Given:
Consider the completer question is "Find the derivative [tex]\dfrac{dy}{dx}[/tex] for [tex]y=\dfrac{x^2-4x}{x^3-5}[/tex]."
To find:
The derivative [tex]\dfrac{dy}{dx}[/tex].
Solution:
Chain rule: [tex]\dfrac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)[/tex]
Quotient rule: [tex]\dfrac{d}{dx}\dfrac{f(x)}{g(x)}=\dfrac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}[/tex]
We have,
[tex]y=\dfrac{x^2-4x}{x^3-5}[/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}\left(\dfrac{x^2-4x}{x^3-5}\right)[/tex]
Using chain rule and quotient rule, we get
[tex]\dfrac{dy}{dx}=\dfrac{(x^3-5)\dfrac{d}{dx}(x^2-4x)-(x^2-4x)\dfrac{d}{dx}(x^3-5)}{(x^3-5)^2}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{(x^3-5)(2x-4)-(x^2-4x)(3x^2)}{(x^3-5)^2}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{2x^4-4x^3-10x+20-3x^4+12x^3}{(x^3-5)^2}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}[/tex]
Therefore, the required answer is [tex]\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}[/tex].
HELP PLEASE
given the relation y=x^2 +3 if the input is 4 what is the output
Answer:
19
Step-by-step explanation:
x = 4
y = 4^2 + 3 = 16 +3 = 19
525 people visited the mall today and 68% of these people made a purchase. How many people made a purchase?
Group of answer choices
The number of people made a purchase: 357
What is the percentage?A number can be expressed as a fraction of 100 using a percentage. It is frequently used, particularly in financial and statistical contexts, to depict ratios and proportions in a more practical and intelligible way. For instance, 50% denotes 50 out of 100, or half of a specified amount. It is represented by the letter "%".
To find out how many people made a purchase, we need to multiply the total number of visitors by the percentage of visitors who made a purchase.
Number of people who made a purchase = Total number of visitors × Percentage of visitors who made a purchase.
Percentage can be converted to a decimal by dividing by 100.
Number of people who made a purchase = 525 × (68/100)
Number of people who made a purchase = 357
Therefore, 357 people made a purchase.
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Find the shortest distance from point A to the given line.
y = 3x +1 ; A (3,0)
What is the shortest distance from point A to the line?
Step-by-step explanation:
please i work on by paper worksheet, see it
how can i work it
Larry answered 8 out of every 10 questions on a test correctly. The test had 70 questions. How many correct answers did Larry give?----- What is the first complete ratio? (numbers)
Answer:
56
Step-by-step explanation:
70 / 10 = 7 > 8 * 7= 56 hha hope this helps
Help? I would appreciate it
Answer:
$6.50 per candle
Step-by-step explanation:
19.50 / 3 = 6.50
Answer:
$6.50
Step-by-step explanation:
$19.50 divided 3 is 6.50
1.) A man invested $600 at 8% per annum for 5 years. Calculate: a.) The simple interest payable b.) The total amount of money the man collected at the end of the 5-year period. 2.) Mr. Ford invested $12 450 in a bank at 7.25% per annum simple interest for 6 years. Calculate: a.) The interest he was paid b.) The total of amount of money he would have received at the end of the period of investment. 3.) The simple on $15 000 for 9 years is interest is paid when $800 is invested for 5 years.
Answer:
Following are the solution to this question:
Step-by-step explanation:
Using formula:
[tex]\text{Simple Interest} = \frac{P \times R \times T}{100} \\\\\text{ Total amount} = \text{principle}+ \text{Simple Interest}[/tex]
In question (1):
[tex]Principle= \$ 600\\Rate = \ 8 \%\\Time= \ 5[/tex]
In point a:
[tex]\to \frac{P \times R \times T}{100} \\\\\to \frac{(600 \times 8 \times 5)}{100}\\\\ \to 240[/tex]
In point b:
[tex]\to amount = principle \ +\ simple \ interest[/tex]
[tex]= 600 + 240 \\\\= 840[/tex]
In question (2):
[tex]Principle= \$ 12,450\\Rate = \ 7.25 \%\\Time= \ 6[/tex]
In point a:
[tex]\to \frac{P \times R \times T}{100} \\\\\to \frac{(12,450 \times 7.25 \times 6)}{100}\\\\ \to 5,415.75[/tex]
In point b:
[tex]\to amount = principle \ +\ simple \ interest[/tex]
[tex]= 12,450 + 5,415.75 \\\\= 17,865.75[/tex]
The 3 question is incomplete, that's why it can't be solved.
What is the opposite of 6.6
-6.8
6.8
Answer:
-6.6
Step-by-step explanation:
I don't really understand the question but I believe it is correct.
have a good day
SOLVE THISSS (3x+6)/3=-1
Answer:
x = −3 TRUSSSSSSTTTT MEE
Step-by-step explanation:
Find the range of the function y=3/4x+17 when the domain is {-12, -4, 8}.
Answer:
77
Step-by-step explanation:
The range of the given function y=3/4x+17 is {8, 13.4}
What is domain and range ?
The bis the set of possible input values, and the range is the set of all possible output values of the graph.
The given equation is :
y=3/4x+17
the domain of the function = {-12, -4, 8}
Now, for x = -12 :
y = 3/4 (-12) + 17
y = -9 + 17
y = 8
Now, for x = -4.8 :
y = 3/4 (-4.8) + 17
y = -3.6 + 17
y = 13.4
Therefore, the range of the given function is {8, 13.4}
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I bet no one can solve this
(+)^=∑24_(=0)^▒〖(¦) ^ ^(−) 〗
HAHAHAAAAAAAAAAAAA
Answer:
free points nice
Step-by-step explanation:
What's this? Cute. Thnx for the freee pointttssss <3
50 POINTS HELPPPPPPPPPPP
Answer:
p(Sports U Work)=1/4
Step-by-step explanation:
13+2/20
15/20
3/4
4/4-3/4=1/4
1/4
If this helps please mark as brainliest
Determine if x=2 is a solution.
Answer:
Do you have a picture for the problem that you want to be solved?
Median of 40,2,31,15,29,16 and X is 21. then X= ?
Answer:
Let us arrange this data in ascending order.
2, 15, 16, 29, 31, 40.
x has to be in the middle if it is the median.
So it becomes 2, 15, 16, x, 29, 31, 40.
There are seven numbers. The median is the 4th one.
The median is given as 21.
So x = 21.
HOPE IT HELPS YOU, PLS MARK IT AS THE BRAINLIEST :D
Tricia drove 102 miles on three gallons of gas. How far can she drive on seven gallons of gas ?
Carli can walk 40 dogs in 8 hours how many dogs can she walk in 12 hours ?
Maria tenia 6.500kg de patatas. Las envaso en sacos de 25kg y los puso a la venta a 30$ cada uno. Vendio la mitad de los sacos a ese precio y el resto los vendio todos a 2$ menos cada saco. ¿ Cuanto dinero obtuvo?
Responder:
$ 7540
Explicación paso a paso:
Dado que:
Kilogramos totales de papa = 6500
Número de kilogramos por paquete = 25
Precio por paquete = $ 30
La mitad se vendió a $ 30
El resto se vende a ($ 30 - $ 2)
Número total de paquetes de 25 kg:
6500 kg / 25 kg = 260 paquetes
Por lo tanto, paquete total = 260 paquetes
La mitad se vende a $ 30:
(260/2) * 30
130 * $ 30 = $ 3900
Resto vendido a $ 28:
(260 - 130) * $ 28
130 * $ 28 = $ 3640
Cantidad total realizada:
$ (3640 + 3900) = $ 7540
area of a square field is 1600 square metre. find the cost of boundary wall if the rate of per metre is Rs. 500
Answer:
Rs. 20,000
Step-by-step explanation:
the boundary wall will act as a perimeter.
the perimeter of a square field is 4S( S = side)
S x S = area
S2 = area
S =
square root of S2= square root of area
square root of S2 = S
S = square root of area
S = square root of 1600
S = 40m
perimeter = 4 x S
= 4 x 40
= 160m
1m = rs. 500
40m = 40m x rs.500
1m
=Rs. 20,000
1) Slope =-1, y-intercept = 0
3.
1
A) y =
B) y=-1
4
4
ID) -
1
C) y = -x
D) y = -x +
4
Answer:
1. C 2.D 3.D 4.A
Step-by-step explanation:
The first one would be C because the slope is -1, which can also be -x and the y-intercept is 0, meaning you don't need to add or subtract anything.
The second one is D because the slope is -3, meaning it's -3x, and the y-intercept is positive, meaning you add 5.
The third one is D because the slope is 5/4, which is 5/4x and the y-intercept is positive 3, meaning you add 3.
And the fourth one is A because there is no slope, so y would just equal 3.
The average teenager spends 2.9 hours a day watching television. How much time do they spend each week watching television?
Answer:They spend 8 hours
Step-by-step explanation:2.9 times 3
Find the missing side:
Which is the right one
Answer:
D , drinking coffee
Step-by-step explanation:
hope this helps you somehow
8) Choose which postulate proves the triangles congruent. *
A) SAS
B) SSS
C) AAS
D) ASA
E) HL
HELP ILL GIVE BRAINLIEST AND LOTS OF POINTS
Use the formula d = rt to find the distance, rate, or time
24. r = 5, t = 12
25. d = 24, t = 8
Answer:
24) 60, 25) 3
Step-by-step explanation:
d=r*t
5*12=60
24) 60
d=r*t
to find rate:
d/t=r
24/8=3
25) 3
What is the discriminate?
2. A formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
If the length of a rectangle is 34 centimeters and the width is 12 centimeters, what is the perimeter?
a. 78 cm b. 105 cm c. 85 cm d. 92 cm
Mrs. Jackson bought 4 gallons of juice for a party. Each gallon has 16 cups. After the party, 4 cups of juice were left over. At the party, how many cups did people drink? Show your work and complete the explanation of how you found your answer.
Answer:
60 cups
Step-by-step explanation:
Mrs. Jackson bought 4 gallons of juice for a party. Each gallon has 16 cups.
From the above question:
1 gallon of juice = 16 cups
Then:
4 gallons of juice = c
Cross Multiply
1 × c = 4 × 16 cups
c = 64 cups of juice
Hence, 4 gallons of juice = 64 cups of juice
We are told that :
After the party, 4 cups of juice were left over.
The cups of juice people drank at the party is calculated as:
Total cups of juice - Number of cups of juice left over.
64 cups of juice - 4 cups of juice
= 60 cups of juice
Jackie wants to purchase a class ring. She found the same ring for $225 at three different stores. The discounts the stores are offering are shown in the table below.
Jewelry Stores
Store Discount
1 25%
2 $25
3 1/3
Which statement about the sales price of the ring is true?
A. Store 1 and Store 2 have the same sales price of $200.
B. Store 3 has the best sales price of $150.
C. Store 1 has the best sales price of $168.75.
D. Store 3 has the best sales price of $75.00.
Answer:
A
Step-by-step explanation:
im not sure tho
Select the correct answer from each drop-down menu.
Aerial's grandmother gave her $5,500.00 to save for her college education. She went to the bank to open a savings account. The bank told her they had two options available.
Account A will pay 5.5% simple interest until the account is closed.
Account B will pay 4.5% simple interest and if the account is left open for longer than 3 years, then at the end of the third year a bonus account will be opened with $250 that also earns 4.5% for the remainder of the time the initial account is open. When the initial account is closed, the bonus account will be closed as well and the money from the two accounts will be combined.
If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account
is the better choice earning her
more.
If Aerial is planning on leaving the money in the account for 4 years and then withdrawing all funds, then account B is the better choice earning her $41.25 more.
If m∠13=2x-3 and m∠15=71°, find the value of x.
Show work please
Here ∠13 & ∠15 are corresponding angles , so they are equal [ ∠13 = ∠15 ]
As per the question ,
⇒ 2x - 3 = 71°
⇒ 2x = 71 + 3
⇒ 2x = 74
⇒ x = 74 ÷ 2
⇒ x = 37
Hence , x = 37
Answer pls question in the picture
write and solve an equation to find the number.
The perimeter of a patio is 64 feet. The length (L) is 10 feet longer than the width (W). What is the width of the patio?
9514 1404 393
Answer:
11 feet
Step-by-step explanation:
Let L and W represent the length and width of the patio. Then ...
L = W + 10
P = 2(L + W)
Substituting for the known values, we have ...
64 = 2((W +10) +W)
64 = 4W +20 . . . . simplify
44 = 4W . . . . . . . . subtract 20
11 = W . . . . . . . . . . divide by 4
The width of the patio is 11 feet.
Did i do it correctly? if no please give the explanation and answer! :):):)
Answer:
yeah man good job im proud
Step-by-step explanation:
Answer:
You did a very good jod
Step-by-step explanation:
Hope this helped have an amazing day!