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
Which of the following does not represent a function?
Answers
Answer:
D,
Step-by-step explanation:
D would be the only one that doesn't represent a function because the y-value never changes while the x-value does.
Tony buys 3 bags of oranges there are 6 oranges in each bag. which expression represents the total number or oranges
Answers
X = 18 oranges
Answer:
3x6
Step-by-step explanation:
What is the result when 12x3 + 20x2 + 11x + 2 is divided by 3x + 2?
Answers
Answer: 3x + 2) 12x� + 20x� + 11x + 2
Divide the first term 12x� by 3x: %2812x%5E3%29%2F%283x%29=4x%5E2
and write 4x� above the 20x�:
4x�__________
3x + 2) 12x� + 20x� + 11x + 2
Multiply the 4x� by the (3x + 2) getting 4x%5E2%283x%2B2%29=12x%5E3%2B8x%5E2 and
write it under the first two terms and draw a line underneath:
4x�__________
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
Subtract %2812x%5E3%2B20x%5E2%29-%2812x%5E3%2B8x%5E2%29=12x%5E3%2B20x%5E2-12x%5E3-8x%5E2=12x%5E2,
and write 12x� under the line under 8x�, like this:
4x�__________
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x�
Now bring down the next term + llx and write in next to the 12x�
4x�__________
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
Divide the first term on the bottom 12x� by 3x: %2812x%5E2%29%2F%283x%29=4x
and write + 4x above the 11x at the top, like this:
4x� + 4x____
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
Multiply the 4x by the (3x + 2) getting 4x%283x%2B2%29=12x%5E2%2B8x and
write it under the first two terms and draw a line underneath:
4x� + 4x____
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
12x� + 8x
Subtract %2812x%5E2%2B11x%29-%2812x%5E2%2B8x%29=12x%5E2%2B11x-12x%5E2-8x=3x,
and write 3x under the line under 8x, like this:
4x� + 4x____
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
12x� + 8x
3x
Now bring down the last term + 2 and write in next to the 3x
4x� + 4x____
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
12x� + 8x
3x + 2
Divide the first term on the bottom 3x by the 3x at the left:
%283x%29%2F%283x%29=1 and write + 1 above the + 2 at the top,
like this:
4x� + 4x + 1
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
12x� + 8x
3x + 2
Multiply the + 1 by the (3x + 2) getting 1%283x%2B2%29=3x%2B2 and
write it under the two terms at the bottom and draw a line
underneath:
4x� + 4x + 1
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
12x� + 8x
3x + 2
3x + 2
Subtract %283x%2B2%29-%283x%2B2%29=3x-3x=0,
and write 0 under the line under 2, like this:
4x� + 4x + 1
3x + 2) 12x� + 20x� + 11x + 2
12x� + 8x�
12x� + 11x
12x� + 8x
3x + 2
3x + 2
0
Now you are done and the answer is 4x%5E2%2B4x%2B1 and
since the remainder is 0 you do not have to put it over
the divisor 3x+%2B+2 and add it on like you do when
the remainder is not 0.
Step-by-step explanation:
An angle's measure is 43 less than 6 times the measure of its
complement. Find the measure of both angles,
Answers
Step-by-step explanation:
A = 6(90-A)-43 Simplify and solve for A.
A = 540-6A-43
A = 497-6A Add 6A to both sides.
7A = 497 Divide both sides by 7.
A = 71 degrees
The complement of A = 90-A = 09-71 = 19
Hope this help :)
Brainliest to the correct answer
Answers
No, x and y do not have a proportional relationship because if we do cross multiplication they are not equal to each other.
Please help! I’ll mark brainlist and 5 stars!
(You have to see which one is right for the sentence provided, and which ones are false out of A-D)
A. The equation of the line is y = 1/2x
B. Sasha can make 60 gift bags in 2 hours.
C. The constant of proportionality is l = 1/2
D. Sasha can make 2 bags per minute.
Answers
Answer:
D
Step-by-step explanation:
The reason D is false is because it states that Sasha can make 2 bags per minute while she cant make 2 bags per minute. She can make half a bag per minute. D is wrong 100%
Answer:
Step-by-step explanation:
Distance covered = speed × time.
Sasha runs at a constant speed of 3.8 meters per second for 1/2 hour.
This means distance covered while running would be
3.8 × 1/2 = 1.9 meters
Then she walks at a constant rate of 1.5 meters per second for 1/2 hour. This means distance covered while walking would be
1.5 × 1/2 = 0.75 meters
Total distance that Sasha covered while running and walking in 60 minutes would be
1.9 + 0.75 = 2.65 meters
Step-by-step explanation:
PLZ ANSWER CORRECTLY 1 2⁄6 ÷ 4 1⁄3
Answers
Answer:
0.30715935334
Step-by-step explanation:
8/6 ÷ 13/3
1.33÷ 4.33
0.30715935334
Answer:
4/13
Step-by-step explanation:
i know im 6 days late but i tried to find this answer but i got it wrong so 4/13 is the answer(im answering this incase if someone else is looking for the answer)
Given the following formula, solve for l.
P=2(l+b)
Answers
Answer:
D
Step-by-step explanation:
P=2(L + B)
P = 2L + 2B
P - 2B = 2L
OR P - 2B BY 2 = L
THEREFORE, D.
Answer:
D.
Step-by-step explanation:
PLEASE HELP MEEE!!!!! GIVE YOU ANYTHING YOU WANT JUST GIVE ME THE ANSWER! well, i wouldn't give you everything but i will give you brainlest and points. that's really all you need correct?
Which binomials are factors of x2−9x−36?
Select the two correct answers.
x + 9
x−3
x + 3
x−4
x + 4
x−12
x + 12
x−9
Answers
Answer:
Step-by-step explanation:
x²-9x -36 =(x+3) (x -12)
because
x² -12x +3x -36 =
x( x-12) +3( x-12)=
(x-12) (x+3)
Find the 52nd term of the arithmetic sequence-8, -12, -16,...
Answers
Answer:
-212
Step-by-step explanation:
This question seems to be incrementing by steps of -4, starting at -8. To get the 52'nd term, we can simply start at the first term and add that -4 51 more times.
Assuming that negative eight is the first term then, we get:
-8 - 4 * 51
= -8 - 204
= -212
The 52nd term of the sequence will be -212.
What is a sequence?A sequence of events or things is a number of events or things that come one after another in a particular order.
Given a sequence, -8, -12, -16,...
nth term of a sequence is given by
an = a + (n-1)*d
a(-212) = -8 + (52-1)*-4
a(-212) = -8-204
a(-212) = -212
Hence, The 52nd term of the sequence will be -212.
For more references on sequences, click;
https://brainly.com/question/21961097
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Use distributive property to rewrite
1. 4(x + 9)
2. 3 (-2x + 4)
Answers
1. 4x+36
2. -6x+12
and aww your pfp
At a real estate agency, an agent sold a house for $396,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 20% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answers
Answer:
$29,700 and $79,200
Step-by-step explanation:
Step one:
given
The selling price of the house is $396,000
The commission rate is 7.5% for the real estate agency
The commission rate for the agent is 20%
Step two:
1. How much did the agency make on the house?
This amount is 7.5% of $396,000
= 7.5/100*396,000
= 0.075*396,000
=$29,700
2. How much did the agent earn in commission?
This amount is 20% of $396,000
= 20/100*396,000
= 0.2*396,000
=$79,200
Helppppppppppppppppppp
Answers
Answer:
The answer to the question is 23
3. Taka Barrow purchased fishing gear from a store in Illinois, where the tax rate is 6.25%. She purchased a spinning combo rod and reel for $59.99, 4 spinner baits at $5.49 each, 3 lures for $3.89 each, and a landing net for $24.99 a. What is the total selling price?' b. What is the sales tax?
Answers
Answer:
a.126.023125
b.7.413135
Step-by-step explanation:
a. ((59.99)+(4*5.49)+(3*3.89)+(24.99))*1.0625(sales tax)
118.61*1.0625
126.023125 final price
b. final price-price before tax.
126.023125-118.61
7.413135
If the height of Mount Everest is about 8.8 time 10 to the third power meters and the height of the Empire State Building is about 3.8 times 10 to the second power meters which of these statements is a true
Answers
Answer: C. Mount Everest is about 23 times as tall as the Empire State Building
Step-by-step explanation:
The options are:
A.There is no way to compare these heights
B.Mount Everest is about 40 times as tall as the Empire State Building
C.Mount Everest is about 23 times as tall as the Empire State Building
D.The Empire State Building is about 23 times as tall as Mount Everest
Mount Everest = 8.8×10^3 meters = 8800 meters
Empire State Building = 3.8×10^2 = 380 meters
Mount Everest is (8800 / 23) = 33 times as tall as the Empire State Building. Therefore, the correct option is C.
Answer:
Mount Everest is about 23 times as tall as the Empire State Building. Hope that helps!
WILL GIVE BRAINLIEST
Answers
Answer:
e
Step-by-step explanation:
pls helppp
math work
bleh
Answers
Answer:
m = -10
Step-by-step explanation:
>:)
Answer:
m= -10
Step-by-step explanation:
2< -7 - (-10)
2< -7 + 10
2< 3
There are 10 crustaceans and 25 fish the deep blue tank has the same ratio of crustaceans to fish. There are 50 crustaceans in the deep blue tank.
Answers
Answer:
125
Step-by-step explanation:
C : F
10: 25
×5: ×5
50: ?
No. of fish in the tank = 25 × 5
= 125
1+5= what does this equal
Answers
Answer:
1+5=6
Step-by-step explanation:
solve by factoring
[tex]x^{4}+x^{3}-6x^{2}[/tex]
Answers
What is the domain of f(x)=(1/2)^x
Answers
Answer:
x is greater than zero c is correct
a linear function contains the following points
what are the slope and y-intercept of this function?
A. the slope is 4
the y-intercept is (0,5)
B. the slope is -4
the y-intercept is (0,5)
C. the slope is -1/4
the y-intercept is (0,5)
D. the slope of 1/4
the y-intercept is (0,5)
Answers
Answer:
I believe the answer is C.
Step-by-step explanation:
Hope this helps you.
PLEASE HELP I REALLY NEED IT! PLEASE ASAP!
If possible please give a short explanation of your answer, I just don't want people choosing random answers for points. Thank you so much! :D
1. Let f(x)=3x+1 and g(x)=2x2−1
Find f(g(2))
A 97
B 28
C 10
D 22
2. Let f(x)=2x and g(x)=(x−3)2
Find g(f(x)) (there may be more than one answer)
A 4x^2−9
B 4x^2−12x+9
C 4x+9
D 4x^2+10x−9
Answers
Steve Conway wants his team to win more than 57 games this year. His team has already won 2 games this season and there are 5 more months to play. Based on his goal, how many games must his team win per month? Write answer as an inequality.
Answers
Answer:
11
Explanation:
Because 57 minus 2 games already equals 55, so 55 games divided by 5 months equals 11, so 11 games each month will get u to 57.
The number of games must his team win per month will be;
⇒ x > 11
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Steve Conway wants his team to win more than 57 games this year.
And, His team has already won 2 games this season and there are 5 more months to play.
Now,
Let number of games must his team win per month = x
So, We can formulate the inequality as;
⇒ 5x + 2 > 57
Solve for x as;
⇒ 5x > 57 - 2
⇒ 5x > 55
⇒ x > 11
Thus, The number of games must his team win per month will be;
⇒ x > 11
Learn more about the inequality visit:
https://brainly.com/question/25275758
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Which statement is NOT true about the absolute value of -6?
Answers
Answer:
2: it describes the distance between 6 and -6 on the number line.
Please help I will mark you brainliest if you’re right!!
Answers
Answer:
C
Step-by-step explanation:
What is the value of x? (Please help ASAP)
Answers
Answer:
110
Step-by-step explanation:
Bigger then 90 less than 120
Nathan has a 16 ounce energy drink. He drinks 9 ounces. Enter the percentage of ounces Nathan has left of his energy drink. Round your answer to the nearest hundredth
Answers
Answer:
56%
Step-by-step explanation:
Let me know if you need an explanation! Hope this helped :)
Answer:
43.75%
Step-by-step explanation:
step 1
16-9=7
7ounce remains
step2
7 of 16 ounce remains
convert into percentge
7/16×100=43.75%
Find the value of f (-2)for the function f (c) = 5x+8
Answers
F(-2) means to replace x in the equation with -2 and then solve.
5(-2) +8 = -10 + 8 = -2
The answer is -2
Tell whether (-1,3) is a solution of the inequality whose graph is shown.
Answers
Answer: No.
Reason: (-1, -3) is (x, y) so, let's find -1 on the X scale first. Alright, -1 is in the blue, which is a great start. Now, it's -3 on the Y portion. And when you graph that, it's not in the blue shaded area, so no, it's not a solution. (TIP: Solution is the Shaded Area)