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 will give brainliest to who answers this. Please answer quick
Answer:
Im pretty sure it would just be g= -p+15
Step-by-step explanation:
I really hope this helps, if not I am so sorry
Answer:
G= 1/6p -15
Step-by-step explanation:
Let's solve for g.
p=6g+90
Step 1: Flip the equation.
6g+90=p
Step 2: Add -90 to both sides.
6g+90+−90=p+−90
6g=p-90
Step 3: Divide both sides by 6.
6g/6 = p−90/6g
=1/6p−15
triangle ABC has perimeter 22cm
AB= 8cm
BC= 5cm
by calculation deduce whether triangle ABC is right-angled triangle
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Answer:
not a right triangle
Step-by-step explanation:
The perimeter is 22, so we have ...
AB +BC +CA = 22
8 + 5 + CA = 22
CA = 22 -13 = 9
If this is a right triangle, the sum of the squares of the short sides will be equal to the square of the long side.
AB² +BC² = 8² +5² = 64 +25 = 89
This is not the same as ...
CA² = 9² = 81
The triangle is not a right triangle.
_____
Additional comment
If you're familiar with a few Pythagorean triples, you know that a couple involving a side length 5 are (3, 4, 5) and (5, 12, 13). That is, (5, 8, 9) is NOT a Pythagorean triple, so you know immediately that those side lengths do not form a right triangle. (No calculation is necessary.)
How do you write equations for horizontal and vertical lines?
Answer:
y=_
x=_
Step-by-step explanation
horizontal for y=_
vertical for x=_
what is 9 : 45 = 6 : ?
Answer:6:45
Step-by-step explanation:
Answer:
x = 30
Step-by-step explanation:
a ratio is just a fraction
9:45 = 9/45
6:x = 6/x
now you have 9/45 = 6/x
cross multiply:
9 * x = 45 * 6
9x = 270
divide both sides by 9
9x/9 = 270/9
x = 30
Find the measure of each missing angle.
Answer:
m< 3 = 180 - 93
m< 3 = 87 degrees
m< 4 = 180 - 87 - 49
m< 4 = 44 degrees
m< 2 is vertically opposite to the 49 degree angle given
m< 2 = 49 degrees
m< 1 = 180- 68 - 49
m< 1 = 63 degrees
The measure of each missing angle are; m< 1 = 63, m< 2 = 49, m< 3 = 87 and m< 4 = 44 degrees
What are vertically opposite angles?The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.
We can determine angle 3 as;
m< 3 = 180 - 93
m< 3 = 87 degrees
Also,
m< 4 = 180 - 87 - 49
m< 4 = 44 degrees
We can see that m< 2 is equal to 49-degree angle by a vertically opposite angle.
m< 2 = 49 degrees
m< 1 = 180- 68 - 49
m< 1 = 63 degrees
Hence, the measure of each missing angle are; m< 1 = 63, m< 2 = 49, m< 3 = 87 and m< 4 = 44 degrees
Learn more about vertically opposite angles;
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If you tell me all the right answers I will mark you brainliest!!
Answer:
11 is natural, real, integer and whole number.
1% is irrational and real, integer.
√25 = 5 hence it's natural, real, integer and whole
√50 is rational and real, integer.
1.333… is natural, real and integer
2.3×10^5 is natural, real, integer and whole number.
Expand.
Your answer should be a polynomial in standard form.
(9+ m)(-m +9)=
Answer: -1m²+81
Step-by-step explanation:
correct standard form means that the terms are ordered from biggest exponent to lowest exponent.The leading coefficient is the coefficient
of the first term in a polynomial in standard form.
FoR example, (9+ m) (-m+9) = *(m+9) (-m+9) *m(-m+9) +9 (-m+9)* -1.mm+9m +9(-m+9) * -1m² +9m +9(-m+9) *-1m²+9m- 9m +81
answer -1m²+81
HELP HELP HELP!!!!! Please help!
Answer:
Regular peanut butter - .23
Family Size Peanut Butter - .15
Answer:
#1: 0.23
#2: 0.15
Step-by-step explanation:
1.38/ 6= 0.23
6*0.23= 1.38
7.80/ 52= 0.15
0.15*52= 7.80
When a system of linear equations has a
solution.... what am I actually finding when I
solve for x and y?
Answer:
You are finding the intersection point of the system of linear equations.
Step-by-step explanation:
You can use methods like substitution, elimination, and/or equal values to find the solution for the system of linear equations.
9. The hypotenuse of a 45°-45°-90° triangle is 5 sqrt 6. Find the length of one leg of the right triangle.
Answer:
5 ✓ 3
Step-by-step explanation:
using Pythagoras Theory
(5 ✓ 6 )2 =, 2 x square side
square leg length= 150/ 2=, 75
length =5 ✓ 3
please help . me . i will even help . you mark you brainliest
A = Not sure
B= 12.0
Hope I helped
Find the x-intercept and y-intercept
from the following linear equation:
- 7x + 4y = 56
x-intercept ([?],[ ])
y-intercept ([?],[ ])
You are printing out information packets for your company. You will need a total of 6,400 pages to complete all of the packets. How many reams of 500 pages each will you need in order to print out all of these packets?
Answer:
13 reamsStep-by-step explanation
Given
Total number of pages to complete the packet = 6400 pages
If each ream contains 500pages, then:
Total number of reams needed = Total pages/number of pages per ream
Total number of reams needed = 6400/500
Total number of reams needed = 12.8
Hence you will need about 13 reams for all the packets
on a certain day the temperature at midday was 14°c.By midnight the temperature had fallen by 17°c what was the temperature at midnight
Answer:
-3c
Step-by-step explanation:
Answer:
-3c
Step-by-step explanation:
according to my calculations this is right
Can you please help
This is due today
I need the equation and answer
Equation/the way to do it :
Answer:
Select all the correct answers
Answer:
12^3,
Step-by-step explanation:
The Nguyen family is traveling cross-country, driving 300 miles each day. Let 2 represent the number of days in the trip and let y represent the total number
of miles driven.
Write an equation to model their trip.
Enter the correct equation in the box.
Step-by-step explanation:
y = Total number of miles driven
= Number of days * Number of miles per day
= (x) * (300).
Therefore the equation is y = 300x.
When x = 2, y = 300(2) = 600.
The Nguyen family drove 600 miles during the 2 days.
While completing a DLA test virtually, Deidra answered 8 out 30 questions incorrectly. If the ratio remains constant, how many questions should Deidra answer correctly out of 45 questions?
Answer:
I wnat to say its 19
Step-by-step explanation:
I want to know how to expand x(4 - 3.4y)
Answer:
X(4-3.4y)
= 4x - 3.4xy
Step-by-step explanation:
Which of the following uses the reciprocal property to rewrite x/5 = 72/4
Please help me :)
Answer:
??You texted incomplete question.
By the way, x = 90
Solve for x:
7x = 105
Answer:
X=15
Explanation: You have no like terms to combine and are at the last step of the algebraic equation. So, you would divide 7 on both sides. 7 by 7 cancels it out and 105 divided by 7 equals 15. Hope this helps ^-^.
The solution to the equation 7x = 105 is x = 15.
We have the equation: 7x= 105
To solve for x in the equation 7x = 105, we need to isolate x on one side of the equation.
Divide both sides of the equation by 7:
(7x)/7 = 105/7
Simplifying:
x = 15
Therefore, the solution to the equation 7x = 105 is x = 15.
Learn more about Equation here:
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- Find the value of x for which ABCD must be a parallelogram.
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Answer:
x= 5
Step-by-step explanation:
Sides BC and AD will be parallel when the two marked angles have the same measure:
5x -3 = 14x -48
45 = 9x . . . . . . . . . add 48-5x
5 = x . . . . . . divide by 9
16-2k=14. what is the value of k
Answer:
k = 1
Step-by-step explanation:
16 - 2k = 14
- 16 - 16
-2k = -2
-2 -2
k = 1
Can someone explain how to work this out please ?
Answer:
x=4
Step-by-step explanation:
f(x) = (x-2)^5 +3
Let f(x) = 35
35 = (x-2)^5 +3
Subtract 3 from each side
35-3 = (x-2)^5 +3-3
32 = (x-2)^5
Take the fifth root of each side
32 ^ (1/5) = (x-2)^5^ 1/5
2 = x-2
Add 2 to each side
2 +2 = x-2+2
4 =x
Find the Missing side length for #8
Answer:
A
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{LM}{QR}[/tex] = [tex]\frac{KL}{PQ}[/tex] , substitute values
[tex]\frac{x}{15}[/tex] = [tex]\frac{28}{21}[/tex] ( cross- multiply )
21x = 420 ( divide both sides by 21 )
x = 20 → A
What is the simplified expression in the box by combing like terms and removing zero pairs?
-4 ( 2x+ 4) + 5
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Answer:
-8x -11
Step-by-step explanation:
Use the distributive property to eliminate parentheses. Then combine the constant terms.
-4(2x +4) +5
= -8x -16 +5
= -8x -11
[tex]\sf \longmapsto-4 ( 2x+ 4) + 5[/tex]
[tex]\sf \longmapsto(−4)(2x)+(−4)(4)+5[/tex]
[tex]\sf \longmapsto−8x+−16+5[/tex]
[tex]\sf \longmapsto(−8x)+(−16+5)[/tex]
[tex]\sf \longmapsto−8x+−11[/tex]
[tex]\sf \longmapsto - 8x - 11[/tex]
Find the value of x in the isosceles triangle
Step-by-step explanation:
Since all 3 sides of the triangle is equal, it is not only an isosceles, but an equilateral triangle.
x = 8sin60° = 6.928 or sqrt48.
That is a question about triangles.
In my answer I will show 2 ways to solve that question, ok? Let's go.
First way - Pythagoras's theoremThe line segment x divide the biggest triangle in 2 equals right triangles.
Let's choose one of them and note that is a triangule with hypotenuse equals to 8 and one cathetus equals to half of 8.
The Pythagoras's theorem says that:
[tex]\boxed{a^2 = b^2 + c^2}[/tex]
a is the hypotenuse and b and c are cathetus.
So, in our case, we know the hypotenuse and one cathetus, let's substitute that in the expression:
[tex]a^2 = b^2 + c^2\\8^2 = 4^4 + c^2\\64 = 16 + c^2\\c^2 = 64 - 16\\c^2 = 64 -16\\c^2 = 48\\c = \sqrt{48}\\c= 4\sqrt{3}[/tex]
Therefore, the value of x is [tex]4\sqrt{3}[/tex].
Second way - The equilateral triangle heightThat way to solve the question is a consequence of the previous way.
That triangle has all the sides equals, so it is a equilateral triangle.The line segment x is the height of that triangle. And we can find the equilateral triangle height using that expression:
[tex]\boxed{h = \frac{S\cdot \sqrt{3} }{2} }[/tex]
h is the height and S is the triangle's side.
So, we know that the side of our triangle is 8. Let's change S value in the expression:
[tex]h = \frac{S\cdot \sqrt{3} }{2} \\h = \frac{8\cdot \sqrt{3} }{3} \\h = 4\sqrt{3}[/tex]
Thus, the value of x is [tex]4\sqrt{3}[/tex].
Note that in the 2 ways we find the same result, so that answer is correct.
I hope I've helped. :D
Enjoy your studies! \o/
What is the solution to this inequality?
-6x + 5 > -1
A: x > -1
B: X 1
D: X < -1
Step-by-step explanation:
-6x + 5 > -1
-6x > -6 (subtract 5 on both sides)
x < 1 (divide -6 on both sides, flip the sign)
Hence the answer is x < 1.
Answer:
b i hope
Step-by-step explanation:
Would the answer be 8?
Answer:
Step-by-step explanation:
yes i think so because from point d to point s it’s 4 and then from a to l it’s the same length so i do think it would be 8. 4+4 is 8
can someone help please