Answer:
[tex]\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}[/tex]
Step-by-step explanation:
We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².
Power Rule: [tex]\displaystyle \frac{d}{dx}[ x^n] = nx^n^-^1[/tex]Rewrite [tex]\displaystyle \frac{3}{x^2}[/tex] as [tex]\displaystyle 3\cdot \frac{1}{x^2}[/tex] which is equivalent to [tex]3\cdot x^-^2[/tex].
Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.
3(-2)x⁻³ = -6x⁻³This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex].
Quotient Rule: [tex]\displaystyle \frac{d}{dx} \Big [ \frac{f(x)}{g(x)} \Big ]=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}[/tex]Substituting 3 for f(x) and x² for g(x), we get:
[tex]\displaystyle \frac{(x^2)(0)-(3)(2x)}{(x^2)^2}[/tex]Simplify.
[tex]\displaystyle \frac{-6x}{x^4}[/tex]Using exponent rules, we can rewrite this as:
[tex]-6x^1^-^4 = -6x^-^3[/tex]This can be rewritten as [tex]\displaystyle -\frac{6}{x^3}[/tex], which is the same as what we got using the product rule.
Answer:
[tex]\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}[/tex].
Step-by-step explanation:
Let [tex]f(x)[/tex] and [tex]g(x)[/tex] denote two functions of [tex]x[/tex]. Assume that [tex]g(x) \ne 0[/tex]. The quotient rule states that:
[tex]\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}[/tex].
In this question:
The numerator of the fraction is [tex]f(x) = 3[/tex] (a constant function.)The denominator of the fraction is [tex]g(x) = x^{2}[/tex].Find [tex]{f}^{\prime}(x)[/tex] and [tex]{g}^{\prime}(x)[/tex].
Notice that the value of [tex]f(x)[/tex] is constantly [tex]3[/tex] regardless of the value of [tex]x[/tex]. By the constant rule, [tex]{f}^{\prime}(x) = 0[/tex].
For [tex]{g}^{\prime}(x)[/tex], consider the power rule:
if [tex]m[/tex] represents a rational number (such as [tex]2[/tex],) then by the power rule, [tex]\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}[/tex].
Apply this rule to find [tex]{g}^{\prime}(x)[/tex].
[tex]\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}[/tex].
Substitute [tex]f(x) = 3[/tex], [tex]{f}^{\prime}(x) = 0[/tex], [tex]g(x) = x^{2}[/tex], and [tex]{g}^{\prime}(x) = 2\, x[/tex] into the quotient rule expression to find [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right][/tex]:
[tex]\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}[/tex].
Therefore, [tex]\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}[/tex].
Uhhh help please
I need helppppp
Answer:
1?
Step-by-step explanation:
11/12 closest to
Solve.
-5 3/4 - 3 1/2
Answer:
The answer is
[tex] - 9 \frac{1}{4} [/tex]
Whatcha number produces a rational number when added to 0.5
Answer:
B
Step-by-step explanation:
1/4+0.5=3/5 3/5=0.75 it is a rational number
the other ones are not rational because they are endless numbers
i need help please right answers only
Answer:
-3/2
Step-by-step explanation:
Count up three times and to the left twice. Let me know if you need help with other questions!
The circumference of a circle is 9.37cm.
Find the length of the diameter.
Give your answer rounded to 2 DP
Answer:
9.37 divide by two = 4.685
4.685 in 2DP = 4.68
Step-by-step explanation:
i hoped this helps.
Answer:
2.98 :)
Step-by-step explanation:
the circumference is when you do pi times diameter.
do 9.37 divided by 3.14(pi) to work out the diameter.
9.37/3.14=2.984
rounded its 2.98
What is the slope of the equation y = 5x - 7?
o
-7
o
7.
Answer:
slope = 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 5x - 7 ← is in slope- intercept form
with slope m = 5
Answer:
The slope is 5.
Step-by-step explanation:
y=mx+b is the equation used to plot a line, where m is the slope and b is the y intercept.
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 meters ×80 meters. How much shorter is the root across the park than the route around its edges?
Pls help!!! It's due today in about 6 hours!!!!! I would also like a proper explanation instead of the answer itself!!!!
Answer:
The route across the park is 40 meter shorter than the route around its edges.
Step-by-step explanation:
We have to calculate the distance for both routes
As the route around the edges is straight, we have to find the sum of length of both edges
Let [tex]R_E[/tex] be the distance of route around edges
[tex]R_E = 80+60 = 140\ meters[/tex]
Now we know that a diagonal divides a rectangle in two right angled triangles in which the diagonal is the hypotenuse.
We can use Pythagoras theorem to find the length of the diagonal
So,
[tex]H^2 = P^2 + B^2[/tex]
In the given scenario
P = 60
B = 80
Now
[tex]H^2 = (60)^2 + (80)^2\\H^2 = 3600+6400\\H^2 = 10000\\\sqrt{H^2} = \sqrt{10000}\\H = 100\ meters[/tex]
In order to calculate that how much shorter is the path across the park, we have to subtract the distance across park from the distance across edges.
[tex]= 140-100 = 40\ meters[/tex]
Hence,
The route across the park is 40 meter shorter than the route around its edges.
What is an equation that represents a non proportional relationship???
I really need help(I know nothing about proportional and non proportional equations)
Can someone explain to me how I can find the domain and range of a rational graph?
example:
Answer:
no but try socratic
Step-by-step explanation:
it will help very much;)
GIVING BRAINLY AND THANKS find the value of x show your work
answers for both boxes please
Answer:
(-3, -6)
Step-by-step explanation:
y=2x
-3x-15=y
Use Substitution Method
-3x-15=2x
+3x +3x
-15=5x
/5 /5
-3=x
y=2x
y=2(-3)
y=-6
Answer:
(-3, -6)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Solving systems using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x
-3x - 15 = y
Step 2: Solve for x
Substitute in y: 2x = -3x - 15Isolate x terms: 5x = -15Isolate x: x = -3Step 3: Solve for y
Define equation: y = 2xSubstitute in x: y = 2(-3)Multiply: y = -6what is the answer to..
Negative 10 is no less than 2 times a number plus 14
Which table does not represent a
function?
Answer: G, I think? It’s been awhile
Step-by-step explanation: There is 14 in every box, if i remember correct that means it’s not a function.
The cost of a daily rental car is as follows: The initial fee is $69.99 for the car, and it costs $0.30 per mile. If John initially pays $200.00 before taxes and does not want to exceed that amount, how many miles can he drive?
x ≥ 433 miles
x = 450 miles
x ≥ 450 miles
x ≤ 433 miles
x [tex]\geq[/tex] 433
explanation:
let m equal miles
0.30m + 69.99 = 200
-69.99 -69.99
0.30m = 130. 01
130.01 / 0.30 = 433. 36...
but we're gonna round it to 433
so 433 miles
Help pls I will mark as brainlest if correct
Answer:
The slope is [tex] \frac{3}{8} [/tex].
Step-by-step explanation:
Remember: [tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
☆Just plug in.
[tex]m = \frac{ - 7 - ( - 10)}{0 - ( - 8)} = \frac{3}{8} [/tex]
PLEASE HELP GIVING BRAINLIEST!!! INTERNET Kilroy's Web site business has increased every year for the last 3 years. Write the percent its increase during the second year as a decimal and as a fraction in lowest terms.
Answer:
1.15
Step-by-step explanation:
when you have a % above 100 you divide that by 100 so it's 115 divided by 100 which is 1.15
find the estimates of x^2-x-2=3
Answer:
[tex]x=\frac{1+\sqrt{21}}{2}\approx 2.79\\or\ x=\frac{1-\sqrt{21}}{2}\approx -1.79[/tex]
Step-by-step explanation:
Given
Quadratic equation is
[tex]x^2-x-2=3\\x^2-x-5=0[/tex]
Roots of the quadratic equation [tex]ax^2+bx+c=0[/tex] are
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]
So, for the given equation roots are
[tex]x=\frac{1\pm\sqrt{(-1)^2-4(1)(-5)}}{2\cdot 1}\\x=\frac{1\pm\sqrt{21}}{2}\\so, x=\frac{1+\sqrt{21}}{2}\approx 2.79\\or\ x=\frac{1-\sqrt{21}}{2}\approx -1.79[/tex]
help pls lol
choose the 3 equations that could be used to solve the following problem. an apartment charges $1200 each month for rent plus a one time rental fee of $500. if a person has paid 10,700, how many months has the person rented the apartment
Answer:
Options :
A.
C.
D.
Step-by-step explanation:
1200m + 500 = 10700
find the measure of the missing angles
Answer:
b=80
c=80
Step-by-step explanation:
the angle opposite to the 100 degree angle is congruent to it
same goes for b and c
so far we have 2 angles that measure 100 degrees 100+100=200
the sum of the 4 angles is 360
360-200=160
160/2=80=b=c
45 marbles in 9 bags; 150 marbles in 36 bags
is this rate proportional?
Answer:
No, the rate is not proportional.
Step-by-step explanation:
If there are 45 marbles in 9 bags, we can assume that there are 5 marbles in each bag.
Going by that rate, we can do 5 * 36 = 180, NOT 150.
Thus, the rate is not proportional.
Another way to solve would be to do 45/9 and 150/36. If the rate is proportional, the answer for both should be the same.
However, 45/9=5 and 150/36=4.16666666667.
Those two answers are NOT equal.
Thus, the rate is not proportional.
find the measure of
someone help me please
Answer:
Angle B = 131 degrees
Step-by-step explanation:
We know that since there's an angle labeled 139 degrees and a straight line is 180 degrees in total, the other angle is equal to 180 - 139 = 41 degrees.
Since all triangles have 3 angles that add up to 180 degrees and we know that theres a right angle, a 41 degree angle, then angle A must equal to 180 - 41 - 90 = 49 degrees.
We know that vertical angles are congruent, therefore angle C is also equal to 49 degrees.
Angle B and angle A form a straight line, which we have defined as 180 degrees.
180 - 49 = 131 degrees.
Angle B = 131 degrees
What's the circumference of a
circle with a diameter of 15 inches?
(Use 3.14 for pi)
Answer:
47.1 inches
Step-by-step explanation:
circumference is pi times diameter
3.14 times 15 is 47.1
Answer:
Step-by-step explanation:
47.1
In the diagram the length of segment VS is 39 units what is the length of segment TV
Answer:
33
Step-by-step explanation:
Answer: B. 38
Step-by-step explanation:
Got it right, Edge 2022.
f(x)=5(X-2)^2+4
Find vertex, Direction of parabola, and axis of symmetry
I need help now btw i am in middle school
Answer: x= 3
Step-by-step explanation:
2x + 5 = 11
2x = 6
x = 3
which one is greater , 65% or 3/5
Answer:
Step-by-step explanation:
65% is greater
What are the values of x and y, based on the figure on the right?
Answer:
the values of x and y, based on the figure on the right is of b
x=76°,y=48°
Solve 3x - 4 ≤ 2 or 2x + 11 ≥ -1.
please help
Answer:
x≤2 or x≥-6
Step-by-step explanation:
Isolate the variables on both equations
3x-4≤2
3x≤6
x≤2
2x+11≥-1
2x≥-12
x≥-6
A ton might weigh 2000 pounds. How many six grades might weigh 2000 pounds?
Answer:
25
Step-by-step explanation:
An average 6th grader weight 80 pounds and 2000/80 is 25
25 six graders might weigh 2000 pounds, considering the average weight of a six grader is 80 pounds.
Average is the mean value of the data. It is a measure of central tendency.
Given the following information:
A ton might weigh 2000 pounds.
We need to find the total number of six graders require to collectively weigh 2000 pounds.
Let the total number of six graders require = x
Consider the average weight of a six grader is 80 pounds.
Total weight= average weight of a six grader x total number of six graders x
Total weight= 80x
2000=80x
To calculate the value of x, divide 80 both the sides.
2000/80=80x/80
25=x
x=25
Thus, 25 six graders might weigh 2000 pounds.
Learn more about average, here:
https://brainly.com/question/32511583
#SPJ6
Calvin evaluated Negative two-thirds times 5 and one-sixth using the steps below.
Step 1: Negative two-thirds time (5 + one-sixth)
Step 2: (Negative two-thirds + 5) times (Negative two-thirds + one-sixth)
Step 3: 4 and one-third times negative one-half
Step 4: Negative 2 and one-sixth
Which describes Calvin’s error?
In step 1, he incorrectly broke up 5 and one-sixth.
In step 2, he distributed the Negative two-thirds instead of the 5.
In step 2, he confused the multiplication and addition signs.
In step 3, he computed the addition and multiplication incorrectly
Answer:
Step-by-step explanation:
-2/3 * 5 1/6 .....step 1.....correct
(-2/3 * 5) + (-2/3 * 1/6).....his error is here...it should be like I have written it, but Calvin is getting his addition and multiplication mixed up
-10/3 + (-1/9) =
-30/9 - 1/9 =
-31/9 =
- 3 4/9
Answer:
Step 1
Step-by-step explanation:
Edge 2020