We are asked to find the first derivative of,
[tex]\longrightarrow g(x) = \sqrt{x^2+2x}[/tex]
Here we can write the term [tex]x^2+2x[/tex] by adding and subtracting 1 as,
[tex]x^2+2x = x^2+2x+1-1[/tex]
[tex]x^2+2x = (x+1)^2-1\quad[\because\, x^2+2x+1=(x+1)^2][/tex]
Thus,
[tex]\longrightarrow g(x) = \sqrt{(x+1)^2-1}\quad\dots(1)[/tex]
Now take,
[tex]x+1=\sec\theta\quad\dots(2)[/tex]
[tex]x=\sec\theta-1[/tex]
[tex]dx=\sec\theta\tan\theta\, d\theta[/tex]
[tex]\dfrac{d\theta}{dx}=\dfrac{1}{\sec\theta\tan\theta}\quad\dots(3)[/tex]
Then (1) becomes,
[tex]\longrightarrow g(x) = \sqrt{sec^2\theta-1}[/tex]
We have,
[tex]\sec^2\theta-1=\tan^2\theta[/tex]
So we get,
[tex]\longrightarrow g(x) = \tan\theta[/tex]
Now,
[tex]\longrightarrow g'(x) = \dfrac{d}{dx}\,[\tan\theta][/tex]
By chain rule,
[tex]\longrightarrow g'(x) = \dfrac{d}{d\theta}\,[\tan\theta]\cdot\dfrac{d\theta}{dx}[/tex]
[tex]\longrightarrow g'(x) = \sec^2\theta\cdot\dfrac{1}{\sec\theta\tan\theta}\quad\quad\textrm{[From (3)]}[/tex]
[tex]\longrightarrow g'(x) = \sec\theta\cdot\dfrac{1}{\tan\theta}[/tex]
[tex]\longrightarrow g'(x)=\dfrac{1}{\cos\theta}\cdot\dfrac{\cos\theta}{\sin\theta}[/tex]
[tex]\longrightarrow g'(x)=\dfrac{1}{\sin\theta}\quad\dots(4)[/tex]
But we have,
[tex]\sin^2\theta+\cos^2\theta=1[/tex]
[tex]\sin\theta=\sqrt{1-\cos^2\theta}[/tex]
[tex]\sin\theta=\sqrt{1-\dfrac{1}{\sec^2\theta}}[/tex]
[tex]\sin\theta=\dfrac{\sqrt{\sec^2\theta-1}}{\sec\theta}[/tex]
[tex]\sin\theta=\dfrac{\sqrt{(x+1)^2-1}}{x+1}\quad\quad\textrm{[From (2)]}[/tex]
[tex]\sin\theta=\dfrac{\sqrt{x^2+2x}}{x+1}[/tex]
Hence (4) becomes,
[tex]\longrightarrow\underline{\underline{g'(x)=\dfrac{x+1}{\sqrt{x^2+2x}}}}[/tex]
This is the first derivative of the given function.
HELP FOR 7 AND 8 Pleaseeeee
Solve for x. Round answer to the nearest tenth.
17
54°
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To amend a country's constitution, 5 6 of the 52 states in that country must approve the amendment. If 44 states approve an amendment, will the constitution be amended
Answer: Yes. It will be amended
Step-by-step explanation:
Since 5/6 of the 52 states in a country must approve the amendment before the country's constitution is amended, then the number of states that must approve it will be:
= 5/6 × 52
= 43.33
= 43 approximately
Since 44 states approve an amendment, the constitution be amended since it's more than 5/6 of the 52 states.
What is the value of s?
_______units
Answer:
it's asking for hypothesis your answer is in the picture
helppppppppppppppppppppp plzzzzzzzzzzz answer
Answer:
Maria randomly selects a number from the list of numbers below.
56, 90, 88, 76, 12
What is the probability that she selects an even number?
Step-by-step explanation:
so fd jwshydd +3 b4--
Answer:
3/2
Step-by-step explanation:
4x+17=23
-17 on both sides
4x=6
divided by 4
x=3/2
Find the perimeter of the trapezoid. ROUND YOUR ANSWER TO THE
NEAREST TENTH (One number past the decimal.)
Answer:
49.41
Fine the lengths of the top, bottom, and left side first. the do bottom - top and you get 6. To get the length of the right side, do left side squared + 6 squared and you get the length of the right side squared. The answer is top + bottom + left side + square root of right side squared.
40 points!
You are framing a picture with a frame of equal width on each side.
a. Write a polynomial that represents the area of the picture including the frame
b. Find the area of the picture including the frame when the width of the frame is 2 inches
Answer:
Part A)
The polynomial is:
[tex]A=4(x+8)(x+10)[/tex]
Or, expanded:
[tex]A=4x^2+72x+320[/tex]
Part B)
When the width of the frame is two inches, the area of the picture including the frame is 480 square inches.
Step-by-step explanation:
Part A)
For solely the picture, the width is 16 inches, and the length is 20 inches.
If we include the width of the frame, then we will have to add x to both sides of the 16 inches. Then the new width will be (16 + 2x) inches.
Likewise, the new length will be (20 + 2x) inches.
The area of a rectangle is given by its width multiplied by its length. Then the polynomial that represents the area will be:
[tex]A=(16+2x)(20+2x)[/tex]
To simplify calculations, we can factor out a two from both factors. Thus:
[tex]A=2(8+x)\cdot 2(10+x)=4(x+8)(x+10)[/tex]
Expanded, this will be:
[tex]A=4(x^2+18x+80)=4x^2+72x+320[/tex]
Part B)
When the width of the frame is two, x = 2. Then the area is:
[tex]A=4(2+8)(2+10)=4(10)(12)=40(12)=480\text{ inches}^2[/tex]
The area of the picture including the frame will be 480 square inches.
Find the 100th term for the sequence. -9,-4, 1, 6, 11, .......
Answer:
486
Step-by-step explanation:
for the 2nd term, add 5 to -9
for the 3rd, add 5 × 2 to -9
for the 4th, add 5 × 3 to -9
:
for the 100th, add 5 × (100 - 1) to -9
=> 5 × 99 + (-9)
=> 486
(6,3); (1,4)
Slope
Giving brainless answer
Answer:
-1/5. When you do y^2 - y^1/ x^2 - x^1 = It will lead to -1/5
Step-by-step explanation:
True or false.
A counter-clockwise turn of 270° will land you at the same location as a 90° clockwise turn.
Please help me name the parts of the circle
Answer:
radius is gf diametor is ce chord is Ab and secant is ge tangent is dc
This box plot shows the heights (in feet) of a sample of pine trees.
Pine tree heights
A pine tree that is 8 feet tall is added to the sample. How will this outlier
affect the shape of the box plot?
When a pine tree that is 8 feet tall is added to the sample, A. The new box plot will be negatively skewed.
What is negative skewness?Negative skewness occurs when the tail of the left side of the box plot is longer than the tail on the right side.
Negative skewness highlights the risk of left tail events or negative outliers known as “black swan events.”
Thus, when a pine tree that is 8 feet tall is added to the sample, A. The new box plot will be negatively skewed.
Learn more about negative skewness at https://brainly.com/question/20378699
#SPJ1
Answer:
A
hope this helps
Given h(x)=4x-4h(x)=4x−4, find h(-3)h(−3).
Answer:1
Step-by-step explanation:
4x-4x+4=4h(x)
4=4h(x)
h(x)=1
h(-3)h(-3)=(1)(1)=1
Distribute and combine like terms: −4(7r + 7)
Answer:
r=1
Step-by-step explanation:
-4(7r+7)
-28r-28
r=1
Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.
24f2+11
Answer:
24t^2 + 11
Step-by-step explanation:
There is a lot left out of this question. If you are allowed rational numbers, a common factor could be 24.
24(t^2 + 11/24) is one possibility.
I think what you mean is there an integer that is a common factor. There is not.
So the answer is 24t^2 + 11
There is one more thing that needs to be clarified. Can you give t a value? If you can, then t = 11
the common factor would be
11(24 * 11 + 1)
I doubt very much that this is what is meant, but the question really should make it clear.
Answer:
1(24f²+11) is your answer
Step-by-step explanation:
24f2+11
taking common
1(24f²+11)
HELPPPPP PLSSSSSSSSSS PLSSSSSSSS DRFTGYHUYGTFRDCGV PLSSSSSSSSSSSSSSSSSSSSSSSSSSSS PLSSSSSSSSSSSSSSSSSSSSSS FRTGYHUJTRCVBJHGB ASAPP PLSSSSSSSSS NNOWWW FGHUJIKHTFVBNGB.
Answer:
B, C, and D
Step-by-step explanation:
They are both true the ones I said.
The cost of boring a tube well 600 meter deep is as follows 25 paisa for the first metre and an additional 4paisa for every subsequent meter find the cost of boring a 500th meter long
Find the slope of the line
Answer:
Slope is undefined.
Step-by-step explanation:
Slope of 0 is a horizontal line.
Slope of undefined is a vertical line.
Any other slope is something in between.
Answer:
(A) undefined
Step-by-step explanation:
Here’s a little trick
If the line is horizontal, the slope is always 0
While if the line is vertical, the slope is always undefined.
In other words, if you can walk on the line, its 0 if you can’t its undefined
HELP I WILL GIVE BRIANLY
If 1/3 of my money is 80, what is 25% of my money?
Answer:
60 = 25% of ur money
Step-by-step explanation:
80×3=100%of ur money (240)
to get 25% we need to divide 240 by 4 bcs 4= 25%
I don’t have any of the stuff pls help
Answer:
so 6/10 prefered ebooks pretty much and 1/10 didn't have a preference the other 3/10 liked traditional books you should be able to do the rest after that
3a=a+36 find the value of a
Answer:
a=18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
Step 1: Write out your equation
3a=a+36
Step 2: Subtract a on both sides
2a=36
Step 3: Divide by 2 on both sides
a=18
Hope I helped
I NEED HELP RN PLSSS!!! (check whole picture) i’ll give brainiest if u don’t give a link just pls help immediately!!!)
Answer:
So I would say your answer is..............A
Step-by-step explanation:
For most places, global warming will result in more frequent hot days and fewer cool days, with the greatest warming occurring over land. Longer, more intense heat waves will become more common. Storms, floods, and droughts will generally be more severe as precipitation patterns change
Also, A is correct because lets say you put an ice cube in the sun...okay well if it keeps getting hotter and hotter multiply ice cubes into ice caps. Well same thing will happen. It will melt causeing water from the ice caps. Which will result into more water. Which will cause water to go above sea level!
Hope this helps!!!
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33
Question 9 (1 point)
In the middle school PTA there is a total of 47 men and women. The number of women
in the PTA is 2 more than four times the number of men. How many women are in the
PTA?
a
42
38
ОООО
30
d
35
Answer:
38 women
Step-by-step explanation:
Question 9 (1 point)
In the middle school PTA there is a total of 47 men and women. The number of women the PTA is 2 more than four times the number of men. How many women are in the
PTA?
Let the number of men = x
Let the number of women = y
x + y = 47
y = 2 + 4x
We substitute
x + 2 + 4x = 47
Collect like terms
5x = 47 - 2
5x = 45
x = 45/5 = 9
y = 2 + 4x
y = 2 + 4 × 9
y = 2 + 36
y = 38
Therefore, the number of women = y = 38 women
help me find the perimeter please:)
Answer:
79.2 cm
Step-by-step explanation:
Add up all the lengths of all of the sides of the figure:
16.2 + 7.5 + 7.5 + 18 + 18 + 12 = 79.2
Answer:
79.2 m
Step-by-step explanation:
Well since all the units are the same and you have already labeled the missing/ congruent sides. Just add up all the sides and you’d end up with 79.2
What is the area of this rectangle? A rectangle that is partitioned into two rectangles. The first rectangle has a measurement of five meters along the top, and a measurement of eight meters along the side. The second rectangle has a measurement of five meters along the top, and a measurment of eight meters along the side. 50 square meters 60 square meters 70 square meters 80 square meters
Answer:
80 square meters
Step-by-step explanation:
A rectangle that is partitioned into two rectangles; rectangle A and rectangle B
Rectangle A:
Top = 5 meters
Side = 8 meters
Area of rectangle A = length × width
= 5 meters × 8 meters
= 40 meters ²
Rectangle B:
Top = 5 meters
Side = 8 meters
Area of rectangle B = length × width
= 5 meters × 8 meters
= 40 meters ²
Total area of the partitioned rectangle = area of rectangle A + area of rectangle B
= 40 meters ² + 40 meters ²
= 80 meters ²
Can someone help asap
It’s timed can sb please help me
Answer:
D
Step-by-step explanation:
The intersection of the graphs is at (-3,4).
Answer:
(-3,4)
Step-by-step explanation:
we have to find the point in common of the two lines, that is where they intercept.
when we write a point, we have to sign first the coordinate of the x, and then the coordinate of the y.
So the answer is : (-3,4)
HELPPPP ME NOW PLS LLS
Answer:
Angle one is 107 degrees and angle 2 is 83 degrees
Step-by-step explanation:
This table shows how many male and female students attended two different
movies. What is the probability that a randomly chosen person from this
group is male?
Round your answer to two decimal places.
Action
Drama
Total
Male
105
124
229
Female
99
151
250
Total
204
275
479
Answer:
the correct answer is
229/479 = 0.48
The probability that a randomly chosen person from this group is male is 0.48.
What is the probability that a male is chosen?Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
The probability of choosing a male = number of males / total number of males and females
229/479 = 0.48
To learn more about frequency tables, please check: https://brainly.com/question/26577861
The mulraneys hired a contractor to build an addition to their home. The contractor proposed a rectangular room with a perimeter of 50 feet. The mulraneys asked the contractor to change the perimeter to 60 feet by increasing both he length and the width by the same distance. By how many feet did the mulranys ask the contractor to increase the length of the room?