Answer:
[tex]\frac{dy}{dx}=(\frac{(2x-2)(x^3+3)-(x^2-2x)(3x^2)}{(x^3+3)^2})[/tex]
Step-by-step explanation:
So we want to find the derivative of the rational equation:
[tex]y=\frac{x^2-2x}{x^3+3}[/tex]
First, recall the quotient rule:
[tex](\frac{f}{g})'=\frac{f'g-fg'}{g^2}[/tex]
Let f be x^2-2x and let g be x^3+3.
Calculate the derivatives of each:
[tex]f=x^2-2x\\f'=2x-2[/tex]
[tex]g=x^3+3\\g=3x^2[/tex]
So:
[tex]\frac{dy}{dx}=(\frac{x^2-2x}{x^3+3})'[/tex]
Use the above format:
[tex]\frac{dy}{dx}=\frac{f'g-fg'}{g^2}\\\frac{dy}{dx}=(\frac{(2x-2)(x^3+3)-(x^2-2x)(3x^2)}{(x^3+3)^2})[/tex]
And that's our answer :)
(If you want to, you can also expand. However, no terms will be canceled.)
About 1.15 million people live in a circular region with a population density of about 18,075 people per square kilometer.Find the radius of the region
Answer:
radius is 4.5 km
Step-by-step explanation:
Given :
Total number of people living in the area = 1.15 million = 1150000
Population density = 18075 people per sq kilometer
To find:
Radius of region = ?
Solution:
Population density of a region is defined as the ratio of total population divided by the area of the region.
Area here is circular. Let the radius be = r
Area of circle is given as [tex]\pi r^2[/tex]
Formula:
[tex]Population\ Density = \dfrac{Total\ population}{\pi r^2}[/tex]
Putting the values:
[tex]18075 = \dfrac{1150000}{\pi r^2}\\\Rightarrow r^2 = \dfrac{1150000}{18075\pi }\\\Rightarrow r^2 = \dfrac{63.62}{\pi }\\\Rightarrow r^2 = 20.26\\\Rightarrow \bold{r=4.5\ km}[/tex]
Therefore, radius is 4.5 km.
3 ( 2x + 5 ) = 19 + 16
Answer:
x=10/3 or x=3 1/3
(Same thing)
Step-by-step explanation:
First, we distribute the 3 to 2x and 5:
6x+15=19+16
6x=20
x=20/6
x=10/3
x=3 1/3
A cyclist rides 250 meters in 1 minute. Find the speed in km/hr.
Answer:
250 meters/min = 15 km/hr
Step-by-step explanation:
The approximate number to divide from is 16.667. Divide the speed value by 16.667
22.34÷3 please help
Respuesta es 7.4466666667
The asnwer is 7.4466666667
Answer:
7.45 is the answer if u round it up it equals to this
multiply:
(-4 + i)(-1 + 5i)
Answer:
[tex]( - 4 + i) ( - 1 + 5i) \\ = 4 - 20i - 1i + 5 {i}^{2} \\ = 4 - ( -21i )+ 5i {}^{2} [/tex]
If 1/4 in. represents 1 ft. what distances are represented by lines of the following lengths: 2 in., 5 in., 1 1/2 in., 2 2/3 in., 4 7/8 in.?
Answer:
Step-by-step explanation:
Make q clear
Answer:
2 > 8
5 > 20
1.5 > 6
2 2/3 > 10.667
4 7/8 > 19.5
Step-by-step explanation:
(Use cross multiplication or algebra to solve)
Is y= x/2 + 6 linear or nonlinear
Answer:
It is linear
Step-by-step explanation:
Its linear because y=x/2 + 6 is equal to y = 1/2x+6 which is a linear function
Please help me solve this geometry proof problem with detailed steps!
Step-by-step explanation:
in triangle pqr and trs
statement reason
1. pr=rt ( s ) 1. given
2. angle prq = angle srt (a) 2. vertically opposite angle
3. rq = sr ( s ) 3 .given
4 triangle pqr ~= triangle trs 4. by SAS axiom/fact
5. pq = st 5. from statement 4
6. pq\\st 6. from statement 5
proved
If US = 14, find the value of x
Answer:
4-6+2x=14
2x=14+6-4
2x=16
x=8
Step-by-step explanation:
Answer:
Step-by-step explanation:this is easy just find x and times it by 2 and then it will equal 14 so the awser is 7
Write an expression for the quotient of b divided by the difference of two minus three.
Answer:
b/(2-3)
Step-by-step explanation:
The expression for the quotient of b divided by the difference of two minus three is q = b / (2 - 3) and can be simplified as q = -b.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Given:
The quotient of b divided by the difference of two minus three,
The expression for the above statement can be written as,
Assume the quotient is q then,
q = b / (2 - 3)
The denominator can be simplified as,
q = b / (-1)
q = -b
To know more about the expression:
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A restuarant bill is $35.50. How much EXTRA money should you leave if you want to add a %20 tip?
Answer: $ 7.20
Step-by-step explanation:
Multiply the cost ( 35.50) by 20% or 0.20 and you get your answer ( 7.20 ). Hope this helps!
what is the image of (-2, 3) after a rotation of a 180° counterclockwise?
Answer:
-3,2
Step-by-step explanation:
just flip the minus and plus
Answer:
-3,2
Step-by-step explanation:
you just rotate it 180 degrees on counterclockwise and it land on area 4
What Is a domain of a function?
Answer: a set of all possible inputs for the function.
Step-by-step explanation:
Answer: A domain of a function is all set of inputs that make the function definable.
Step-by-step explanation:
I need the answer please
Answer:
D - All rational numbers are integers.
Step-by-step explanation:
This is because integers is a subcategory of rational numbers, so there are other rational numbers that aren't integers.
A store in Wildgrove purchased an antique pull toy at a cost of $890 and marked it up 200%. Later on, Jeffrey bought the antique pull toy. If the sales tax in Wildgrove is 10%, how much did he pay in all?
Answer: Jeffery paid $ 2937 in all.
Step-by-step explanation:
Given: The cost of antique pull = $890
Mark up percentage = 200%
New price = (cost) + (Mark up percentage) x (cost)
[tex]=\$( 890+\dfrac{200}{100}\times890)\\\\=\$( 890+2(890))\\\\=\$2670[/tex]
After a tax of 10% , the amount needs to be paid = New price + 10% of New price
[tex]=\$(2670+\dfrac{10}{100}\times2670)=\$(2670+267)\\\\=\$2937[/tex]
Hence, Jeffery paid $ 2937 in all.
Classify each of the following numbers as real, whole, integer, rational or irrational. Some numbers will have more than one classification. 1. -98 2. 1.98 3. 1270 4. 1,232,323
Marco has $75 to spend on new clothes for a job interview. He buys a shirt for $18.28, pants for $42.39, and a tie for $12.97. How much money will Marco have left after he buys these clothes?
Answer:
$1.36
Step-by-step explanation:
First, add together the prices of all the clothes:
18.28 + 42.39 + 12.97
= 73.64
Then, subtract this from 75:
75 - 73.64
= 1.36
So, he will have $1.36 left after buying the clothes
The money Marco have left after he buys his clothes is $1.36.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Marco has $75 to spend on new clothes for a job interview.
Let the money left after he purchase his clothes be x.
Cost of shirt=$18.28, cost of pants=$42.39 and cost of tie =$12.97
Now, x=75-(18.28+42.39+12.97)
x= 75-73.64
x= $1.36
Therefore, the money Marco have left after he buys his clothes is $1.36.
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A new Sports complex is being built in Madison . The perimeter of the rectangular playing field is 466 yards. The length of the field is 3 yards less than triple the width. What are the dimensions of the playing field?
w = 57.5 yards
l = 169.5 yards
Step-by-step explanation:P = 2w + 2l
466 = 2w + 2l
l = 3w - 3
466 = 2w + 2(3w - 3)
466 = 2w + 6w - 6
466 - 6 = 8w
8w = 460
w = 460 : 8
w = 57.5 yards
l = 3w - 3
= 3×57.5 - 3
= 169.5
l = 169.5 yards
Bob's Bike Shack charges a set fee of $6, plus $4 per hour, to rent a bike. If your total bill is $30, how many hours did you rent the bike for?
20
Step-by-step explanation:
30-6=24-4=20 that how you find your a answer
Convert this number expressed in standard form to scientific notation. 28,500,000 1. Move the decimal to create the coefficient: 2.8500000 2. Write in scientific notation: 2.85 × 10x What is the value of x in the scientific notation? x =
Answer:
7
Step-by-step explanation:
We know the decimal place is after all those zeroes. Move the decimal x places to the left, until it is located between the 2 and 8. Since it moved 7 spaces, that is how you know the power of the ten. A faster way of doing this is the power is always one less than the number of digits of the number.
Answer: 7
Step-by-step explanation:
Q is between P and R. PR=145,PQ=8x & QR=11x-7. What is the value of QR?
Answer:
QR = 81
Step-by-step explanation:
PR = 145
= PQ + QR
= (8x) + (11x - 7)
8x + 11x - 7 = 145
19x = 145 + 7
19x = 152
x = 8
substitute x=8 into QR:
11(8) - 7 = 81
Question is down below
Answer:
B
Step-by-step explanation:
p(x) = x² - 2√2x + 1
p(2√2) = (2√2)² - 2√2*2√2 + 1
=2²*(√2)² - 2*2*√2*√2 + 1
= 4 *2 - 4*2 + 1
= 8 - 8 + 1
= 1
Answer:
B
Step-by-step explanation:
Given
p(x) = x² - 2[tex]\sqrt{2}[/tex] x + 1, then
p(2[tex]\sqrt{2}[/tex] )= (2[tex]\sqrt{2}[/tex] )² - 2[tex]\sqrt{2}[/tex](2[tex]\sqrt{2}[/tex] ) + 1 = 8 - 8 + 1 = 1 → B
Ms. Davis' is one less than 7 dozen. Ms. Davis is 7.2 more than 60% of her mother's age. Ms. Davis daughter is 3.5 more than 1/2 her mother's age. How old are ms. Davis, her mom, and her daughter?
Answer:
Ms. Davis=83 years
Her mom=126.33 years
Her daughter=66.67 years
Step-by-step explanation:
Let her mother's age=x
Ms. Davis= 7 dozens - 1
=(7*12)-1
=84-1
= 83 years
Ms. Davis= 7.2 + 60% of x
83=7.2 + .6x
83 - 7.2= .6x
75.8= .6x
Divide both sides by .6
75.8 / .6 = x
126.33 years
Ms. Davis daughter = 3.5 + 1/2 of x
=3.5 + 1/2(126.33)
=3.5 + 126.33 / 2
=3.5 + 63.165
=66.665
Approximately 66. 67 years
A golfer recorded the following scores for each of four rounds of golf: 86, 81, 87, 82. The mean of the scores is 84. What is the sum of the squared deviations of the scores from the mean?
Answer:
26
Step-by-step explanation:
Subtract the mean (84) from each of the four scores, obtaining
2, -3, 3, - 2
These are the "deviations."
Next, square each of these four deviations, obtaining
(2)^2 = 4, and:
(-3)^2 = 9, and:
(3)^2 = 9, and:
(-2)^2 = 4
Then the sum of the squared deviations of the scores from the mean is 26.
-42=4v-18 Solve each equation
Answer:
v=6
Step-by-step explanation:
-42=4v-18
Add 18 to each side
-42+18=4v-18+18
-24 = 4v
divide each side by 4
-24/4 = 4v/4
-6 = v
Answer:
v = -6
Step-by-step explanation:
Isolate the variable, v. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, add 18 to both sides:
-42 (+18) = 4v - 18 (+18)
-42 + 18 = 4v
4v = 18 - 42
4v = -24
Next, divide 4 from both sides:
(4v)/4 = (-24)/4
v = -24/4
v = -6
v = -6 is your answer.
~
When the digits of two-digit, positive integer M are reversed, the result is the two-digit, positive integer N. If M > N, what is the value of M
Answer:
The value of M is 91.
Step-by-step explanation:
Suppose T represents the tens digit and U represents the units digit.
Then the numbers M and N are:
M = 10T + U
N = 10U + T
Compute the value of M - N as follows:
M - N = 10T + U - 10U - T = 9T - 9U = 9 (T - U)
Given:
M > N
⇒ T - U > 0
⇒ T > U
Also, M - N is a multiple of 9.
Since M - N is a two-digit number, the possible values of M - N are:
18, 27, 36, 45, 54, 63, and 72
The values 81, 90 and 99 would not be considered since:
9 × 9 = 81
9 × 10 = 90
9 × 11 = 99
T - U = 9 (T - U) = 9 , 10 or 11 respectively and the largest difference for T − U we can get is 9 - 0 = 9 - 0 = 9.
Even this would result in N = 9, which is not a 2-digit number.
It is provided that the integer (M - N) has 12 factors.
Of the possible values of M - N the integer with 12 factors is 72.
The factors of 72 are:
1×72
2×36
3×24
4×18
6×12
8×9
So, M - N = 72.
⇒ M - N = 9 (T - U)
72 = 9 × 8
⇒ T - U = 8
And since T > U, the values of T and U are:
T = 9 and U = 1
We cannot use T - U = 8 - 0 = 8, because then N will be not a two-digit number.
So, M = 91 and N = 19 and their difference is 72.
Thus, the value of M is 91.
PLEASE HELP!! IM HAVING A HARD TIME UNDERSTANDING THIS QUESTION.
Given the values of exponential function g below, what is g(3)?
g(0) = 60.4
g(1) = 30.2
g(2) = 15.1
O A.
3.775
OB. 7.55
OC.
8.0
D.
14.6
Answer:
14.6
Step-by-step explanation:
For his long distance phone service, Ali pays a 7 monthly fee plus 7 cents per minute. Last month, Ali's long distance bill was 19.53 . For how many minutes was Ali billed?
Answer:
179 minutes
Step-by-step explanation:
From the information given, you know that the total cost of the long distance service is equal to 7 plus the result of multiplying 0.7 for the number of minutes:
Total cost=7+0.07x, where x is the amount of minutes.
Now, you can replace the total cost with 19.53 that is the amount Ali was billed and solve for x:
19.53=7+0.07x
19.53-7=0.07x
12.53=0.07x
x=12.53/0.07
x=179
According to this, the answer is that Ali was billed for 179 minutes.
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (9,8) Midpoint (0,9)
Answer:
(-9, 10)
Step-by-step explanation:
The location of the midpoint of a line with endpoint at ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) is given as (x, y). The location of x and y are:
[tex]x = \frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}[/tex]
Given the endpoint (9,8) and Midpoint (0,9), the location of the other endpoint can be gotten from:
[tex]0=\frac{9+x_2}{2}\\ \\9+x_2=0\\\\x_2=-9\\\\Also,9=\frac{8+y_2}{2}\\ \\8+y_2=18\\\\y_2=18-8\\\\y_2=10[/tex]
Hence the endpoint is at (x2, y2) which is at (-9, 10)
what statement is true about the angles in triangle PQR
Answer:
(C) The sum of the measures of ∠P, ∠Q, and ∠R is 180°
Step-by-step explanation:
All triangles, when their three angles are added up, gets us 180°.
This goes without saying, even with scalene triangles.
Additionally, the angles in squares add up to 360°, the angles in a pentagon add up to 540°.
Hope this helped!