Answer:
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
Step-by-step explanation:
Differentiate both sides of the equation (consider y as a function of x).
[tex] \frac{d}{dx} ( {x}^{4} + {y}^{4} (x)) = \frac{d}{dx} (16)[/tex]
the derivative of a sum/difference is the sum/difference of derivatives.
[tex]( \frac{d}{dx} ( {x}^{4} + {y}^{4} (x))[/tex]
[tex] = ( \frac{d}{dx} ( {x}^{4} ) + \frac{d}{dx} ( {y}^{4} (x)))[/tex]
the function of y^4(x) is the composition of f(g(x)) of the two functions.
the chain rule:
[tex] \frac{d}{dx} (f(g(x))) = \frac{d}{du} (f(u)) \frac{d}{dx} (g(x))[/tex]
[tex] = ( \frac{d}{du} ( {u}^{4} ) \frac{d}{dx} (y(x))) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule:
[tex](4 {u}^{3} ) \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
return to the old variable:
[tex]4(y(x) {)}^{3} \frac{d}{dx} (y(x)) + \frac{d}{dx} ( {x}^{4} )[/tex]
apply the power rule once again:
[tex]4 {y}^{3} (x) \frac{d}{dx} (y(x)) + (4 {x}^{3} )[/tex]
simplify:
[tex]4 {x}^{3} + 4 {y}^{3} (x) \frac{d}{dx} (y(x))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx} (y(x)))[/tex]
[tex] = \frac{d}{dx} ( {x}^{4} + {y}^{4} ))[/tex]
[tex] = 4( {x}^{3} + {y}^{3} (x) \frac{d}{dx}(y(x))) [/tex]
differentiate the equation:
[tex]( \frac{d}{dx} (16)) = (0)[/tex]
[tex] = \frac{d}{dx} (16) = 0[/tex]
derivative:
[tex]4 {x}^{3} + 4 {y}^{3} \frac{dy}{dx} = 0[/tex]
[tex] \frac{dy}{dx} = - \frac{ {x}^{3} }{ {y}^{3} } [/tex]
2. An electronic watch is sold for Rs 840 at a profit of Rs 90. Find its cost price and the profit per cent.
Answer:
750 CP AND PROFIT%=12%
Step-by-step explanation:
SP=rs 840
profit=90
CP=SP-profit
=840-90
=750
profit %=profit/CP*100%
=90/750*100%
=12%
lucy made 3 cakes that each weighed 32 ounces. how many pounds of cake did lucy make
Answer:
6 pounds
Step-by-step explanation:
1 pound = 16ounces
32ounces*3cakes= 96ounces/16ounces=6pounds
HELP PLEASE
Find the length of AB
Step-by-step explanation:
hopefully it makes sense and is visible
:)
please i need to know
Answer:
the answer is 28
Step-by-step explanation:
PEMDAS:
(8-2) = 6
6^2= 36
36/2= 18
18+10= 28
Answer:
D. 28
PEMDAS:
Parenthesis, exponents, multiplication, division, addition, subtraction
10 + (8 - 2)^2 / 2
1. Parenthesis comes first so we're left with
10 + (6)^2 / 2
2. Then we do the exponents
10 + 36 / 2
3. Then it's division
10 + 18
4. Finally we add
28
help plz answer quickly
Answer:
plane EBG
Step-by-step explanation:
plane C is also named plane EBG
Answer:
[tex]\\ \sf\longmapsto Plane EBG[/tex]
We can't name it EBF as it is a axis and coplanar points
Also nEF is not a satisfactory name .
So the correct option is C
a structure The table shows the distance below ground of items found at an archaeological site Researchers also found a mouse fossil at the same site. Which, if any, of the items in the table were a greater distance below ground than the mouse fossil shown? 1 Item Distance below ground (feet) Spoon key cup 42 62 bowl for Problems 14-17, find the LCM of the number pair
Spoon ;
[tex]5 \frac{3}{8} = \frac{43}{8} = 5.375[/tex]
Key ;
[tex]6 \frac{3}{4} = \frac{27}{4} = 6.75[/tex]
Cup ;
[tex]4 \frac{3}{12} = \frac{17}{4} = 4.25[/tex]
bowl;
[tex]5 \frac{5}{6} = \frac{35}{6} = 5.83[/tex]
The distance from the smallest to the largest ; 4.25 , 5.375 , 5.83 , 6.75 So the greater distance —> Key = 6.75[tex]key = 6 \frac{3}{4} = \frac{27}{4} = 6.75[/tex]
I hope I helped you^_^
brainiest to whoever right
write 45 as a product of prime numbers
Answer:
3²×5
Step-by-step explanation:
Product of its prime numbers its more like having the number in its simplest form by factorising it
Find ef if e (1,-2) and f (7,6)
6 bannas cost $0.75. How much do 20 bannas cost
Answer:
15
Step-by-step explanation:
Answer:
The answer is 15
Step-by-step explanation:
How do they get Question 3
Answer:
400÷10=40
Step-by-step explanation:
the question asks for you to divide each number in the pattern by 10.
the first number is 400
400÷10=40
then you would do 40÷10=4
then 4÷10=0.4
then 0.4÷10=0.04
so the pattern would be
400 , 40 , 4 , 0.4 , 0.04
hope this helped!
|72| ÷ |-12| =
?????????
Answer:
6
Step-by-step explanation:
|72| ÷ |-12|
Absolute value of 72 = 72
Absolute value of -12 = 12
72 ÷ 12 = 6
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Simplify. 2–3 Write your answer in the form a+b.
Answer:
2 + -3
Step-by-step explanation:
2 - 3 in the form a + b is:
2 + -3
where a = 2
and b = -3
If f(x)=10x+7 and g(x)= x^2-7x, find (f-g)(x).
Answer:
Choice C. [tex](f-g)(x)=-x^2+17x+7[/tex]
Step-by-step explanation:
Recall that [tex]f-g[/tex] is defined by
[tex](f-g)(x)=f(x)-g(x)[/tex]
Therefore we compute
[tex](f-g)(x)=f(x)-g(x)=10x+7-x^2+7x=-x^2+17x+7[/tex]
please help with the screenshot
Answer:
[tex] \sin(x) = \frac{16}{17} [/tex]
Step-by-step explanation:
sin = opposite/ hypotenuse
PLEASE HELP
write and solve an equation to find the value of X. please explain in details and show your work!
Answer:66.5 degrees
Step-by-step explanation:
Find the solution for
h - 12 =6
Answer:
H-12=6
H−12+12=6+12
h=18
Answer:
h=18
Step-by-step explanation:
h-12=6
is the normal eqaution, you need to determine the value of h, on the left side of the eqaution you have negative twelve we must get the h on its own by moving the 12 to the right side using of basic math rules you must know that when you have a negative and want to move it to the right hand side it must become a positive
so in formula it wil look like this
h = 6 + 12
Add up 6 with 12 that wil give you 18
so the value of h is then 18
h = 18
Slope-Intercept Form
Directions: Re-write the equation of
the line in slope-intercept form.
Slope must be in simplest/fraction
form. Do NOT put any spaces in
your answer.
Standard Form
2x+y=8
3x-y=7
5x+2y=8
4x+3y=9
X-y=0
x+4y=16
4x-3y=6
x+2y=-10
x+y=3
3x-2y=9
(Please vote me Brainliest if this helps!):
y = -2x + 8y = 3x - 7y = [tex]-\frac{5}{2}x[/tex] + 4y = [tex]-\frac{4}{3}x[/tex] + 3y = x + 0y = [tex]-\frac{1}{4}x[/tex] + 4y = [tex]\frac{4}{3}x[/tex] - 2y = [tex]-\frac{1}{2}x[/tex] - 5y = -x + 3y = [tex]\frac{3}{2}x - \frac{9}{2}[/tex]
brainiest to whoever rightt.
Answer:
Perimeter of a square
Step-by-step explanation:
The formula for finding out the perimeter of a square is P = 4s
Rachael made 4 pounds of potato salad. How many ounces of potato salad did Rachael make?
Answer:
i think the answer is 64 ounces
A number is 10 more than another number. Twice the sum of the two numbers is 44. Find the two numbers.
Answer:
The two numbers are 6 and 16
Step-by-step explanation:
16+6=22
22+22=44
The numbers are 6 and 12.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number are x and y.
A number is 10 more than another number then
x + 10 = y...............(1)
and, Twice the sum of the two numbers is 44.
2(x+y)= 44...........(2)
Solving the above equation we get
x+ y= 22
y-10 + y = 22
2y = 32
y= 16
and, x= y-10 = 16-10= 6
Learn more about Algebra here:
https://brainly.com/question/24875240
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the mean of seven numbers is 15. when three numbers are added, the mean of ten numbers becomes 12. find the mean of the three numbers.
Answer:
3 is the value I guess because with seven it becomes 15 where as with 10 it become 12 so there is 3 numbers gap
I don't know exactly so I just try
Answer:
13 is the answer
Step-by-step explanation:
Calculate the distance between the points -8,2 and 3,2 on a coordinate plane
[tex]\\ \rm\Rrightarrow \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{(3+8)^2+(2-2)^2}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt{11^2}[/tex]
[tex]\\ \rm\Rrightarrow 11[/tex]
Can someone help me with this question? please
Answer:
6 cm3
Step-by-step explanation:
3 x 2 x 1 = 6
Whats the answer to it i can't figure it out
Answer:
-0.1
...............................
5.
A bag contains three types of candy (gumdrops, jelly beans, and jawbreakers). If
chosen at random, the probability of getting a gumdrop is 1/6 and the probability
of getting a jellybean is 1/3 What is the probability of getting a jawbreaker?
Answer:
P) = 1/2 jawbreaker
simplified P) 3/6 = 1/2 jawbreaker
Which both mean the same, so show simplified if asked and either answer if not asked would be marked high.
as 2/6 + 1/3 = 3/6
1 - 3/6 = 3/6
= 1/2 are the workings.
Step-by-step explanation:
Jelly bean = 1/3 = 2/6
Gumdrop = 1/6
2/6 + 1/6 = 3/6 = the difference of 1
1-3/6 = 3/6
Therefore; P) = 3/6 jawbreaker
A property sells for $140,000 two years after it was purchased. If the annual appreciation rate is 6%, how much did the original buyer pay for it?
Answer:
$123,200
Step-by-step explanation:
0.06 x 2 = 0.12
140,000 x 0.12 = 16,800
140,000 - 16,800 = 123,200
The original buyer paid the amount of $123,200 for the property.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The property appreciated by 6% per year, so in two years it would have appreciated by 6% × 2 years = 12%.
Once we know the total appreciation, we can subtract that value from 100% to find the original purchase price as a percentage of the final sale price.
If the property appreciated by 12%, then the original purchase price must have been 100% - 12% = 88% of the final sale price.
Now, multiply the final sale price by the original purchase price as a percentage to find the original purchase price.
So, the original buyer paid the amount = 88% × $140,000 = $123,200
Therefore, the original purchase price was $123,200.
Learn more about the percentages here:
brainly.com/question/24159063
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A display case of glitter stickers are marked 15 for $2. If Cathy wants to buy 30 glitter stickers, how much will Cathy spend?
Answer:
$4, 15 x 2=30
2 x 2=4
Answer:
4 dollars
Step-by-step explanation:
We can write a ratio to solve
15 stickers 30 stickers
----------------- = -------------
2 dollars x stickers
Using cross products
15x = 2*30
15x = 60
Divide by 15
15x/15 = 60/15
x = 4
√400=x² what is x? Thanks
Answer:
x=4.47213
I hope it's helps you
15
Determine whether the ordered pairs (1,0) and 4,
(4:15)
are solutions of the following equation.
- 5x + 7y= -5
BRE
Is (1,0) a solution of - 5x + 7y = - 5?
O Yes
Ο Νο
(ANSWER QUICKLY)
Answer:
yes
Step-by-step explanation:
x = 1, y = 0
so,
-5×1 + 7×0 = -5
-5 + 0 = -5
-5 = -5
true, therefore (1, 0) is a solution (a point on the graph) of the equation.
I am not sure what the other pair should be.
