Find d^2y/dx^2 if 5x^3 - y^3 = 25
A. -250x/y^5
B. (10x(y^2-x))/y^3
C. 5x^2/y^2
D. (10(y^2-5x^4))/y^3
E. 30x - 6y
Answer:
[tex]y''=\frac{-250x}{y^5}[/tex]
Choice A.
Step-by-step explanation:
We are given:
[tex]5x^3-y^3=25[/tex]
We are asked to find:
[tex]\frac{d^2y}{dx^2}[/tex]
This requires we first find:
[tex]\frac{dy}{dx}[/tex]
Let's begin.
We will differentiate the right hand side using the constant rule since 25 is just a constant. We will differentiate the left hand side using difference rule and then constant multiple rule and then power rule and chain rule.
[tex](5x^3-y^3=25)'[/tex]
[tex](5x^3-y^3)'=(25)'[/tex]
[tex](5x^3)'-(y^3)'=0[/tex]
[tex]5(x^3)'-(y^3)'=0[/tex]
[tex]15x^2-3y^2y'=0[/tex]
Now let's solve for [tex]y'[/tex].
Add [tex]3y^2y'[/tex] on both sides:
[tex]15x^2=3y^2y'[/tex]
Divide both sides by [tex]3y^2[/tex]:
[tex]\frac{15x^2}{3y^2}=y'[/tex]
Symmetric property of equality:
[tex]y'=\frac{15x^2}{3y^2}[/tex]
Simplify right hand side:
[tex]y'=\frac{5x^2}{y^2}[/tex]
Now let's find the second derivative by differentiating both sides of this equation. We will use the quotient rule on the right hand side:
[tex]y''=\frac{(5x^2)'y^2-5x^2(y^2)'}{(y^2)^2}[/tex]
[tex]y''=\frac{10xy^2-5x^2(2yy')}{y^4}[/tex]
We can replace [tex]y'[/tex] with [tex]\frac{5x^2}{y^2}[/tex]... since we just got this result before differentiating both sides of an equality again.
So we have:
[tex]y''=\frac{10xy^2-5x^2(2y\frac{5x^2}{y^2})}{y^4}[/tex]
Let's simplify the 2nd term on top by cancelling a common factor of y in that term from top and bottom:
[tex]y''=\frac{10xy^2-5x^2(2\frac{5x^2}{y})}{y^4}[/tex]
We still don't like having this compound fraction (a mini fraction inside a bigger fraction). Let's get rid of that...Multiply numerator and denominator by [tex]\frac{y}{y}[/tex] for the big fraction to clear the mini fraction out.
[tex]y''=\frac{y}{y}\frac{10xy^2-5x^2(2\frac{5x^2}{y})}{y^4}[/tex]
Distribute:
[tex]y''=\frac{10xy^3-5x^2(2)5x^2}{y^5}[/tex]
Simplifying a bit more:
[tex]y''=\frac{10xy^3-50x^4}{y^5}[/tex]
We could factor the top a bit... both terms on top of a common factor of [tex]10x[/tex]:
[tex]y''=\frac{10x(y^3-5x^3)}{y^5}[/tex]
Notice the thing in ( ) on top is the exact opposite of the left hand side of our original equation: [tex]5x^3-y^3=25[/tex].
This implies we can replace it with -25:
[tex]y''=\frac{10x(-25)}{y^5}[/tex]
[tex]y''=\frac{-250x}{y^5}[/tex]
What is the value of the question mark in the picture below.
Use the vocabulary to explain your answer.
Answer:
84°
General Formulas and Concepts:
Geometry
Alternate Interior AnglesAlternate Exterior AnglesCorresponding AnglesStep-by-step explanation:
According to the picture, we can see that the 2 angles are Alternate Interior Angles. By definition, these 2 angles will be congruent.
help! open the attachment below!
Answer:
yes it is
Step-by-step explanation:X=side lenghths 2/3
Y=perimeter 12/18
2 time 6=12 and 3 times 6=18 and it is paraticly telling you
2/6 and 3/6 i beleve i need a lil more info
B. Determine the values of a and b so that f is continuous
f(x)= { x^2 +a if x > or = 3
bx+a if x is > 3 and if x is less than 3
root -b-x if x < or = -3
Answer:
Step-by-step explanation:
For a function to be continuous
The right hand limit f'+(x) must be equal to the left hand limit f'-(x)
The right hand limit exist at where x>3
The resulting function is. x²+a
If x = 3
f'+(3) = 3²+a
f'+(3) = 9+a
For the left hand limit, this exist where
bx+a
f'-(x) =bx+a
f'-(3) = 3b+a
Since f'+(3) = f'-(3)
9+a = 3b+a
9 =3b
b = 9/3
b = 3
At the end point x = -3
For the left hand limit
f-(x)= √-b-x
f-(-3) = √-b-(-3)
f(-3) = √-b+3
For the right hand, the function is bx+a
f'+(x) = bx+a
f+(-3) = -3b + a
Equate both limits
√-b+3 = -3b+a
√-3+3 = -3(3)+a
0 = -9+a
a= 9
Hence a = 9 and b = 3
What are three expressions that have the sum or difference of 3/4
Answer:
-11/12 − 1/6
-3/5 + 3/20
-2/3 + 1/12
Step-by-step explanation:
Which ordered pair is a solution of the equation? y=-2x-5y=−2x−5
Answer:
x=3y
Step-by-step explanation:
Step 1: flip the equation.
2x−5y=y
Step 2: Add 5y to both sides.
2x−5y+5y=y+5y
2x=6y
Step 3: Divide both sides by 2.
2x
2
=
6y
2
x=3y
Answer:
if this is for khan academy and is a multiple choice choose the answer (neither) if not its 5
Step-by-step explanation:
y - 2x - 5y = 2x - 5
4x+ 4y = 5
10 .find the partial sum S10 of the arithmetic series with a1 = 4, d = 5.
Answer:
S10 = 320
Step-by-step explanation:
The formula for calculating the sum of the nth term of an AP is expressed as
Sn = n/2(2a+(n-1)d))
Given
a = 4
d = 5
n = 10
S10 =10/2{2(5)+(10-1)5}
S10 =5{10+9(6)}
S10 =5{10+54}
S10 = 5(64)
S10 = 320
Hence the sum of the first ten terms of the sequence is 320
3 ice cream cones cost $8.25. At this rate, how much do 2 ice cream cones cost? Type your answer as a number with no other symbols or spaces.
Answer:
5.50
Step-by-step explanation:
8.25/3 = $2.75 each
2.75*2 = $5.50
Please help me with this as soon as you can. I have no idea how to do it so please help me.
Answer:
x=10
Step-by-step explanation:
The lines the angles are on are 180 degrees so
(11x+23) + (7x-23)= 180
Let's rearrange them first
11x+7x + 23-23=180
Combine the like terms
18x + 0=180
Remove the 0
18x=180
Then divide 18 on each side
x=10
A 0.8-liter bottle of Mexican wine costs 100 pesos. At that price, how much would a halfgallon jug of the same wine cost in dollars? Mexican peso Dollars per foreign: 0.07855 Foreign per dollar: 12.73
Answer:
$11.83
Step-by-step explanation:
1 gallon = 3.785 litres
0.5(1/2gallon) = x liters
x = 0.5 × 3.785 liters
x = 1.89271 liters
0.8 liter = 100 pesos
1.89271 liters = x pesos
x = 1.89271 × 100/0.8
x = 236.58875 pesos
Converting to dollars
1 mexican peso = $0.050
236.58875 pesos = x
x = 236.58875 × $0.050
x = $11.8294375
Approximately = $11.83
A half gallon jug of the same wine cost in dollars $11.83
Question 1 (1 point)
(05.01)
The graph of a system of equations will intersect at more than 1 point. (1 point)
a
Always
b
Sometimes
c
Never
Answer: Sometimes
Step-by-step explanation:
A system of equations can intersect at no points; this is when the lines are parallel, which means they have the same slope and different y-intercept.
A system of equations can intersect at one point; this is when the lines have different slopes.
A system of equations can intersect in infinitely many points; this is when the graphs overlay one another, which means they are graphs of the same line. The two equations would equal the same thing.
not sure need help
Answer:
X=35
Step-by-step explanation:
Those 2 angles equal each other, meaning they're the same.
Knowing that you put them to equal each other.
2x+15=3x-20
Then you solve it.
20+15=3x-2x
35=1x
X=35
HURRY!! At the snack bar, hot dogs cost $4 each and bottled water costs $2 each:
Answer: (2,1) (1,3)
Step-by-step explanation: Assume that the number of hot dogs is X and the number of water bottles is y.
Sally walks away from her
house. She walks 25 m west
then 15 m south. How far, in
meters, is she from her house?
Answer:
40 meters
Step-by-step explanation:
A football team gains 8 yards, looses 15 yards, than gains 20 yards. What was their total yards gained?
Answer:
The total yards gained was 13 yards.
Step-by-step explanation:
If you do 8-15+20=13
PLEASE MARK BRAINLIEST
On its first visit to the vet, Emma’s kitten weighed 30 ounces. On its second visit, the kitten had gained 8 ounces. On its third visit, the kitten had gained another 6 ounces. What is the percent increase, rounded to the nearest percent, of the kitten’s weight since its first visit?
Answer:
46.667% increase of 30.
Step-by-step explanation:
44 is a 46.667% increase of 30.
Step-by-step explanation:
Thank you rhhtthrhrgrgtnymuge hjk it is the right
in a study of 300 students under 25 years old, 21have not yet learned to drive. What percentage can drive?
Answer:
93%
Step-by-step explanation:
From the question given above, the following data were obtained:
Total number of student = 300
Number of student that can not drive = 21
Percentage of student that can drive =.?
Next, we shall determine the number of student that can drive. This can be obtained as follow:
Total number of student = 300
Number of student that can not drive = 21
Number of student that can drive =?
Number of student that can drive = (Total number of student) – (Number of student that can not drive)
Number of student that can drive = 300 – 21
Number of student that can drive = 279
Finally, we shall determine the percentage of student that can drive as illustrated below:
Total number of student = 300
Number of student that can drive = 279
Percentage of student that can drive =?
Percentage of student that can drive =
279/300 × 100
= 93%
Thus, 93% of the student can drive.
Find the percent increase from the first number to the second in the following pairs.
A. 100, 140
B. 80, 125
C. 60, 80
D. 9,1
Gail collects trading cards. Her favorites are baseball and football cards. For
every 10 baseball cards she owns, Gail has 17 football cards. What is the
ratio of baseball cards to football cards in her collection?
O A. 17:10
B. 10 and 17
O c. 12
O D. 17 to 10
Step-by-step explanation:
its ratio so it has to be A
15 POINTS! PLEASE HELP WILL MARK BRAINLIEST
Answer:
B) 1
Step-by-step explanation:
When reading the problem it tries to trip you up with the black dot. A line of symetery marks where you can cut the shape in half and have both parts equal. With the black dot a part of the shape there is only one way for a line of symetery to work as it can only be split in half that one way. No other corners have a black dot so there is no other way to split it where it would be symetrical.
False regarding Earnest money
Answer:
?
Step-by-step explanation:
Answer:
Earnest money is typically in the form of a check.
Step-by-step explanation:
Not everyone writes checks. Can be paid in any form.
In the figure, AB is a midsegment of XYZ, CD is a midsegment of XAB. and AY - BZ
Answer:
xyz is isosceses triangle
Zoey can tile 1 1/4 square yards in 1/3 hour. What is her unit rate?
(Ill give brainliest!!)
Alan travels eight and two thirds kilometers to get to school. He ran one and ten elevenths kilometers and walked the rest. How many kilometers were left to walk?
A) six and two thirty thirds kilometers
B) five and twenty five thirty thirds kilometers
C) six and twenty five thirty thirds kilometers
D) six and twenty thirty thirds kilometers
Answer:
c
Step-by-step explanation:
L'architecte___________beaucoup.
parle
dessine
écrit
mange
what is the correct answer ♂️♂️?
PLEASEEE HELPPP. 20 points
In a certain company a salesman is paid a fixed salary for $3140 per month plus an annual commision of 2% on the TOTAL value of cars sold for the year. If the salesman sold cars valued at $720000 in 2009 calculate:
(i) his fixed salary for the year
(ii) the amount he recieved in commision for the year
(iii) his TOTAL income for the year
Answer:
i. $ 37,560
ii. $14,400
iii. $51,960
Step-by-step explanation:
3130 x 12 = 37,560
2% of 720,000 = 14,400
14,400 + 37,560 = $51,960
Answer:
(i) 3 140 × 12 = 37 680
(ii) 720 000 × 2% = 720 000 × 0.02 = 14 400
(iii) 37 680 + 14 400 = 52 080
Consider the statement: "The president of the United States is a United States citizen."
Is the statement a grammatically correct sentence?
What is the subject of the sentence? What is the verb in the sentence?
Is the sentence true?
What is the slope of the line through the points (-2, -1) and (4, 3)?
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
slope formula: [tex]\frac{y{2}-y{1} }{x{2}-x{1}}[/tex]
x1 and y1 are (-2, -1)
x2 and y2 are (4, 3)
[tex]\frac{3-(-1)}{4-(-2)}[/tex]
[tex]\frac{3+1}{4+2}[/tex]
[tex]\frac{4}{6}[/tex]
[tex]\frac{2}{3}[/tex]
4x-3y≤27 solve for y
Answer:
y≥−9+4x/3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
If a household appliance had a wattage of 4,694 amd is in use for 10 hours, how much Co2 was produced
Answer: 4.64805 pounds of CO₂ was produced
Step-by-step explanation:
Given that;
wattage = 4694 watt = 4694 /1000 = 4.694 kW
time in use t = 10hrs
CO₂ was produced = ?
Total Energy produced = wattage × time = 4.694 kW × 10hrs = 46.95 kWh
we know that 1 kWh produces 0.99 pounds of CO₂
so
46.95 kWh will produce ⇒ 46.95 kWh × 0.99 = 4.64805 pounds of CO₂
Therefore 4.64805 pounds of CO₂ was produced