Step-by-step explanation:
Approximate
= √5
≈ 2,23607
≈ 2,23 + 0,01
≈ 2,24
√5 ≈ 2,24
Show that the function is always increasing
[tex] \sf{f(x) = log(1 + x) - \dfrac{2x}{x + 2}f(x)=log(1+x)−x+22x}\ \textless \ br /\ \textgreater \ [/tex]
ᑎO Տᑭᗩᗰ ᑭᒪᗴᗩՏᗴ
Answer:
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
☼︎~Given function is[tex]\rm \: f(x) = log(1 + x) - \dfrac{2x}{x + 2}[/tex]
~Let first define the domain of f(x).
[tex]{ \underline { \underline{ {\rule{200cm}{0.4cm}}}}}[/tex]
Now, log(1 + x) is defined when x + 1 > 0☼︎~Now, Consider[tex]\sf \: f(x) = log(1 + x) - \dfrac{2x}{x + 2}[/tex]
☼︎~On differentiating both sidesw. r. t. x, we get
[tex]\rm {\: \longmapsto\dfrac{d}{dx}f(x) =\dfrac{d}{dx}\bigg[ log(1 + x) - \dfrac{2x}{x + 2}}[/tex]
☼︎~We know,[tex]\boxed{\sf{ \longmapsto\dfrac{d}{dx}logx \: = \: \dfrac{1}{x}}}[/tex]
❀And[tex]\boxed{\sf{\longmapsto \dfrac{d}{dx} \dfrac{u}{v} = \dfrac{v\dfrac{d}{dx}u \: - \: u\dfrac{d}{dx}v}{ {v}^{2} } \: }}[/tex]
~So, using these results, we get
[tex]\sf {\:\longmapsto f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)\dfrac{d}{dx}2x - 2x\dfrac{d}{dx}(x + 2)}{ {(x + 2)}^{2} }}[/tex]
☼︎~We know,[tex]\boxed{\rm{\longmapsto \dfrac{d}{dx}x = \sf \pink{ 1 \:} }} [/tex]
And-
[tex]\begin{gathered}\boxed{\sf{\longmapsto\dfrac{d}{dx}k = 0 \: }} \\ \end{gathered}[/tex]
☼︎~So, using this result, we get
[tex]\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)2 - 2x(1 + 0)}{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)2(x+2)2−2x(1+0)
[tex]\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{(x + 2)2 - 2x(1 + 0)}{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)2(x+2)2−2x(1+0)\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{2x + 4 - 2x}{ {(x + 2)}^{2} }[/tex]
[tex]\rm \: f'(x) = \dfrac{1}{x + 1} - \dfrac{4 }{ {(x + 2)}^{2} }f′(x)=x+11−(x+2)24[/tex]
[tex]\rm \: f'(x) = \dfrac{ {(x + 2)}^{2} - 4(x + 1)}{(x + 1) {(x + 2)}^{2} }[/tex]
[tex]\rm \: f'(x) = \dfrac{ {x}^{2} + 4 + 4x - 4x - 4}{(x + 1) {(x + 2)}^{2} }[/tex]
[tex]\rm \: f'(x) = \dfrac{ {x}^{2} }{(x + 1) {(x + 2)}^{2} }[/tex]
☼︎~Now, as[tex]\longmapsto\rm {\: {x}^{2} \geqslant 0x2⩾0}[/tex]
[tex]\longmapsto\sf\:{(x+2)}^{2} > 0[/tex]
[tex]\longmapsto\sf\: x + 1 > 0x+1>0[/tex]
☼︎~So,[tex]\sf\longmapsto \:\rm \: f'(x) = \dfrac{ {x}^{2} }{(x + 1) {(x + 2)}^{2} } \geqslant 0[/tex]
☼︎~Therefore, f'(x) is always increasing when x > - 1[tex]{ \underline { \underline{ \bold {\rule{200cm}{0.4cm}}}}}[/tex]
Additional Information:-[tex]\boxed{\begin{array}{c|c} \bf f(x) & \tt \dfrac{d}{dx}f(x) \\ \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf k & \sf 0 \\ \\ \sf sinx & \sf cosx \\ \\ \sf cosx & \sf - \: sinx \\ \\ \sf tanx & \sf {sec}^{2}x \\ \\ \sf cotx & \sf - {cosec}^{2}x \\ \\ \sf secx & \sf secx \: tanx\\ \\ \sf cosecx & \sf - \: cosecx \: cotx\\ \\ \sf \sqrt{x} & \sf \dfrac{1}{2 \sqrt{x} } \\ \\ \sf logx & \sf \dfrac{1}{x}\\ \\ \sf {e}^{x} & \sf {e}^{x} \end{array}}[/tex]
[tex]{ \underline { \underline{ \bold {\rule{200cm}{0.3cm}}}}}[/tex]
A box of cereal advertised their new boxes hold 45% more cereal. The old
boxes held 48 oz, how many oz does the new box hold?
Answer:
69.6 oz
Step-by-step explanation:
So we have to calculate 45% of 48 then add it to 48 to get the the weight of the new box.
(45/100)*48 = 21.6
48+21.6=69.6
Therefore, the weight of the new box is 69.9oz
If v varies inversely with w and v=18 when w=13, find the equation that relates v and w.
Answer:
v = 234 / w
Step-by-step explanation:
v varies inversely with w
v = k/w
Find the constnt of variation
v = 18 when w = 13
18 = k/13
k = 18 * 13
k = 234
find the equation that relates v and w
v = 234 / w
7 pounds of organic cheese costs $40.60. What is the constant of proportionality that relates y the cost of pounds of
organic cheese
5.80
7.15
5.98
40.60
Answer:
5.80
Step-by-step explanation:
it is
40.60/7=5.80
Answer:
5.8
Step-by-step explanation:
Simplify these fraction 9 1/3-5 3/4
Answer:
Hiiiiiiii
The answer is 3.58/ 3 7/12
casey has 42 necklaces and 70 pairs of earrings to put into sets to sell. The greatest common factor for the number of necklaces and the number of pairs of earrings is equal to the number of sets Casey can sell. Find the number of sets Casey can prepare to sell?
Answer:
0.3
Step-by-step explanation:
Answer:
14 sets
Step-by-step explanation:
14 x 3 = 42
14 x 5 = 70
These numbers are multiples of __________.
4, 8, 16, 24
A) 3
B) 4
C) 5
D) 6
please help ! worth 30 points
How does fermats last theorem relate to a famous high school math theorem? What is that theorem called?
(Will give BRAINLIEST ANSWER If you got it correct)
Perform the following binary multiplication.
1111X111
123,321
Easy maths bro
Help me At my Math
Its in the pic
Answer:
18 C
19 A
20 C
I am not sure about 16 and 17
Hope it helps
Answer:
Step-by-step explanation:
16) B
17) A
18) C
19) f(X ) = -2x² + 5
f(-3) =-2*(-3)² + 5 = -2*9 + 5 = -18 + 5 = -13
Ans: A
19)f(x) = - x² - 1
f(-5) = -(-5)² - 1 = -25 - 1 = -16
Ans: C
3.3×10 to the power of 7+7.7×10 to the power of 8
Answer:
803000000 is the right answer
I need to convert this equation from vertex into standard form.
x^2 = 44(y-12)
I don’t understand the whole leading coefficient thing.
Answer:
If you want to solve x it will be 11
If you want to solve y it will be y
=
x
2
44
+
12
Step-by-step explanation:
what is this 1 times 11 =2 times m 45
Answer:
m = 0.122
Step-by-step explanation:
1 * 11 = 2 *45m
11 = 2*45m
11/2 = 45m
5.5/45 = m
Using these numbers, make a proportion. then see if you can make a different proportion. 2; 5; 20; 8
Answer:
2:8 and 5:20
Step-by-step explanation:
2 and 8 correlate with each other as 8/4 = 2
5 and 20 correlate with each other 20/5 = 4
What was the formula for slope again?
Answer:
M=rise / run
Y^2/y^1/x^2/x^1
Question
Find the area of the parallelogram.
Area =
in.²
Answer:
256.5
Step-by-step explanation:
19 · 13.5 = 256.5
I hope this helps
Given the equation F = C + 32 where is the temperature in degrees Celsius and F is the corresponding temperature in degrees
Fahrenheit, and the following ordered pairs:
(30, F1).(-15, F 2)
Step 1 of 2: Compute the missing y values so that each ordered pair will satisfy the given equation.
Answer:
Step-by-step explanation:
Can someone help me is this correct?
Answer:
its incorrect
Step-by-step explanation:
the triangles are congruent as they are the exact same but flipped, so it would be the rule of SAS
The function f is one-to-one. Find its inverse. F(x) = 2/x+5
what is the reciprocal of 4/9
Answer:
9/4
Step-by-step explanation:
Just flip it upside down
Answer:
It's 9/4.
<3
(something)
Solve 4x + 2(x + 8) = 58.
O A. x = 3
O B. x = 6
O C. X = 5
O D. x = 7
Answer:
D- x = 7
Step-by-step explanation:
Calculate how many cups of butter your new recipe will need.
What is 1 and 1/2 cups x 1 and 1/2?
In a box there are 6 orange balls, 4 green balls and blue "x" balls. If the probability of drawing one blue ball is 1/3, what is the probability of drawing two blue bags?
Answer:
well you could write this as
1) 0.5/3
2) 1/6
so yeah.
if its 1/3 to get one blue ball, for two you would divide the numerator in half so you'd get 0.5/3
Step-by-step explanation:
Mixed multiplication
1 1/3 x 1 3/4
Solve for 29 will give brainliest
Answer:
Step-by-step explanation:
JuJust give it to me please please I need
the derivative of |x| with respect to x is x/|x|.
x/|x|
Answer pls will mstk brainliest
Answer:
1 pie
Step-by-step explanation:
1/3 + 1/3 +1/3= 3/3
simplified = 1/1 or 1 whole
Answer:
1 pie
Step-by-step explanation:
1/3 +1/3 + 1/3 =3/3 = 1
If the denominator is the same you can keep it the same and just add the numerators.
Hope this helps:)
352 is 125% of…
Bwkssndndndbej
Answer:
281.6
Step-by-step explanation:
=281.6 × 125 %
= 352
Answer:
35.51%, or, if rounded is 36%
Step-by-step explanation:
1. We assume, that the number 352 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 352, so we can write it down as 100%=352.
4. We know, that x% equals 125 of the output value, so we can write it down as x%=125.
5. Now we have two simple equations:
1) 100%=352
2) x%=125
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=352/125
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 125 is what percent of 352
100%/x%=352/125
(100/x)*x=(352/125)*x - we multiply both sides of the equation by x
100=2.816*x - we divide both sides of the equation by (2.816) to get x
100/2.816=x
35.511363636364=x
x=35.511363636364
now we have:
125 is 35.511363636364% of 352
1 and 2 please - Write the details (what you know)
- Write what the question is asking (what do you want to know)
- Show your work
- Use correct unit labels
Answer:
x≤90 and 30x+20y≥380,000
Step-by-step explanation:
1. x=original price of shoe
"at most" means inequality where the money you can spend is less than or equal to
so x-10≤80
solve for original price
x≤90
2. x=number of floor tix
y=number of bleacher seats
"at least" means bigger than or equal to
30x+20y≥380,000
Guys please just answer honestly I really need help I’m begging you this is my 4th time re submitting this question today please
Answer:
1) Parallel line: y = 4x + 1
4) Perpendicular line: y = -5x + 9
6) Perpendicular line: y = 3x + 2
Step-by-step explanation:
Note:I will only provide solutions to question 1, 4, and 6, in accordance with Brainly's guidelines. Since the given problem essentially involves the same type of questions, the solutions that I will provide should allow you to apply the same techniques in solving for the remainder of the questions.
Definitions:Parallel lines have the same slope.
Perpendicular lines have negative reciprocal slopes. This means that when you multiply the slopes of two lines that are perpendicular from each other will result in a product of - 1.
In other words, if the slope of a line is m₁, and the slope of the other line is m₂, then it means that they are perpendicular from each other if: m₁ × m₂ = - 1
Solutions:1) y-intercept = 1, parallel to y = 4x - 3.According to the definitions provided on parallel lines, since the given linear equation has a slope, m = 4, then it means that the other line parallel to it must have the same slope.
Given the y-intercept of the other line as b = 1, and its slope, m = 4, then the equation of the line parallel to y = 4x + 3 is:
Equation of Parallel line: y = 4x + 1.
4) y-intercept = 9, perpendicular to y = ⅕x + 4.
Given the linear equation, y = ⅕x + 4, where its slope, m₁ = ⅕
Then it means that the negative reciprocal of ⅕ must be ⇒ [tex]\large\mathsf{-\frac{5}{1}\:\:or\:\:-5}[/tex]
Because: m₁ × m₂ = - 1
⅕ × -5 = -1
Therefore, if the y-intercept of the other line is b = 9, and its slope is m₂ = -5, then the equation of the line perpendicular to y = ⅕x + 4 is:
Perpendicular line: y = -5x + 9.
6) Through point (2, 8) and perpendicular to y = - ⅓x - 8Given the equation of the first line, y = -⅓x - 8, where its slope, m₁ = -⅓.
Then it means that the slope of the other line must be m₂ = [tex]\large\mathsf{\frac{3}{1}\:\:or\:\:3}[/tex] because:
m₁ × m₂ = - 1
-⅓ × 3 = -1
Next, substitute the slope of the other line, m₂ = 3, and the values of the given point, (2, 8) into the slope-intercept form, y = mx + b, in order to solve for the y-intercept of the other line.
y = mx + b
8 = 3(2) + b
8 = 6 + b
Subtract 6 from both sides to isolate b:
8 - 6 = 6 - 6 + b
2 = b
Therefore, the equation of the line perpendicular to y = - ⅓x - 8 is:
Perpendicular line: y = 3x + 2.
HELP HELP PLEASE
In the basketball game, Rachael scored 6 points less than triple the number of points Trina scored. Trina scored 16 points, How many points did Rachael score?
Answer:
Rachael scored 42 points.
Step-by-step explanation:
In order to solve this, we must first find triple Trina's score, so we multiply 16 * 3 which simplifies to 48. Since the question asks for 6 points less than this score, we find subtract 48 - 6 which simplifies to 42.