Answers
[tex]f_x(0,0)[/tex] is the partial derivative of [tex]f[/tex] with respect to [tex]x[/tex] evaluated at the origin. By definition of derivative, this is the limit
[tex]\displaystyle f_x(0,0) = \lim_{x\to0} \frac{f(x,0) - f(0,0)}{x-0} = \lim_{x\to0} \frac{f(x,0)}x[/tex]
We have by definition of [tex]f[/tex],
[tex]f(x,0) = \dfrac{x^5}{x^4+0^4} = \dfrac{x^5}{x^4}[/tex]
so
[tex]\displaystyle f_x(0,0) = \lim_{x\to0} \frac{\frac{x^5}{x^4}}x = \lim_{x\to0} \frac{x^5}{x^5} = \lim_{x\to0} 1 = \boxed{1}[/tex]
Related Questions
simplify 1/2 of √81×√16
Answers
Answer:
18
firstly you solve √81×√16
that is the square root of 81 × the square root of 16
so that equal to 1/2 × 9×4
another name for of is multiplication
1/2× 36
you divide 2 in 36 which is 18 and the 1 you multiple 1 ×18
= 18
The distance from Earth to the Sun is approximately 9 x 10^7 miles. The distance from Earth to the moon is approximately 2 x 10^5 miles. Approximately how many times the distance from the Earth to the Moon is the distance from Earth to the Sun?
A:18
b:45
C:222
D:450
its 8th grade math
Answers
Answer:
D
Step-by-step explanation:
[tex]\frac{9x10^{7} }{2x10^{5} }[/tex] = 9/2 is 4.5 The quotient property principle tells us that when the bases are the same and we are dividing powers, we subtract the exponents. 7-5 = 2
4.5 x [tex]10^{2}[/tex] In standard notation, this is 450
Given that lines A and B are parallel, if angle 1 measures 48 degrees and angle 2 measures 51 degrees, what is the measure of angle 3?
Answers
Answer:
81°
Step-by-step explanation:
m∠1 + m∠2 + m∠3 = 180° because they add to form a straight angle.
How to multiply 2*3*5*7 (I need explanation)
Answers
Answer:
Look the answer is simple...just multiply one by one
Step-by-step explanation:
For example;
2*3*5*7
2x3=6
6x5=30
30x7=210
Amy, bill and cara each played a game. amy's score was ten times bill's score. cara's score was half of amy's score. write down the ration of amy's score to bill's score to cara's score. give your answer in its simplest form
Answers
Answer:
2:1:1
Step-by-step explanation:
A:B:C
10:1:5
÷5. ÷5
=2:1:1
If two of the angles in a scalene triangle are 54 87 degrees, what is the other angle
Answers
If two of the angles in a scalene triangle are 54° and 87°, the value of the other angle is 39°.
What is a scalene triangle?A scalene triangle is a triangle that has three unequal sides.
We have,
Two angles of a scalene triangle are 54° and 87°
We know that,
A scalene triangle has all its three angles different in measures and obeys the angle sum property.
i.e Sum of the three interior angles = 180 degrees.
Let M is the other angle.
M + 54° + 87° = 180°
M = 180 - 141
M = 39°
Thus the value of the other angle is 39°.
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= 1
2
3
= 4
= 5
4
A line passes through point (-9, -6) and has a slope of 4/3
Write an equation in Ax+By=C form for this line.
Use integers for A, B, and C.
Answers
Answer:
4x-3y=-18.
Step-by-step explanation:
1) common form of slope-interception form: y=slope*x+interception;
2) if according to the condition slope=4/3, thenthe slope-interception form is y=4/3*x+interception;
3) it is possible to calculate the interception if to substitute given coordinates (-9;-6) into the slope-interception form:
-6=4/3*(-9)+interception; ⇒ interception=6, then
4) the slope-interception form is y=4/3*x+6;
5) finally, 3y=4x+18, ⇔ 4x-3y= -18 (A=4, B=-3, C=-18).
Use the picture to answer the following question.
Which of the following statements BEST proves that lines k and m are parallel?
A. Angle 2 is congruent to angle 6 because corresponding angles are congruent if two parallel lines are cut by a transversal.
B. Angle 3 is congruent to angle 4 because supplementary angles are congruent if two parallel lines are cut by a transversal.
C. Angle 1 is congruent to angle 6 because alternate exterior angles are congruent if two parallel lines are cut by a transversal.
D. Angle 4 is congruent to angle 5 because alternate interior angles are congruent if two parallel lines are cut by a transversal.
Answers
The statement which best proves that lines k and m are parallel is: C. Angle 1 is congruent to angle 6 because alternate exterior angles are congruent if two parallel lines are cut by a transversal.
What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure.
In this context, we can reasonably infer and logically deduce that the statement which best proves that lines k and m are parallel is angle 1 is congruent to angle 6 because by definition all alternate exterior angles are congruent, if two parallel lines are cut by a transversal.
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Only answer if you are 100000% sure it's correct, if it's not correct I'm reporting <3
Answers
Answer: 0.000435
Step-by-step explanation:
1. Convert to decimal notation
More Icon
The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s):
4.35 -> 0.000435
Scientific notation, or standard form, makes things easier when working with very small or very big numbers, both of which come up frequently in the fields of science and engineering. It is used in science, for example, to convey the mass of the heavenly bodies: Jupiter’s mass is kg, which is easier to comprehend than writing the number 1,898 followed by 24 zeroes. Scientific notation also makes solving problems that use such high or low numbers more straightforward.
Answer:
0.000435
Step-by-step explanation:
10^-4 = 0.0001
0.0001 × 4.35 = 0.000435
Write the equation of the line in slope-intercept form for each question below.
7. slope = 3, y-intercept = 2
holow
Answers
Answer:
General linear equation;
[tex]{ \tt{y = mx + c}} \\ [/tex]
Where m is the gradientWhere c is the y-intercept[tex]{ \boxed{ \tt{y = 3x + 2}}}[/tex]
Area of a Field A rectangular field is 364 yards in length and 433 yards in width. Find the area of the field in ACRES (1 acre = 43,560 square feet). Round to the nearest tenth of an acre
Answers
The area of the yard is 32.56 acres.
What is the area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given,
the length of the field = 364 yards
width of the field = 433 yard
area of the field = length × breadth
area = 157612 sq. yards
1 sq. yard = 0.000207 acres
area in acres = 32.56 acres
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Find the missing side length, m.
Answers
Answer:
I believe the answer is 6.6
Step-by-step explanation:
If you multiply 6 by 10 you get 60. Divide 60 by 9 you get 6.6
Convert 8.67 into fraction
Answers
8.67 as a mixed fraction is
8 and 67/100
you could also say 867/100
Cuántos kilogramos pesan 11 metros de alambre, si 154 metros de alambre del mismo grueso pesan 7 kilogramos?
Answers
Answer:
0,5 Kg
Step-by-step explanation:
help me help me pleasee
Answers
-4(-8) - 4 - 4 - 2
32-10
22
Hope this helps
Answer:
g = -11
Step-by-step explanation:
The question is giving you the answer of (x)
1) Plug in -2, into x so it will look like this:
g(-2) = 4x^3 -x^2 +2x -2
2) Plug the -2 into the x, it will look like this:
g(-2) = -4(-2)^3 - (-2)^2 +2(-2) -2
3) Solve!
g(-2) = 8^3 - 4 - 4 -2
g(-2) = 32 - 4 - 4 - 2
g(-2) = 32
-2g/-2 = 22/-2
g = -11
I hope this helped! If you need more help with understanding, let me know! :)
Using the image below, find the x value for the point that divides the line segment AB into a ratio of 2:3.
A. -1
B. -0.4
C. 0
D. 0.5
Answers
Answer:
The value of x for the point that divides the line segment AB into a ratio of 2:3 is (B) -0.4
Step-by-step explanation:
It is given that we need to find the x value for the point that divides the line segment AB into a ratio of 2:3 from the option given in the question.
Now, let us find the difference between the values of x of point A and of point B;
=> 5 - (-4)
=> 5 + 4
=> 9
Now, let us divide 9 by 5 so that we get the ratio 2:3;
=> 9/5
=> 1.8
Further, for getting the segments as 2 + 3;
=> 1.8 × 2
=> 3.6
and
=> -4 + 3.6
=> -0.4
Therefore, the value of x for the point that divides the line segment AB into a ratio of 2:3 is (B) -0.4
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Can A contains 2,5 litres of juice and Can B contains 3 litres 250 millilitres of juice. If the juice from both can is mixed then what will be the total volume of juice? Give the answer in millilitres.
Answers
The total volume of the juice in milliliters is 5750ml.
Here, we know that, using unit conversion,
1 liter = 1000 milliliters
Juice contained in Can A is 2.5 liters.
converting it into milliliters,
2 liters = 2 x 1000ml
2 liters = 2000ml
the juice volume becomes 2500ml in Can A.
Juice contained in Can B is 3 liters and 250 milliliters
converting it into milliliters,
3 liters and 250ml = 3 x 1000ml + 250ml
3 liters and 250ml = 3250ml.
the juice volume becomes 3250ml in Can B.
When both Cans are mixed,
Total volume of the juice = volume of juice of can A + volume juice of can B
Total volume = 2500ml + 3250ml
Total volume = 5750ml.
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I need help on this question 4 4/5 - 1 9/10 also show the work.
Answers
Answer:
29/10 or 2 9/10
4 4/5 - 1 9/10
make them into improper fractions
4 4/5 = 24/5
1 9/10 = 19/10
24/5 - 19/10 we need to get common denominators
24/5 × 2 = 48/10
48/10-19/10 = 29/10 = 2 9/10
Jaydan uses 3/4 water and 1/5 lime juice and reese uses 2/3 water and 1/6 lime juice which one is weaker
Answers
Answer:
1/6 lime juice
Step-by-step explanation:
1/6 is less than 1/5,3/4,and 2/3
Solve the equation. If the equation is an identity, choose identity. If it has no solution, choose no solution.
4y + 2 =-1/3
(8-12y)
Answers
[tex]\displaystyle\\Answer: y=-\frac{7}{12}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\4y+2=-\frac{1}{3}\\\\[/tex]
Multiply both parts of the equation by 3:
[tex]\displaystyle\\(3)(4y+2)=(-\frac{1}{3} )(3)\\12y+6=-1\\12y+6-6=-1-6\\12y=-7[/tex]
Divide both parts of the equation by 12:
[tex]\displaystyle\\y=-\frac{7}{12}[/tex]
Which step in the construction of copying a line segment ensures that the new line segment has
the same length as the original line segment?
Answers
Answer:
Fill in the blanks to declare sum equal to a + b (int _ = a __b
The annual interest on a $9000 investment exceeds the interest earned on a $6000 investment by $135. The $9000 is invested at a 0.5% higher rate of interest than the $6000. What is the interest rate of each investment?
Answers
The interest rate of $9000 and $6000 investment are 3.5% and 3% respectively.
let's assume the interest rates X and Y on $9,000 and $6,000 investments.
The $9000 is invested at an interest rate that is 0.5% higher than the $6000.
Therefore,
9000(X) = 6000(Y) + 135
X = Y + 0.005
In canonical form:
9000X - 6000Y = 135
X - Y = 0.005
or X = 0.005 + Y
Then,
9000( 0.005 + Y) - 6000Y = 135
Then Y = 0.3 , therefore X = 0.3
So, X = 3.5% (the rate on $9,000 investment) and;
Y = 3% (the rate on $6,000 investment).
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what is the greatest factors of 28,42,63
Answers
The greatest common factor of 28, 42, 63 is 7
Depending on the quantity and size of the numbers in the set, there are several possible approaches to calculate the GCF.
Finding the greatest common multiple of smaller numbers can be done by simply looking at each number's factors or multiples.
We'll find the factors for 28, 42 and 63 which are as follows :
Factors for 28: 1, 2, 4, 7, 14, and 28
Factors for 42: 1, 2, 3, 6, 7, 14, 21, and 42
Factors for 63: 1, 3, 7, 9, 21, and 63
As to find the GCF, we need to check the greatest factor which is common in all the three numbers individual factors. So, we find that 7 is the common factor in all three.
Hence, the greatest common factor of 28, 42, 63 is 7
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a scuba diver is swimming at the depth -46 feet and then swims 0.5 foot toward the surface every 3 seconds. what is the location of the scuba diver relative to the surface after 15 seconds
Answers
Answer:
-43.5
Step-by-step explanation:
After 15 second he would have swam to a level of -43.5.
Math on the Spot Suppose there are 3 groups of
4 trumpet players. In front of the trumpet players are
9 saxophone players. How many students play the
trumpet or saxophone?
Answers
The number of students who play the trumpet or saxophone will be 21 students.
How to illustrate the information?From the information, there are 3 groups of
4 trumpet players. In front of the trumpet players are 9 saxophone players.
Therefore, the number of students who play the trumpet or saxophone will be the addition of both values given. This will be:
= (3 × 4) + 9
= 12 + 9
= 21
Consequently, there will be 21 students who play the trumpet or saxophone.
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Consider these graphed number lines. 4 number lines going from negative 5 to positive 5. Graph A: points are at 1 and 4. Everything between the points is shaded. Graph B: Points are at 1 and 4. Everything to the left of 1 and to the right of 4 is shaded. Graph C: Open circles are at 1 and 4. Everything between the points is shaded. Graph D: Open circles are at 1 and 4. Everything to the left of 1 and to the right of 4 is shaded. Which number line represents the solution for the inequality |2x – 5| Greater-than-or-equal-to 3? graph A graph B graph C graph D
Answers
The graph of the inequality |2x - 5| ≥ 3 represents 4 ≤ x ≤ 1 which is
B: Points are at 1 and 4. Everything to the left of 1 and to the right of 4 is shaded.
What is inequality?Inequality is a comparison between two nonequal quantities and they are of four types.
We know |2x - 5| ≥ 3 is,
2x - 5 ≥ 3.
2x ≥ 3 + 5.
2x ≥ 8.
x ≥ 4.
OR
-(2x - 5) ≥ 3.
-2x + 5 ≥ 3.
-2x ≥ - 2.
-x ≥ 1.
x ≤ 1. ( Think of moving the terms on other sides to make x positive)
So, the graph of the inequality |2x - 5| ≥ 3 is 4 ≤ x≤ 1.
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A sky diver descended 132 meters in 12 seconds. How far did he fall in one second? how many meters?
Answers
Answer:
he fell 11 meters
Step-by-step explanation:
132 divided by 12 is 11.
Janet rents a booth at the farmers market
that costs $150 a day. She sells jars of fresh
honey from her family farm for $8 each. At
the end of the day, she splits all the
money she brings home with her mom
who takes care of the bees. If j is the
number of jars of honey sold, write a
function f(j) representing how much
money Janet makes each day.
Answers
Hope this helps!
Whats the unit value of the 6 in 261
Answers
The unit value of 6 in the number 261 is: tens.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsUnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.In this scenario, the unit value of each digit in the number 261 are as follows:
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Xochitl is buying tacos and sodas for her friends. Each taco, t, costs $1.50 and each soda, s,
costs $2.00. Xochitl spends $39.00 total. Write an equations that models the situation.
Answers
The equations that model the situation is 1.50t + 2s = $39
What is the equation that models the situation?The total amount spent is the sum of the total cost of the tacos and the total cost of soda. The total cost of tacos is the product of the cost of one taco and the number of tacos bought. The total cost of sodas is the product of the cost of one soda and the number of sodas bought.
The mathematical operations that would be used is multiplication and addition. Addition is the process of determining the sum of two or more numbers. The sign used to represent addition is +.
Multiplication is the process of determining the product of two or more numbers. The sign used to represent multiplication is x.
Total amount Xochitl spends = total cost of tacos + total cost of sodas
Total amount Xochitl spends = (1.50 x t) + (2 x s)
39 = 1.50t + 2s
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