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].
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 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
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
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.
what is the answer to..
Negative 10 is no less than 2 times a number plus 14
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°
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
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
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
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
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
GIVING BRAINLY AND THANKS find the value of x show your work
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.
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.
I need help now btw i am in middle school
Answer: x= 3
Step-by-step explanation:
2x + 5 = 11
2x = 6
x = 3
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
f(x)=5(X-2)^2+4
Find vertex, Direction of parabola, and axis of symmetry
Solve.
-5 3/4 - 3 1/2
Answer:
The answer is
[tex] - 9 \frac{1}{4} [/tex]
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.
Uhhh help please
I need helppppp
Answer:
1?
Step-by-step explanation:
11/12 closest to
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 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]
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;)
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
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 = -6Solve 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
which one is greater , 65% or 3/5
Answer:
Step-by-step explanation:
65% is greater
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]
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.