Answers
Answer:
[tex]\frac{8}{\left(-x+2\right)^2}[/tex] & [tex]x = 1, x = 3[/tex]
Step-by-step explanation:
I'm sure you are familiar with the product rule,
If y = u*v => dy/dx = u * dv/dx + v * dy/dx <----- product rule
In this case:
[tex]u=3x+2,\:v=\left(2-x\right)^{-1},\\=>\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)[/tex]
Now remember the sum rule:
[tex]\frac{d}{dx}\left(3x+2\right) = \frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(2\right),\\\frac{d}{dx}\left(3x\right) = 3,\\\frac{d}{dx}\left(2\right) = 0\\\frac{d}{dx}\left(3x+2\right) = 3[/tex]
For this second bit we apply the chain rule:
[tex]\frac{d}{dx}\left(\left(2-x\right)^{-1}\right) = -\frac{1}{\left(2-x\right)^2}\frac{d}{dx}\left(2-x\right),\\\frac{d}{dx}\left(2-x\right) = -1,\\\\=> -\frac{1}{\left(2-x\right)^2}\left(-1\right)\\=> \frac{1}{\left(2-x\right)^2}[/tex]
If we substitute these values back into the expression...[tex]\frac{d}{dx}\left(3x+2\right)\left(2-x\right)^{-1}+\frac{d}{dx}\left(\left(2-x\right)^{-1}\right)\left(3x+2\right)[/tex]
...we get the following:
[tex]3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)[/tex]
The rest is just pure simplification:
[tex]3\left(2-x\right)^{-1}+\frac{1}{\left(2-x\right)^2}\left(3x+2\right)\\= \frac{3}{-x+2}+\frac{3x+2}{\left(-x+2\right)^2}\\= \frac{3\left(-x+2\right)}{\left(-x+2\right)^2}+\frac{3x+2}{\left(-x+2\right)^2}\\\\= \frac{3\left(-x+2\right)+3x+2}{\left(-x+2\right)^2}\\\\= \frac{8}{\left(-x+2\right)^2}[/tex]
Now let's equate this to equal 8 for the second bit and solve for x:
[tex]\frac{8}{\left(-x+2\right)^2}=8,\\\frac{8}{\left(-x+2\right)^2}\left(-x+2\right)^2=8\left(-x+2\right)^2,\\8=8\left(-x+2\right)^2,\\\left(-x+2\right)^2=1,\\x = 1, x = 3[/tex]
Related Questions
BRAINLIEST Please help i'd appreciate it thanks, Have a nice day :)
Answers
Explanation: The area of a parallelogram is base times height.
Because the parallelograms are congruent, we can do 4*(3.5*5), which equals 70 square centimeters.
John plants 36 tulip bulbs in his
garden. He has used half of the tulip
bulbs. How many did he have to
begin with
Answers
Answer:
72
Step-by-step explanation:
if he has half then its 36x2=72
1. Malik has $30,000 in a savings account that earns 8% annually.
The interest is not compounded. How much total money will he
have in 2 years after collecting the interest?
a. How much simple interest did Malik receive?
$
b. How much total money does Malik have after the 2 years?
$
Answers
Step-by-step explanation:
I= prt
I= 30000×8%×2
I= 4800
total = 30000+4800
=34800
The Gonzalez family sold their home for $256,000. Their real estate agent earned 5.5% in commission of that sale. How much did the Gonzalez family get to keep from the sale?
Answers
Answer this real-world question
Xavier had $100 in his lunch account. He spends $6 for lunch each day. Zack has $160 in his lunch account. He spends $10 each day. After how many days will the boys have the same amount of money in their accounts? How much money will they each have on that day?
Answers
Answer:
After 15 days they'll both have $10
Explanation:
100 (Xavier's total)- 6x (6 dollars every day) = 160 (Zach's total amount) -10x (10 dollars every day)
[tex]100-6x=160-10x\\[/tex]
+10x on both sides
[tex]100+4x=160[/tex]
-100 on both sides
[tex]4x=60[/tex]
/4 on both sides
[tex]x=15[/tex]
NEED HELP ASAP PLEASE AND THANK YOU:
Sherry draws a triangle. The length of side AC is 12 inches. The length of side AB¯ is 9 inches. She wants to draw a line XY that is parallel to BC. If she draws point X 3 inches from B, how far from point A does she need to draw point Y so that XY∥BC?
A. Point Y should be 10 inches from point A.
B. Point Y should be 4 inches from point A.
C. Point Y should be 4.5 inches from point A.
D. Point Y should be 8 inches from point A.
Answers
Answer:
D. Point Y should be 8 inches from point A
Step-by-step explanation:
A painter is placing a ladder to reach the third story window, which is 14 feet above the ground and makes an angle with the ground at 70°
How far out from the base of the building does the ladder need to be positioned? Round your answer to the nearest tenth.
Answers
Answer:
4.8
Step-by-step explanation:
We are given the hypotunese or the slanted side which is the ladder length which is 14.
We are given an angle at the bottom which is 70 degrees.
We are asked to find the horizontal side which is adjacent to the angle at the bottom.
Since we have a hypotunese and a side adjacent to the angle, we are going to use the function cosine.
we use this formula
[tex] \cos(theta) = \frac{adj}{hypo} [/tex]
[tex] \cos(70) = \frac{x}{14} [/tex]
x=4.8
Find the values of x and y in the diagram below
Answers
Answer:
x= 15
y= 21
Step-by-step explanation:
81+6x-11+x+5= 180
7 x + 75= 180
7x= 105
x=15
4y-18+y+14+6×15-11=180
5 y + 75= 180
5y= 105
y= 21
If Gavin has 6 9/20th of time left to play videos, what is that mixed number written in minutes and seconds?
Answers
Answer:
[tex]387\ \text{minutes}[/tex]
Step-by-step explanation:
The time Gavin has is [tex]6\dfrac{9}{20}\ \text{hours}[/tex]
[tex]6\dfrac{9}{20}=\dfrac{20\times 6+9}{20}[/tex]
[tex]=\dfrac{129}{20}\ \text{hours}[/tex]
[tex]=6.45\ \text{hours}[/tex]
[tex]=6\times 60+0.45\times 60=360+27[/tex]
[tex]=387\ \text{minutes}[/tex]
The number of minutes is [tex]387\ \text{minutes}[/tex].
33.52 is 419% of what?
Answers
Answer:
140.4488
Step-by-step explanation:
Answer:419% of 33.52 = 140.4488
Step-by-step explanation: If you multiply .419 by 33.52 you get 140.4488
I need the answer to this question
Answers
9514 1404 393
Answer:
g(x) = (5x +26)/(x+5)
Step-by-step explanation:
To translate the function right h units and up k units, the transformation is ...
f(x -h) +k
You want h=-4 (4 units left) and k=-1 (1 unit down). So, the translated function is ...
[tex]f(x+4)-1=\dfrac{6(x+4)+7}{(x+4)+1}-1\\\\=\dfrac{6x+31}{x+5}-1=\dfrac{6x+31-(x+5)}{x+5}\\\\=\dfrac{5x+26}{x+5}[/tex]
The translated function is ...
g(x) = (5x +26)/(x+5)
__
The original function is in red with asymptotes shown in orange. The translated function is in purple with the asymptotes shown in blue. You can see that the function has been moved 4 left and 1 down.
Rick wants to divide his 11 inch ribbon into sections
spaced apart 2 1/3 centimeters.
How many holes would Rick have on his ribbon?
Answers
Answer:
12
Step-by-step explanation:
since 1 inch equals 2.54 cm then 11 inches equals 27.94 cm
27.94 ÷ 2.33 = 11.99
What expressions equivalent to 25c+15 ? ( more than one answer )
A. 25c+15/5
B. 5c+15
C. 3+5c
D. 1/5(25c+15)
E. 5(25c+15)
Answers
Answer:
The only one that looks familiar is B sorry >-<
Step-by-step explanation:
Answer: The correct answers are C and B
Step-by-step explanation:
help it's my last question!! (slopes) (brainliest)
Answers
Answer:
x- intercept : How many sandwichs he bought
y-intercept : How many drinks he bought
Can someone help me with this??
Answers
9514 1404 393
Answer:
u, AB6.4arctangent51°MN has the opposite direction of NMa ray has infinite length; a vector has finite lengthStep-by-step explanation:
1. The problem preamble gives you the two ways to name the vector. You can use either its name, or the two end points. (The starting point is named first, as it is with a ray.)
The vector shown can be referred to by the names ...
u or AB
__
2. The right triangle has legs 4 and 5, so the length is ...
length = √(4² +5²) = √41
length ≈ 6.4
__
3. Typically, you're given the leg lengths. The ratio of these is the tangent of the angle. The angle can be found using the inverse tangent function.
__
4. The tangent of the angle is the slope of the vector:
tan(A) = 5/4
A = arctan(5/4) ≈ 51°
__
5. The first letter named is the starting point of the vector. Vector MN starts at point M and ends at point N. Vector NM starts at N and ends at M. The directions of the two vectors are opposites.
__
6. A ray is like a vector of infinite length. The name of a ray includes a point on the ray. The name of a vector includes both end points. It is of finite length.
_____
Additional comment
A lot of math is invented to describe how things work in the real world. A vector is often used to represent velocity or force and other things that can be described by a magnitude and direction in the real world. A ray is more often used in problems in geometry, where that abstract concept serves a useful purpose.
could you explain to me how to do this ? I do not understand at all
Answers
Answer:
I believe this is how you do it
Step-by-step explanation:
csc∅tan∅
(1/sin∅)(sin∅/cos∅)
(sin∅)/(sin∅cos∅)
1/(cos∅)
sec∅
csc²∅tan²∅sin∅
1/(sin²∅) * tan²∅ * sin∅
tan²∅/sin²∅ * sin∅
tan²∅/sin∅
Chloe went to Dairy Swirl to get two scoops of ice cream. The two scoops cost $3.39. She asked the server to add hot fudge and m & m’s to her ice cream. If her sundae cost $4.89 after the two toppings were added, how much was each topping
Answers
PLEASE HELP I NEED THIS ASAP
which relation is not a function?
Answers
Answer:
im not completley sure but i think its B
Step-by-step explanation:
Parker drove a total distance of 4 and 1 over 2 miles during the months of June and July. If Parker only drove 1 over 8 of a mile every day, which expression shows the number of days he went driving? 4 and 1 over 2 ⋅
Answers
Answer:
36 days
Step-by-step explanation:
Total distance driven = 4 1/2 miles = 9/2 miles
Months of June and July ;
Miles driven per day = 1/8
Number of days Parker went driving :
Total miles driven / miles driven per day
9/2 miles ÷ 1/8 miles
9 /2 * 8 /1
(9 * 8) / (2 * 1)
72 / 2
= 36 days
Hence, Parker drove for 36 days
Tasha is rolling 2 dice. Use a probability model to determine the theoretical probability that she will roll an even number on the first die and a multiple of 3 on the second die?
Answers
Answer:
4/12 probability
Step-by-step explanation:
there is 4/12 chance she will roll this
can you help me please
Answers
tan = opp/adj
tan 20 = opp/10
x = 10(tan 20)
x = 3.63....
x = 3.6 cm
32) In a triangle, the exterior angle is twice of each of the interior remote angles. The exterior angle is 1200. Find the measure of the three angles of the triangle.
Answers
Answer:
60 degrees each
Step-by-step explanation:
For the triangle, the sum of the interior angles is equal to the exterior
Let x and y be interior
Let z be the third angle
w be the exterior
w = x+y
120 = x+y
If the exterior angle is twice of each of the interior remote angles, then;
2x = 2y
x = y
120 = x+x
2x = 120
x = 60
Since x = y, y = 60 degres
From the triangle, the third angle will be 180 - 120
z = 180-120
z = 60
The measures of the 3 angles are 60 degrees each
Really don’t understand this one
Answers
Answer:
(3,8)
Step-by-step explanation:
First, you need to graph a triangle using the points given.
Then reflect across y = x
R is (3,0) which when reflected across y = x is (0,3)
S is (3,3) which when reflected across y = x is (3,3)
R is (4,0) which when reflected across y = x is (0,4)
John has 44 quarters.
Jan has 100 dimes. Who
has more money?
Answers
John has more.
John has $11 while Jan has $10
Simplify. 28x^2/7x^6
Answers
Answer:
4x^8
Step-by-step explanation:
hope this helps
A store sold 650 bicycles last year. This year the store sold 572 bicycles. What is the percent decrease in the number of bicycles sold from last year to this year? PLEASE HELP
Answers
Answer:
Decreased by 12%
Step-by-step explanation:
to find percentage change --- new-original/original x 100
-78/650 x100 = -12%
Expression that is equivalent to (b^10) ( b^2)in the form of b^m
Answers
Answer:
b^12
Step-by-step explanation:
Multiply b^10 by b^2 by adding the exponents.
b^12
what is the answer of this question?
Answers
9514 1404 393
Answer:
970
Step-by-step explanation:
It turns out that the radical terms cancel, so the result is an integer. You can find the integer value using your calculator. It is ...
(5 +2√6)³ +1/(5 +2√6)³ = 970
_____
The cube of 'a' is ...
(5+2√6)³ = 5³ +3·5²·2√6 +3·5·(2√6)² +(2√6)³
= 125 +3·50√6 +3·120 +48√6
a³ = 485 +198√6
The reciprocal of this is ...
b³ = 1/a³ = 1/(485 +198√6) = (485 -198√6)/(485² -6·198²) = (485 -198√6)/1
b³ = 485 -198√6
Then the sum is ...
a³ +b³ = (485 +198√6) +(485 -198√6) = 970
Which system of equations is in standard form?
Answers
Which inequality is true if n = 81?
F 3n < 84
G n − 29 < 53
H 2n < 162
J n + 5 < 76
Answers
Answer:
G n - 29 < 53
Step-by-step explanation:
Replace n with 81 so it becomes
81 - 29 < 53
If you solve, 81 - 29 would be 52
Then you have
52 < 53
This is true since 53 is greater than 52