Answers
Answer: [tex]\frac{14y}{25x^2}[/tex]
====================================================
Work Shown:
First calculate [tex]\frac{dy}{dx}[/tex] through the use of implicit differentiation.
Don't forget about the chain rule.
[tex]y^5 = x^7\\\\\frac{d}{dx}\left[y^5\right] = \frac{d}{dx}\left[x^7\right]\\\\5y^4\frac{dy}{dx} = 7x^6\\\\\frac{dy}{dx} = \frac{7x^6}{5y^4}\\\\[/tex]
Go back to line 3, shown above, and apply the derivative to both sides.
You'll be using the product rule.
[tex]5y^4\frac{dy}{dx} = 7x^6\\\\\frac{d}{dx}\left[5y^4\frac{dy}{dx}\right] = \frac{d}{dx}\left[7x^6\right]\\\\\frac{d}{dx}\left[5y^4\right]*\frac{dy}{dx}+5y^4*\frac{d}{dx}\left[\frac{dy}{dx}\right] = 42x^5\\\\20y^3*\frac{dy}{dx}*\frac{dy}{dx}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\[/tex]
Use substitution and isolate [tex]\frac{d^2y}{dx^2}[/tex] to get the following:
[tex]20y^3*\left(\frac{dy}{dx}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\20y^3*\left(\frac{7x^6}{5y^4}\right)^2+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5y^5}+5y^4*\frac{d^2y}{dx^2} = 42x^5\\\\\frac{196x^{12}}{5x^7}+5y^4\frac{d^2y}{dx^2} = 42x^5\\\\[/tex]
[tex]\frac{196x^5}{5}+5y^4*\frac{d^2y}{dx^2}=42x^5\\\\5y^4*\frac{d^2y}{dx^2}=42x^5-\frac{196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{210x^5-196x^5}{5}\\\\5y^4*\frac{d^2y}{dx^2}=\frac{14x^5}{5}\\\\[/tex]
[tex]\frac{d^2y}{dx^2}=\frac{14x^5}{5}*\frac{1}{5y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5}{25y^4}\\\\\frac{d^2y}{dx^2}=\frac{14x^5*x^2}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14x^7}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y^5}{25y^4*x^2}\\\\\frac{d^2y}{dx^2}=\frac{14y}{25x^2}\\\\[/tex]
Related Questions
4. Your Language Arts teacher expects
you to read an entire book over the 3 day
weekend. On Tuesday you are on page 60
and are 1/5 of the way done. How many
pages are in the book?
Answers
There are 600 pages in the book.
In this question, we have been given a situation where your Language Arts teacher expects you to read an entire book over the 3 day weekend.
On Tuesday you are on page 60 and are 1/5 of the way done.
We have been given a fraction 1/5.
We need to find the number of pages in the book.
Let 'n' be the number of pages in the book.
60 = 1/5 × n
n = 5 × 60
n = 300
Therefore, there are 600 pages in the book.
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Choose the best answer.
A
B
C
D
Answers
Answer:
D :)
Step-by-step explanation:
help or else the dog dies >:( no silly answers
Answers
Answer:
3
Step-by-step explanation:
3/10 is 1/3 of 9/10
Answer: 2.7?
Step-by-step explanation:
How do I answer this question-
Answers
9514 1404 393
Answer:
18 cm
Step-by-step explanation:
Consider right triangle PCA.
The length PC is the hypotenuse of that triangle. It is also the radius of the circle: 15 cm.
The length AC is AB -CB = (27 -15) cm = 12 cm.
The length AP can be found from the Pythagorean theorem:
AP² +AC² = PC²
AP² = PC² -AC² = (15 cm)² -(12 cm)² = (225 -144) cm² = 81 cm²
AP = √(81 cm²) = 9 cm
Since A is the midpoint of PQ, the length of PQ is double the length of AP:
PQ = 2·AP = 2·9 cm
PQ = 18 cm
9x-6y=20 and -3y=2x-11 parallel perpendicular or neither
Answers
Answer:
-2/3 is the negative inverse of 3/2
A sled team consists of 11 dogs and the musher. Each dog weighs 70 pounds and the musher weighs 160 pounds. What is the average weight of the sled team members?
a
68.5 pounds
b
115 pounds
c
73.5 pounds
d
77.5 pounds
Answers
Answer:
C. 73.5lbs
Step-by-step explanation:
Can someone help me with this pleasePLSSSSSSSS
Answers
Answer:
What is question #3?
Step-by-step explanation:
7 divided by 1/3 help asapp
Answers
Answer:
7 divided by 1/3 is 21
Step-by-step explanation:
How does knowing one linear factor of a polynomial help find the other factors?
Answers
Answer:
How does knowing one linear factor of a polynomial help find the other factors?
Step-by-step explanation:
f(x)=(x−3)(x−1)(x+2)(x+6)
f(x)=(x−2)(x−2)(x+3)(x+5)
f(x)=(x−5)(x−3)(x+2)(x+2)
f(x)=(x−8)(x−1)(x+3)(x+5)
f(x)=(x−2)(x−1)(x+4)(x+4)
Correct answer:
f(x)=(x−2)(x−2)(x+3)(x+5)
Explanation:
We begin by attempting to find any rational roots using the Rational Root Theorem, which states that the possible rational roots are the positive or negative versions of the possible fractional combinations formed by placing a factor of the constant term in the numerator and a factor of the leading coefficient in the denominator.
That was a lot of wordage in one sentence, so let's break that down. We begin with our polynomial.
f(x)=x4+4x3−13x2−28x+60
The constant term is the term without a variable (just a plain number). In our case the constant is 60. What are the possible factors of 60?
1,2,3,4,5,6,10,12,15,20,30,60
The leading coefficient is the number in front of the largest power of the variable. When the terms are listed in descending order (highest to lowest power), the leading coefficient is always the first number. In our case the leading coefficient is hard to spot. Since there is no number in front of x4, the coefficient is 1 by default.
This is nice because the only factor of 1 is well ... 1.
We then create all the possible fractions with a factor of the constant in the numerator and a factor of the leading coefficient in the denominator. This actually isn't as bad as it could be since our only possible denominator is 1. Any fraction with a denominator of 1 is just the numerator. Therfore, our possible "fractions" are simply
1,2,3,4,5,6,10,12,15,20,30,60
However, we must consider the positive or negative versions of these, so our final list of possible rational roots is
±1,±2,±3,±4,±5,±6,±10±,1±2,±15,±20,±30,±60
Unfortunately, this is where the process (at least without the assitance of a graphing calculator) becomes less fun. Using synthetic division, we must simply try each possible root until we have success. There's really no consistent rule to tell us where to start. Generally starting with the smaller whole numbers is best because the synthetic division is easier. Therefore, we could begin with 1 then proceed to −1,2,−2, etc.
For the sake of keeping this explanation as short as possible, I am going to skip straight to 2, where we will first find success.
Therefore, 2 is a root. However, it is always important to check to see if a root is in fact a double root (it works twice). Therefore, let's try it one more time.
2 does in fact work twice and is thus a double root. Since we only have three terms remainng, we can convert from synthetic back to an algebraic expression.
f(x)=x2+8x+15
We can then factor.
f(x)=(x+3)(x+5)
Writing our root of 2 as an algebraic expression gives (x−2). Since we have double root, we need two of these. Therfore, our final factored expression is.
f(x)=(x−2)(x−2)(x+3)(x+5)
1 Evaluate the expression 2a + b - 3 when a=5 and b=2. Please click on "show your work" to set up the problem and show your work. Then, enter your answer in the box to the right. You must complete both of these steps. Evaluate the expression 2a + b - 3 when a=5 and b=2. Set up the expression and show your work.
Answers
Answer:
11
or
2(5)+2-3
Step-by-step explanation:
if a = 5 and b=2,
you add it into the expression.
2a + b -3 --> 2(5) + 2 - 3
all you have to do is replace the letters with the (given) numbers.
then, solve.
2(5) = 10
2-3= 1
10+1 =11
the answer is 11.
:)
The Value for the expression 2a + b -3 is 9.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 2a+ b -3
Now, for a=5 and b=2 thee expression gives
= 2a + b -3
= 2(5) + 2 -3
= 10 +2 - 3
= 12 - 3
= 9
Hence, the Expression valued 9.
Learn more about Expression here:
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5x + 3 ≤ 18 and 4-X<6
Question
A. Solve the inequalities and show your work.
B. graph the solution to the compound sentence on the number line.
Answers
The answer would A! :3
Please help!! Urgent for homework
Answers
Answer:
a) 50
b) 12√6
Step-by-step explanation:
I NEED HELP WILL GIVE BRAINLIEST. PLZZZZ
Answers
Jack has a points card for a movie theater. He receives 55 rewards points just for signing up. He earns 12.5 points for each visit to the movie theater. He needs at least 205 points for a free movie ticket. Write and solve an inequality which can be used to determine vv, the number of visits Jack can make to earn his first free movie ticket.
Answers
Answer: See explanation
Step-by-step explanation:
Since Jack receives 55 rewards points just for signing up and earns 12.5 points for each visit to the movie theater and needs at least 205 points for a free movie ticket.
The inequality which can be used to determine v, the number of visits Jack can make to earn his first free movie ticket will be:
55 + 12.5v ≥ 205
12.5v ≥ 205 - 55
12.5v ≥ 150
v ≥ 150/12.5
v ≥ 12
The number of visits that Jack can make to earn his first free movie ticket will be at least 12 visits
There are 32 marbles to share equally among 8 children. How many marbles does each child get?
Answers
Answer:
each child get 4
Step-by-step explanation:
Answer:
4 marbles
Picture:
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For exercise after work, Albert (A) went running and Tanisha (T) walked for exercise. Their times and distances are shown in the graph below. How much faster was Albert running than Tanisha walking, in miles per hour? Explain how you found your answer.
image
A.
Albert ran 3 miles per hour faster because Albert runs 6 miles per hour and Tanisha walks 3 miles per hour.
B.
Albert ran 10 miles per hour faster because Albert runs 10 miles per hour and Tanisha walks 20 miles per hour.
C.
Albert ran 3 miles per hour faster because Albert runs 10 miles per hour and Tanisha walks 20 miles per hour.
D.
Albert ran 10 miles per hour faster because Albert runs 6 miles per hour and Tanisha walks 3 miles per hour.
Answers
Answer:
c
Step-by-step explanation:
Drag the phrases into the box to match each expression.
(A) 6/x+3
(B) 3x-6
(C) 6(x+3)
(1) 6 divided by a number 3 times
(2) 6 less than 3 plus a number
(3) 3 more than the quotient of 6 and a number
(4) 3 more than the product of 6 and a number
(5) 6 more than a number divided by 3
(6) the product of 6 and the sum of a number and 3
(7) 6 less than the product of 3 and a number
Answers
Answer:
(A) = (3). (B) = (7). (C) = (6)
someone please help me asap
Answers
Answer: B.
Step-by-step explanation:
5 over 30 = x over 90
Answers
[tex]\frac{5}{30} =\frac{x}{90}[/tex]
Match the denominators:
[tex]\frac{5}{30} *\frac{3}{3}= \frac{15}{90}[/tex]
x = 15
Check your work:
[tex]\frac{15}{90} \div \frac{3}{3} = \frac{5}{30}[/tex]
We know that x = 15
Janet picked forty-eight tulips and twenty-two roses to make flower bouquets. If she only
used twenty-three of the flowers though, how many extra flowers did Janet pick?
Answers
Answer:
47
Step-by-step explanation:
48 + 22 = 70
70 - 23 = 47
Hope this helped! Let me know if you need a better explanation!
Which one is it please help
Answers
Answer:
D
Step-by-step explanation:
Hope This has helped you tons a bunch and I would appreciate the giving of what is it called.. um... This Brainliest. I hear it’s your Finest dish! I will be the judge of that .
Rewrite the equation by completing the square.
X^2+ 10x + 25 = 0
(x+
Answers
or (x+5)^2 = 0
CAN SOMEONE PLEASE HELP ME WITH THIS ASAP I NEED THE EXPLANATION PLEASE
Answers
Answer:
could you get a better picture of it so I could answer or for you?
2. QS bisects 2 PQR Р S 29° R What is m
Answers
Answer:
slope
Step-by-step explanation:
Find sin ( A). с 50 14 B -A 48
Answers
Answer: Murder is a sin
Step-by-step explanation:
In the trapezoid below, x = [? ]
Answers
if this trapezoid is to scale, then the scale factor between the shortest and longest side is 1.5
so, that means that 1.5(2x+6) = 4x+2
so, your equation becomes 3x+9 = 4x+2
if you subtract 2 from each side, you get 3x+7 = 4x
meaning that x = 7
i hope this helps, and i'm sorry if it's wrong!! :)
Can someone please help me. really need help. question and answer options are in the photo.
Answers
Answer:
Hey give it a try but my answer is 1.5 miles
Step-by-step explanation:
Answer:
I believe it is B.
Step-by-step explanation:
Hope this helps
Heeeeeeeellllllpppppppppp!
Answers
Answer:
D
Step-by-step explanation:
15 - 2.5x = 40 ( isolate the term in x by subtracting 15 from both sides )
- 2.5x = 40 - 15 = 25 ← Step 1
divide both sides by - 2.5
x = 25 ÷ - 2.5 ← Step 2
x = - 10
Graph the linear equation -3x + 4y = 24
4
Answers
ill convert it to y=mx+b form
4y=3x+24
y=3/4x+6
here's a graph
What is the equation for the
following table:
X Y
1 -5
2 -7
3 -9
4 -11
Answers
y= mx+b
-5= -2(1) + b
-5 = -2 + b
b = -3
equation: y= -2x-3