanation:1111
Use this information to evaluate the following. Hint: do not try to solve for the value of a. loga 2 = 0.36 loga 3 = 0.56 logą 5 = 0.83 (a) loga 15 = 1.39 kor. (E) - log, (b) -.47 (c) log, (8a*) = 8.72
Answers
a) To evaluate loga 15, we can use the property of logarithms that states logab = loga + logb. Since 15 = 3 * 5, we can use this property to find that loga 15 = loga 3 + loga 5. Since loga 3 = 0.56 and loga 5 = 0.83, we can add these values to find that loga 15 = 0.56 + 0.83 = 1.39.
The power to which a number must be increased in order to obtain additional values is referred to as a logarithm. The easiest approach to express enormous numbers is this manner.
Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms may also be represented as multiplication and division of logarithms.
b) To evaluate loga(2/5), we can use the property of logarithms that states log(a/b) = loga - logb. Since 2/5 = 2*(1/5) we can use this property to find that loga(2/5) = loga2 - loga(1/5). Since loga2 = 0.36 and loga(1/5) = -loga5, we can subtract these values to find that loga(2/5) = 0.36 - 0.83 = -0.47
c) To evaluate loga (8a^4), we can use the property of logarithms that states log (a^n) = nloga. We get, loga (8a^4)=loga 8 + log (a^4)
=> loga 8 + loga (a^4)
=>3loga 2 + 4 loga a
=>3loga 2 + 4
=>3 * 0.36 + 4
=5.08
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Find ALL the missing side lengths and angle measurements
Answers
The measure of angle L is 66 degrees, which is found using the sum of the internal angle of a triangle. The length is 3.56 units.
What are internal angles?A polygon's interior angle is the angle created between its two adjacent sides. Alternately, we may state that the internal angle of a polygon refers to the angle measured at the interior portion of a polygon.
Given that the measure of angle M is 24 degrees and angle K is 90 degrees.
The sum of internal angles of a triangle is 180 degrees, thus:
[tex]\angle M + \angle K + \angle L = 180\\\\24 + 90 + \angle L = 180 \\\\\angle L = 66[/tex]
The length of side LK can be found as follows:
tan 24 = LK / MK
tan 24 = LK / 8
0.44 * 8 = LK
LK = 3.56 units.
The length of LM can be found by applying the Pythagorean theorem.
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Rose had 10 cookies she gave away 5 cookies to her friends she baked 20 more how many cookies does rose to have in all?
Answers
Answer: 25
Step-by-step explanation:
simple math
Answer:
25 cookies
Step-by-step explanation:
After she gives away 5 of her 10 cookies she is left with 5 cookies. Then she bakes 20 more. So you add 5 cookies to 20 cookies, and you get 25 cookies.
Or in total with all of the cookies she had before she gave away 5 of the 10, and the newly baked 20 cookies she has 30 cookies.
-Hope this helped
The average age of 5 students is 10 years. The age of one student is 6. What is the average age of the remaining 4 students?
Answers
The the average age of the remaining 4 students is 9.5 years.
Why is mean called the average?The average may be calculated by dividing the total number of values by the sum of all the numbers. An average of the values in a sample of data may be used to determine a mean. In other words, the arithmetic mean is another name for an average. A mean is a term used to describe the average.
The average age of 5 students is 10 years.
∴ Sum of age of 6 students =5 × 10 = 66
⇒ When two more students of age 5 and 1 added to 4 students then, total students will become 8
⇒ Sum of age of 6 students =66 + 6 + 4 = 76
∴ Required average =
76 / 8 = 9.5
=9.5 years
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Here are the weights (in pounds) of a sample of 13 male eleventh graders.
148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170
Send data to calculator
Find the median weight of these students.
pounds?
Answers
Answer:
159
Step-by-step explanation:
Median = When ordered least to greatest, the number in the middle
140, 141, 146, 148, 151, 156, 159, 159, 160, 167, 170, 173, 174
find the value of x in the figure below
assume that the lines are parallel
Answers
In the graphic below, assuming the lines are parallel, the value of x is 15.
What is parallel lines?Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.
Here,
6x+3=7x-12
x=15
The value of x in the figure below assuming that the lines are parallel is 15.
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If ABCD is dilated by a factor of 3, the
coordinate of C' would be:
-5
T
NA
А
B
4
3
2
1
-2 -10
-1
-2
-3
1
2
C
3 4 5
D
C' = ([?], [])
Answers
Reason:
Point C is located at (3,3)
Triple each coordinate since the scale factor is 3. That's how we go from (3,3) to (9,9)
If the scale factor was 5 for instance, then we'd go from (3,3) to (15,15)
This trick works only if the center of dilation is the origin.
Answer:
C' = (-3, 4)
Step-by-step explanation:
When a shape is dilated by a factor of 3, the size of the shape is multiplied by 3 in both the x and y directions. To find the new coordinates of point C' after a dilation by a factor of 3, we can multiply the original coordinates of point C by 3.
The original coordinates of point C are (-2, -10). When we multiply these coordinates by 3, we get (-6, -30) for the new coordinates of C' after the dilation. So the answer is (-6, -30)
The combination lock has three wheels each numbered from 0 to 9 what is the possibility that someone randomly guesses the correct combination in five attempts?
Answers
The possibility that someone randomly guesses the correct combination in five attempts is 1/200
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Given;
There are three wheels
Each numbered from 0 to 9
For the first wheel, you have 10 possible digits.
For the second wheel, you have 10 possible digits.
For the third wheel, you have 10 possible digits.
10 x 10 x 10 = 1000
For 5 attempts= 5/1000
=1/200
Therefore, the probability will be 1/200
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Help me solve this I have all the questions on the paper
Answers
Answer:
x intercepts (-2,0) and (-4,0)
y intercept: (0,8)
Vertex: (-3,-1)
Axis of symmetry x = -3
Step-by-step explanation:
Serena is cycling from dance class to her home. The equation shows Serena's distance (y), in miles, from her home after x minutes:
y = 16 − 6x
What does the number 16 in the equation represent? (1 point)
a
Serena's distance from home when she begins cycling
b
Serena's distance from the dance class when she begins cycling
c
The speed at which Serena is cycling from the dance class to her home
d
The rate of change of Serena's speed while cycling from the dance class to her home
Answers
In linear equation, 16 is represent The speed at which Serena is cycling from the dance class to her home
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
6x + y = 16
6x = 16 - y
x = 8/3 - y/6
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Sketch the graph of h(x) = g (x+3) -6
Answers
Therefore , the solution of the given problem of graph comes out to be
x = 0 , y =22 and x= 1 , y=23.
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
Here,
Given :
=> h(x) = g(x+3) - 6
g(x) = x+ 25
So,
=> g(x+3) = x +3 + 25 = x+28
and
=> h(x) = x + 28 -6
=>y= h(x) = x+ 22
Thus,
y= x+22
the points which can be graph area:
=> x = 0 , y =22
=> x= 1 , y=23
Therefore , the solution of the given problem of graph comes out to be
x = 0 , y =22 and x= 1 , y=23.
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5) Choose the best answer.
Which property is illustrated?
For all expressions a, b, and c, (ab)c = a(bc)
Distributive Property of Equality
Commuttive Property of Multiplication
Multiplication Property of Equality
Division Property of Equality
Associative Property of Multiplication
Answers
The best estimate willl 20
Step-by-step explanation:I
A rectangle has a perimeter of 112. If the sides are 5x & 3x + 5, what is x and what are each of the sides?
Answers
The value of X is 7.625 while the two sides are 38.125 and 27.875.
To find the perimeter:Perimeter = 2(L+B)
112 = 2(5x + 3x + 5)
112 = 2(8x + 5)
Dividing both sides by 2
56 = 8x + 5
56 + 5 = 8x
61 = 8x
x = 61/8
x = 7.625
The sides are;
5x = 5(7.625)
5x = 38.125
3x + 5 = 3(7.625) + 5
3x + 5 = 22.875 + 5
3x + 5 = 27.875
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Please help !! I can’t find the answer
Answers
In the problem, the number is:
3.85663
I’ll tell you the places:
3 is the ones place. Then there’s the decimal, now we’re adding “th.” After the decimal is 8, the tenths place. After that is 5, the hundredths place. Then it’s 6, the thousandths place. Then another 6, ten thousandths place. And last, 3, the hundred thousandths place.
It’s just like the places you learned in elementary school, but backwards and with “th” added, also no “oneths place,” that just sounds weird.
And you should know how to round, but if you don’t, you simply just look at the next number after the number you’re rounding. If the number is greater than 5, round up, if less, round down. And 5 is rounded up in most cases. So here, the number after the hundredths place is 6, so we round the hundredths place up, 5 to 6.
Which verbal expression best represents the equation 2(n - 7) = -14
Answers
Answer:
See below
Step-by-step explanation:
You could say "2 times the difference between n and 7 is equal to -14"
NO LINKS!!
Finish the table below:
n t(n)
1 7.5
2 3.75
3 1.875
4
5
b. Name the type of sequence
c. Find an equation for the sequence
Answers
Answer:
a) See below.
b) Geometric sequence
[tex]\textsf{c)} \quad a_n=7.5(0.5)^{n-1}[/tex]
Step-by-step explanation:
Part (a)From inspection of the given table, t(n) halves each time n increases by 1.
Therefore:
[tex]\implies a_4=1.875 \div 2 = 0.9375[/tex]
[tex]\implies a_5=0.9375 \div 2 =0.46875[/tex]
Completed table:
[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 1& 7.5\\\cline{1-2} \vphantom{\dfrac12} 2& 3.75\\\cline{1-2} \vphantom{\dfrac12} 3&1.875 \\\cline{1-2} \vphantom{\dfrac12} 4& 0.9375\\\cline{1-2} \vphantom{\dfrac12} 5& 0.46875\\\cline{1-2} \end{array}[/tex]
Part (b)As the given sequence has a constant ratio of 0.5, it is a geometric sequence.
Part (c)[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
The first term of the sequence is 7.5. Therefore,:
a = 7.5The common ratio is 0.5. Therefore:
r = 0.5Therefore, to write an equation for the given geometric sequence, substitute the found values of a and r into the formula:
[tex]a_n=7.5(0.5)^{n-1}[/tex]The distance from a focus to a vertex on a graph of a parabola is not the same as the distance from vertex to a perpendicular point on the directrix.
False
True
Answers
Answer:
True
Step-by-step explanation:
True
Luis gana actualmente 12000 pesos mensuales cuánto ganaría si su salario incrementa 14%
Answers
Luis genera $13680 al mess, sir se incremental un 14% ell valor de sub seldom actual.
What is Luis grana accumulate incremental ?De actedron con las condictiones dadas, planter=12000*(14% + 1)
Calculary loss dos primero's terminus =12000*1.14
Calculary loss dos primero's terminus =13680
get the result=13680
Explication paso a paso:
multiplicate ell 14% de 12.000= 1.680
le sulfas ese 1.680 a 12.000 y tee da ell resulted de 13.680
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Joe needs to transfer 28 quarts of oil into one-gallon containers. Joe calculated that he needs 112 containers, but he made a mistake in his calculations. Identify and correct his error.
28 quarts times 4 quarts over 1 gallon = 28 over 1 quarts times 4 quarts over 1 gallon, = 28 times 4 over 1 times 1 gallons = 112 gallons.
Skip to navigation
Answers
Joe made a mistake in his calculations by multiplying 28 quarts by 4.
How to illustrate the word problem?To know the mistake that Joe made and the possible correction, we shall convert 28 quart to gallon.
Recall that 4 quart = 1 gallon
Therefore, 28 quart will be:
= 28 quart × 1 gallon / 4 quart
28 quart = 7 gallon
Therefore, 28 quarts is equivalent to 7 gallons.
Hence, Joe made a mistake in his calculations by multiplying 28 quarts by 4 instead of dividing 28 quart by 4.
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The average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today, how much more time did she have her eyes open than closed.? PLEASE HELP TYSM!!!
Answers
Answer:
she had here eyes open for 12.4 more hours than she had them closed
Step-by-step explanation:
1/10 eyes closed = 9/10 eyes open
9/10 is 90% is 0.9
1/10 is 10% is 0.1
15 1/2 is 15.5
15.5 x 0.9 = 13.95
15.5 x 0.1 = 1.55
13.95-1.55 = 12.4