Answer:
[tex]\displaystyle \frac{dx}{dy} = \frac{3\sqrt{\frac{3}{y}}(y - 1)}{6y}[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{3}{x^2}[/tex]
Step 2: Differentiate
Rewrite Function: [tex]\displaystyle yx^2 = 3[/tex][Implicit Differentiation] Basic Power Rule [Product Rule]: [tex]\displaystyle y^{1 - 1}x^2 + y(2x^{2 - 1})\frac{dx}{dy} = 3[/tex]Simplify: [tex]\displaystyle x^2 + y(2x)\frac{dx}{dy} = 3[/tex]Isolate [tex]\displaystyle \frac{dx}{dy}[/tex] term: [tex]\displaystyle y(2x)\frac{dx}{dy} = 3 - x^2[/tex]Isolate [tex]\displaystyle \frac{dx}{dy}[/tex]: [tex]\displaystyle \frac{dx}{dy} = \frac{3 - x^2}{2xy}[/tex]Substitute in x²: [tex]\displaystyle \frac{dx}{dy} = \frac{3 - \frac{3}{y}}{2xy}[/tex]Simplify: [tex]\displaystyle \frac{dx}{dy} = \frac{3(y - 1)}{2xy^2}[/tex]Substitute in x: [tex]\displaystyle \frac{dx}{dy} = \frac{3(y - 1)}{2y^2(\sqrt{\frac{3}{y}})}[/tex]Simplify: [tex]\displaystyle \frac{dx}{dy} = \frac{3\sqrt{\frac{3}{y}}(y - 1)}{6y}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
£50 is divided between Alex, Peter & Angad so that Alex gets twice as much as Peter, and Peter gets three times as much as Angad. How much does Alex get?
Answer:
Alex gets £ 30Solution,
Let,
Angad get X
Peter get 3x
Alex get 6x
Now,
[tex]x + 3x + 6x = 50 \\ or \: 10x = 50 \\ or \: x = \frac{50}{10} \\ x = 5[/tex]
Replacing value,
[tex]6x \\ = 6 \times x \\ = 6 \times 5 \\ = 30[/tex]
hope this helps...
Good luck on your assignment..
Answer:
Angad gets £5
Peter gets £15
Alex gets £30
Step-by-step explanation:
Let Angad be x, Then Peter = 3x and Alex = 6x
Condition:
x+3x+6x = 50
=> 10x = 50
Dividing both sides by 10
=> x = 5
So,
Angad gets £5
Peter gets £15
Alex gets £30
Mr. Carson traveled from his house in Pennsylvania to a ski resort in upstate New York. He drove 4.25 hours at a rate of 54.6 miles per hours. When a friend asked how far he traveled to get to the resort, Mr. Carson said “about 2,320 miles.” Mr. Carson actually traveled a distance of . Was Mr. Carson’s estimate reasonable?
Answer:
ESTO ES INCORRECTO
Step-by-step explanation:
CON LA ECUACIÓN DE GALILEO GALILEI TENEMOS:
x = 54.6 mph( 4.25 h) = 232 milles
Answer:
Mr. Carson traveled from his house in Pennsylvania to a ski resort in upstate New York. He drove 4.25 hours at a rate of 54.6 miles per hours. When a friend asked how far he traveled to get to the resort, Mr. Carson said “about 2,320 miles.”
Mr. Carson actually traveled a distance of
✔ 232.05 miles
.
Was Mr. Carson’s estimate reasonable?
✔ no
español:
Carson viajó desde su casa en Pensilvania a una estación de esquí en el norte del estado de Nueva York. Condujo 4,25 horas a una velocidad de 54,6 millas por hora. Cuando un amigo le preguntó qué tan lejos había viajado para llegar al resort, el Sr. Carson dijo "aproximadamente 2,320 millas".
Carson en realidad viajó una distancia de
✔ 232.05 millas
.
¿Fue razonable la estimación del Sr. Carson?
✔ no
what is 8 times 1 over 1000??
0.008 if you are looking for a decimal. If you need a fraction it would be simply 8/1000 since 8 times 1 would be 8.
Answer:
Step-by-step explanation:
8 x 1/1000
= 8/1000
Simplified to 1/125
As a decimal it’s 0.008
She wants to build a tower 35 in. tall using dominoes that are 1 and 2/5 in. tall. How many levels will her tower have?
Answer:
25 levels
Step-by-step explanation:
First, convert 1 2/5 to a decimal. Since 2/5=0.4, 1 2/5 is 1.4. Now, you can set up the following expression:
[tex]\dfrac{35\text{in}}{1.4\text{in}}=25[/tex] levels.
Hope this helps!
Sean moved his lawn in 2 ½ hours. Sofiia mowed her lawn for ¼ hours, then stopped. She did this 7 times. Who spent the most time mowing the lawn?
Answer:
Sean
Step-by-step explanation:
We need to find how long Sofia spent mowing and then compare with the time Sean spent.
Sean mowed his lawn in 2 ½ hours.
Sofiia mowed her lawn for ¼ hours, then stopped. She did this 7 times. This means:
1/4 * 7 = 7/4 hours = [tex]1\frac{1}{4}[/tex] hours
Therefore, Sean spent more time mowing his lawn.
I need help once again :(
Line A's equation is y = 6x - 5. Line B is parallel to Line A and and goes through the
point (3, 10). Write the equation for Line B in slope-intercept form.
Answer:
y = 6x - 8
Step-by-step explanation:
line a: y = 6x- 5
10 = 6(3) - b
10 = 18 - b
10 - 18 = -b
-8 = -b
8 = b
give you 15 pints if you help
Answer:
erm
Step-by-step explanation:
0.2
1/4
40%
0.5
3/4
Find the X intercepts of the parabola with vertex (1,405) and Y intercept (0,400)
Answer:
Step-by-step explanation:
The standard form of a parabola is
[tex]y=ax^2+bx+c[/tex]
If we know the y intercept is (0, 400), that means that when x = 0, y = 400. That allows us to begin by finding c:
[tex]400=a(0)^2+b(0)+c[/tex] and c = 400.
Now to find a and b. Using the fact that the vertex is (1, 405), we know that h is 1 and k is 405. If
[tex]h=\frac{-b}{2a}[/tex] and h = 1, then
[tex]1=\frac{-b}{2a}[/tex] and
2a = -b so
b = -2a. Save that for a minute or two.
If
[tex]k=c-\frac{b^2}{4a}[/tex] and k = 405, then
[tex]405=400-\frac{(-2a)^2}{4a}[/tex] and
[tex]405=400-\frac{4a^2}{4a}[/tex] and
405 = 400 - 4a and
5 = -4a so
[tex]a=-\frac{5}{4}[/tex]
We will use that a value now to find the value of b. If b = -2a, then
[tex]b=-2(-\frac{5}{4})[/tex] and
[tex]b=\frac{10}{4}[/tex]
Writing our parabolic equation now:
[tex]y=-\frac{5}{4}x^2+\frac{10}{4}x+400[/tex]
Finding the x-intercepts is just another way of saying "factor this quadratic" so we will begin that by setting the quadratic equal to 0:
[tex]0=-\frac{5}{4}x^2+\frac{10}{4}x+400[/tex] and who hates all those fractions more than I do? Probably nobody, so we are going to get rid of them by multiplying everything by 4 to get
[tex]-5x^2+10x+1600=0[/tex] Assuming you can throw that into the quadratic formula to solve for the 2 values of x where y = 0, you'll find that the x-intercepts are
x = -16.91647287 and 18.91647287
Answer: ( -8,0),(10,0)
Step-by-step explanation:
A bag holds 20 jelly beans: 5 red, 10 green, 4 blue, and 1 black. What is the probability of choosing two consecutive blue jelly beans without replacement
Answer:
10/20 for green, then 4/19 for blue. 10/20 * 4/19 = 2/19
Step-by-step explanation:
Explanation is above. If you need any more help let me know.
The area of a square field is 14400 sq. metre. Find the length of the side
of the square.
Answer:
i think its Let a be the side length, then area=a^2=14400 sq m. Therefore a=√14400=120m.
Step-by-step explanation:
Answer:
[tex]120[/tex] [tex]meters[/tex]
Step-by-step explanation:
Use the formula for the area of a square.
[tex]A=s^2[/tex]
[tex]14400=s^2[/tex]
[tex]\sqrt{14400} =s[/tex]
[tex]120=s[/tex]
Can Someone Help Me Plz?? :D Which sentence is represented by 67z + 8.9 Less-than-or-equal-to–302? A) Sixty-seven times a number is less than negative three hundred two. B) Sixty-seven times a number, plus eight and nine tenths, is not greater than negative three hundred two. C) Sixty-seven times a number, plus eight and nine tenths, is not less than three hundred two. D) Sixty-seven times a number, plus eight and nine tenths, is at least negative three hundred two.
Answer:
BStep-by-step explanation:
the sum of sixty-seven times a number and plus eight and nine tenth is less than or equal to three hundred and two
A) Sixty-seven times a number is less than negative three hundred two.
B) Sixty-seven times a number, plus eight and nine tenths, is not greater than negative three hundred two.
C) Sixty-seven times a number, plus eight and nine tenths, is not less than three hundred two.
D) Sixty-seven times a number, plus eight and nine tenths, is at least negative three hundred two.
the answer closest to this is B (not greater than is the same as less than or equal to)
Answer:
B) Sixty-seven times a number, plus eight and nine tenths, is not greater than negative three hundred two.
Step-by-step explanation:
Let's break down this equation:
67z + 8.9 ≤ - 302
z is "a number" that is being multiplied by 67.
8.9 can be represented as 8 9/10, because 0.9 and a fraction is 9/10.
The less than or equal to sign means that the number represented by the expression 67z + 8.9 cannot be greater than -302. In other words, it is less than or equal to it.
You can see that option B is the only one that correctly compares 67z + 8.9 and -302. Therefore, that is the correct option.
___, 86, 82, 84, 80, 82, 78
fill in the blank
Answer:
88
Step-by-step explanation:
the sequence goes on subtracting 4, 2, 4, 2, 4
hence, with the last number being subtracted by 4, you must then add on 2
86 + 2 = 88
plz help with slope question
Answer:
The equation in slope-intercept form:
[tex]y = -3x - 4[/tex]
Step-by-step explanation:
Use the point-slope formula:
[tex]y-y_{1} = m (x-x_{1})[/tex]
Use the given slope [tex]-3[/tex] and point [tex](0,-4)[/tex] for the formula:
[tex]y + 4= -3 (x-0)[/tex]
-Then, you solve the formula:
[tex]y + 4 = -3 (x-0)[/tex]
[tex]y+4 - 4 = -3 (x-0) -4[/tex]
[tex]y = -3x - 4[/tex]
The equation, which is in slope-intercept form:
[tex]y = -3x - 4[/tex]
Answer:
D. y = -3x - 4
Step-by-step explanation:
→You can figure this out by using the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y+4=-3(x-0)[/tex]
→Distribute the -3 to (x - 0):
y + 4 = -3x
→Subtract 4 from both sides:
y = -3x - 4
Which description of a histogram are true
Answer:
A peak is where the frequency is the highest, A peak is a bar that is higher than the other bars around it, Intervals on a histogram where there are no bars mean the frequency is 0, If the graph is symmetrical, the data is evenly distributed.
Step-by-step explanation:
I will give you 10B points plus mark someone again for the Brainliest if you get this right. a:15 b:7 c:4
For this expression,a=15,b=7 and c=4
Hope it helpsGood luck on your assignment
Does anyone know what this is?
Answer:
[tex] {(4x)}^{ \frac{3}{2}} [/tex]
Step-by-step explanation:
[tex] \huge \sqrt{( {4x)}^{3} } \\ \\ \huge = \: {(4x)}^{3 \times \frac{1}{2} } \\ \\ {\huge {\red{ \boxed{ = {(4x)}^{ \frac{3}{2} }}}}}..required \: answer \\ \\ \huge = ( {4})^{ \frac{3}{2} } {x}^{ \frac{3}{2} } \\ \\ \huge = ( { {2}^{2} })^{ \frac{3}{2} } {x}^{ \frac{3}{2} } \\ \\ \huge = ( { {2} })^{ 3 } {x}^{ \frac{3}{2} } \\ \\ \huge \: = 8 {x}^{ \frac{3}{2} } [/tex]
Choose what the expressions below best represent within the context of the word problem.The length of a rectangle is 12 inches more than its width. What is the width of the rectangle that if the perimeter is 42 inches?
Answer:
L=16.5 inches
Step-by-step explanation:
L=W+12
P= 2L+2W
P=2(W+12)+2W
42=4W+24
4W=42-24
W=18/4=4.5
L=12+4.5=16.5 inches
The winner of a 100 mile race drove his car to victory at a rate of 145.0441mph
Answer:
Is your question, how long did it take for him to do it? If so the answer is: .69 hours
Step-by-step explanation:
100 divided by 145.0441= .6894454859
Avg. Time is .69 hours
Whats 2x+2y=2x answer fassttt!!!!!
Answer:
x=−2/0
Step-by-step explanation:
Steps:
Let's solve for x.
2x+2y=2x
Step 1: Add -2x to both sides.
2x+2y+−2x=2x+−2x
2y=0
Step 2: Add -2y to both sides.
2y+−2y=0+−2y
0=−2y
Step 3: Divide both sides by 0.
00=−2y0x=−20
Answer: x=−2/0
Plz mark brainlies
Hope this helps
Which line is parallel to the line 8x + 2y = 12?
Answer:
Step-by-step explanation:
Our line's equation is;
2y = -8x + 12
Dividing throughout by 2 we get;
y = -4x + 6
The slope of our line = -4
We are to choose a line whose slope is -4 (from those four options)
A slope of -4 means that for every positive 1 move along the x-axis, there is a negative 4 move along the y-axis.
The line that satisfies this condition is the third line.
Answer:
In other words Its C
Step-by-step explanation:
The guy above and Edge 2020
The Tigers won 12 games last year. This year the Tigers won 20 games. What is the percent increase in the number of games the Tigers won from last year to this year?
Answer:
60%.
Step-by-step explanation:
please mark me as brainliestThe the percent increase in the number of games the Tigers won from last year to this year is; 60%
How to solve percentages?We are told that the tigers won 12 games last year.
Now this year the tigers won 20 games.
Thus, if the total number of games to be won is n, then;
Last year = 12/n
This year = 20/n
Thus,
Percentage increase = [(12/n)/(20/n)] * 100%
Percentage increase = 12/20 * 100%
Percentage increase = 60%
Read more about Percentages at; https://brainly.com/question/843074
Which ordered pair (x,y) satisfies the system of equations shown above?
Answer:
So the answer is C hope it helps
find the sum of the even numbers from 26 to 126
Answer:
3876
Step-by-step explanation:
Here first even number is 26
and last even number is 126
we add both of these and divide the sum by 2
26 + 126 = 152
152/2 = 76
now there are total 51 even number from 26 to 126.
so sum of even numbers from 26 to 126 is
sum = 76 × 51 = 3876
Answer:
3,876
Step-by-step explanation:
Sequence of even numbers from 26 to 126 is given as:
26, 28, 30, 32, 35..............,126
Here, a = 26, d = 2, [tex] a_n = 126[/tex]
[tex] \because a_n = a + (n-1)d\\
\therefore 126 = 26 + (n-1) \times 2\\
\therefore 126 - 26 = 2(n-1) \\
\therefore 100= 2(n-1)\\
n - 1 = \frac{100}{2} \\
n - 1 = 50\\
n = 50 +1\\
\red{\bold{n = 51}}[/tex]
[tex]
\because S_n = \frac{n}{2}(a + a_n) \\\\
\therefore S_{51}= \frac{51}{2}(26 + 126) \\\\
\therefore S_{51}= \frac{51}{2}\times 152 \\\\
\therefore S_{51}= 51\times 76 \\\\
\huge \purple {\boxed {\therefore S_{51}=3,876}}
[/tex]
Simplify (x+3)^2 - 6x
Answer:
[tex] {x}^{2} + 9[/tex]
Step-by-step explanation:
[tex] {(x + 3)}^{2} - 6x \\ \\ = {x}^{2} + {3}^{2} + 2 \times x \times 3 - 6x \\ \\ = {x}^{2} + 9 + 6x - 6x \\ \\ = {x}^{2} + 9[/tex]
Answer:
The answer is x² + 9.
Step-by-step explanation:
First, you have to get rid of bracket of square :
[tex] {(a + b)}^{2} \: ⇒ \: {a}^{2} + 2ab + {b}^{2} [/tex]
[tex] {(x + 3)}^{2} [/tex]
[tex] = (x + 3)(x + 3)[/tex]
[tex] = {x}^{2} + 6x + 9[/tex]
Next, you can simplify :
[tex] {x}^{2} + 6x + 9 - 6x[/tex]
[tex] = {x}^{2} + 9[/tex]
Plzz help! Can you also explain. ps. It’s not 4
Answer:
SR =3
Step-by-step explanation:
SR + RQ = SQ
2x+23 + x+21 = 14
Combine like terms
3x+44 = 14
Subtract 44 from each side
3x+44-44= 14-44
3x = -30
Divide each side by 3
3x/3 = -30/3
x = -10
SR = 2x+23 = 2(-10)+23 = -20+3 =3
Answer: 3
Step-by-step explanation:
We can start by making an equation.
Since we know the total length of SQ we can add SR + RQ to equal SQ.
[tex](2x+23)+(x+21)=14[/tex]
The parenthesizes are not necessary but they help for understanding the parts of the equation.
We will remove the parenthesizes and combine like terms.
[tex]3x+44=14\\[/tex]
Now subtract 44 from both sides to cancel it out from the side with x.
[tex]3x=-30[/tex]
Now divide by 3 to isolate x.
[tex]x=-10[/tex]
So x = -10.
Now we can plug in the value of x into SR.
[tex]2(-10)+23 = SR[/tex]
Solve
So SR = 3
6.
In the figure, the perimeter of sector AOB with centre O is 70 cm.
Find the value of r.
(Give your answer correct to 3 significant figures.)
Answer:
Hope this is correct
if Y is directly proportional to x and y = 10 when x = 2, find
I) an equation connecting x and y
ii) the value of y when x = 10
III) the value of x when y = 60
p.s please give me a answer quickly
Answer:
I) Y=5x
II) Y=50
III)X=12
Step-by-step explanation :
I) Y=5x
II) Y=5(10)
Y=50 when x=10
III)Y=5x
60=5x
X=60/5
X=12 when y=60
Hope this helps..
Anyone know this ????
Answer:
The answer is C.
Step-by-step explanation:
As you type into the calculator, you will get 0.707 :
cos(45) = √2/2
cos(45) ≈ 0.707 (3s.f)
The base of a triangle is twice that of its height. If the area is 36 square centimeters, then find the length of its base and height.
Answer:
height = 6 cm
base = 12 cm
Step-by-step explanation:
Let the base of the triangle is denoted by b
Let the height of the triangle is denoted by h
We are given that base of a triangle is twice that of its height,
b = 2h
Recall that area of a triangle is given by,
A = ½×b×h
We are given that area of the triangle is 36 cm²
36 = ½×b×h
Substitute b = 2h in the above equation
36 = ½×2h×h
36 = h×h
h² = 36
h = √36
h = 6 cm
Therefore, the height of the triangle is 6 cm
b = 2h
b = 2(6)
b = 12 cm
Therefore, the base of the triangle is 12 cm
Verification:
A = ½×b×h
A = ½×12×6
A = ½×72
A = 36 cm²
Hence proved