Answers
Derivation of f(x):
[tex]f'(x) = \frac{g(x)*8x-4x^2*g'(x)}{(g(x))^2} -\frac{1}{x+2}[/tex]
Since g(3) = 6 and g'(3) = 3
[tex]f'(3) = \frac{g(3)*8*3-4(3)^2*g'(3)}{(g(3))^2} -\frac{1}{3+2} \\f'(3) = \frac{6*8*3-4*9*3}{36} -\frac{1}{5} \\f'(3) = \frac{36}{36} -\frac{1}{5} =1-\frac{1}{5} =\frac{4}{5}\\ f'(3) = 0.8[/tex]
Thus f'(3) = 0.8
Hope that helps!
A couple of identities I used in derivation:
[tex]\frac{d}{dx} (ln x) = \frac{1}{x}[/tex]
Related Questions
evaluate the expression when c=9 and d=4. 5c+d
Answers
Answer:
5(9)+4= 45+4.....= 49
Step-by-step explanation:
Find the value of x
.
12.5,−10,−7.5,x
; The mean is 11.5
.
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
x = 51
Step-by-step explanation:
If the mean = 11.5, then that means all numbers added together divided by four = 11.5. Let's write this algebraically:
[tex]\frac{12.5+(-10)+(-7.5)+x}{4}=11.5[/tex]
Now, let's solve for x:
[tex]12.5-10-7.5+x=11.5(4)[/tex]
[tex]-5+x=46[/tex]
[tex]x=51[/tex]
I hope this helps!
HELPPPPPPPPPPPPPPPPPPP
Answers
Answer:
i dont know use the internet
Step-by-step explanation:
this is the right way
Researchers randomly surveyed people at two amusement parks, Funland and Thrillville, to find out how many times they visit the park per year. Following are the data from the two surveys.
Funland: 4,1,2,1,5,6,3,2,4,3,2,6,1,3,2
Thrillville: 8,6,5,7,2,5,4,2,1,9,3,8,3,7,5,2,9,4,2,8
How many more times per year, on average, do people visit Thrillville than Funland?
Answers
On average, people visit Thrillville 2 more times per year than Funland.
AveragesTo determine how many more times per year, on average, do people visit Thrillville than Funland, the following calculation must be performed:
Funland: 4,1,2,1,5,6,3,2,4,3,2,6,1,3,2 = 4545 / 15 = 3Thrillville: 8,6,5,7,2,5,4,2,1,9,3,8,3,7,5,2,9,4,2,8 = 100100 / 20 = 55 - 3 = 2Therefore, on average, people visit Thrillville 2 more times per year than Funland.
Learn more about averages in https://brainly.com/question/2426692
The least common denominator of 7/12, 1/3, and 3/4 is
Answers
Answer:
12.
Step-by-step explanation:
3, 4, and 12 all divide into 12 .
Geometry question pic Below
Arc JK = ______°
M<1 = ______°
Answers
Answer:
Step-by-step explanation:
Determine the solution to each linear system by using the substitution method
3x+2y=4
2x-y=5
Answers
Answer:
The solution is x = 2
Step-by-step explanation:
i) 3x+2y=4
ii) 2x-y=5
Let's isolate y for the second equation
2x-y=5
2x-5 = y
y = 2x-5
Now use this y and substitute it in the first equation.
3x+2y=4
3x + 2(2x-5) = 4
3x + 4x - 10 = 4
7x / 7 = 14 / 7
x = 2
What is the value of x?
Answers
Answer:
30 degrees
Step-by-step explanation:
because if its 60 at the bottom and 30 on the left it only makes sense that it would be 30 on the right.
Also can you mark brainlyest you dont have to thoe
Please answer this question throughly and with the work you used to answer it and I’ll give brainliest!
Answers
With the given budget, the inequality that must be used is:
$5.5*s ≤ $350
Which inequality is the correct one?
We know that the budget is $500.
Then, we know that there is a fixed cost of $150, then the budget left is:
$500 - $150 = $350
With these $350 they pay the food for the students, which costs $5.50 per student.
So the number of students that can go must be such that:
s*$5.50 ≤ $350
There says that the cost in food for the s students must be smaller than or equal to the remaining $350.
So the correct option is the second one.
If you want to learn more about inequalities, you can read:
https://brainly.com/question/18881247
Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 28.25 dollars
Answers
Answer:
y = -7.235451 x^2 + 402.5542 x - 2382.736
Is (3, 28) a solution to 4x-y=-16
Answers
Answer:
Yes
Step-by-step explanation:
4(3) - 28 = -16
12= -16 + 28
12 = 12
Hope that helps!
I need help. SO confused
Answers
Answer:
The answer would be 1/4% or 25%.
Step-by-step explanation:
The reason why is that there were 20 students in the class. 5 people wanted to work in groups. That is 25% of the students. That is why 25% or 1/4% is your answer.
vertically stretched by a factor of 2, then translated
4 units left and 1 unit down
Answers
A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:
g(x) = 2*f(x + 4) - 1
How to write the given transformation?
For a general function f(x), a vertical stretch of scale factor K is written as:
g(x) = K*f(x).
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:
g(x) = 2*f(x)
Then we translate it 4 units left:
g(x) = 2*f(x + 4)
Then we translate 1 unit down:
g(x) = 2*f(x + 4) - 1
This is the equation for the transformation.
If you want to learn more about transformations, you can read:
https://brainly.com/question/4289712
I have already done Number one but I need help with 2. Please help when you find time to!
Answers
Answer:
Step-by-step explanation:
Formulae
Area of a triangle = 1/2 x base x height
Area of a rectangle = width x length
Question 1
Surface area of square based pyramid = area of base + 4 × area of triangle
⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)
= 36 + 168
= 204 yd²
Question 2
Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area
⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)
= 120 + 36 + 60
= 216 mm²
Extra credit question
Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas
base area = 3 × 10 = 30 mm²
triangle area = 1/2 × 3 × 2 = 3 mm²
side area = 10 × 2.5 = 25 mm²
⇒ total SA = 30 + (2 × 3) + (2 × 25)
= 30 + 6 + 50
= 86 mm²
❍ Concept :-
We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,
⠀
[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]
Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.
⠀
✰ Solution :-
⠀
1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,
⠀
[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]
⠀
2. Now, here, we can use the formula of total surface area for cuboid, i.e.
⠀
TSA = 2( lb + bh + hl )
⠀
[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
⠀
Extra Credit Question.
⠀
Here, we can find out the total surface area by finding,
⠀
Base area i.e. length x breadth ( B.A. )
Side area i.e. length x breadth ( S.A. )
triangular area = 1/2 x b x h ( T.A. )
⠀
Now,
⠀
TSA = BA + 2 x S.A. + 2 x T.A.
⠀
[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
An integer number is chosen randomly between 1 and 1000. What is the probability that the number picked is divisible by 3 or 5 (i. E. , either 3 or 5 or both)?
Answers
Answer:
Umm..... sorry but.....my answer came.......
The probability that the number picked is divisible by 3 or 5 is 0.555.
What is probability?Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.
An integer number is chosen randomly between 1 and 1000.
The number of numbers divisible by 3, which is;
[tex]\rm \dfrac{1000}{3}=3333.3 = 333[/tex]
The number of numbers divisible by 5, which is;
[tex]\rm \dfrac{1000}{5}=200[/tex]
The probability that the number picked is divisible by 3 or 5 is;
[tex]\rm Probability=\dfrac{Number \ divisble \ by \ 3+ Number \ divisble \ by \ 5}{1000}\\\\ Probability =\dfrac{333+200}{1000}\\\\Probability=\dfrac{533}{1000}\\\\Probability=0.533[/tex]
Hence, the probability that the number picked is divisible by 3 or 5 is 0.555.
Learn more about probability here;
https://brainly.com/question/14461856
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Mark and Henry win some money and share it in the ratio 1:3. Mark gets £9. How much did Henry get?
Answers
Answer:
£27
Step-by-step explanation:
1:3 = M:H
Mark gets £9
1 = £9
3: £9 x 3 = £27
Answer: the answer is £27
Step-by-step explanation: it is related to ratio if mark gets 9 so 9 times 3 . Equals to 27 . You can make criss cross way . 1 won't make the answer different. Hope it helps
Please Help! Will Give Brainlest!
Answers
Answer:
height of tress is 20 feet
Step-by-step explanation:
because tan = perpendicular/ height
we see option only 20 feet satisfy it
Answer:
Option D :- 20 feet
Step-by-step explanation:
[tex] \sf \tan ( \theta) = \frac{height}{distance} [/tex]
[tex] \rightarrow \sf \: \tan (\theta) = \frac{20}{50} [/tex]
[tex] \sf \: height \: = 20 \: ft[/tex]
Figure #3 (Round to the nearest tenth)
Volume =_____cm^3
Answers
The diameter is 4 so the radius is 2.
Pi • 2^2 • 15 = 188.496 / 2 = 94.248
BRAINLIEST FOR CORRECT ANSWER: What is the area of this figure?
Answers
if p(x)=x2+2x-5 and g(x)=x-3, what is p(x) – gx)?
Answers
Answer:
x2+x-2
Step-by-step explanation:
i had this question before
There are only blue sweets, green sweets and red sweets in a box.the ratio of the number of blue sweets to the number of green sweets is 2: 7the ratio of the number of green sweets to the number of red sweets is 3 : 1there are less than 140 sweets in the box.what is the greatest possible number of red sweets in the box? your final answer must include the words, 'red sweets'.
Answers
Answer:
According to question if we observe, number of red sweets are the least
It 's only 1%
Step-by-step explanation:
Evaluate the expression when x = 3.
x² + 6x - 3
Answers
Answer:
X=3
[tex] {3}^{2} + 6(3) - 3 \\ 9 + 18 - 3 \\ 27 - 3 \\ = 24[/tex]
help ! 50 points Savanah is shopping for planters for her new plants. Which measurement should she use to determine how much soil each planter will hold?
A. Area
B. Depth
C. Perimeter
D. Volume
Answers
HELP NO LINKS OR TROLLING
Answers
Answer:
20.28 cm²
Step-by-step explanation:
The rectangle on the bottom is 7 cm by 2 cm.
The semicircle has a diameter of 7 cm - 1 cm - 2 cm = 4 cm
diameter = 4 cm
radius = diameter/2 = 2 cm
total area = area of semicircle + area of rectangle
total area = (1/2)πr² + LW
total area = (1/2)(3.14)(2 cm)(2 cm) + 7 cm × 2 cm
total area = 20.28 cm²
Area of rectangle
2(7)14cm²Area of semicircle
π(7-3/2)²/2(4/2)²π/24π/212.56cm²/26.28cm²Total area
6.28+1420.28cm²Which of the following is equivalent to : 3x + 6 + 2x + 2 + x
A. 5x + 8
B. 6x + 8
C. 14x
Answers
4x−4<8 AND 9x+5>23
Doing Khan Academy
HelP!!
Answers
Answer:
x<3 and x>2
Step-by-step explanation:
write the symbols this < and > to get the correct answer
Evaluate each expression.
a. 1/2(5+13)-4.5
b.(5+11)-(24-15)•(3)
c.6²+3•7-9÷3
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♫[/tex]
Let's solve ~
Expression 1[tex]\qquad \sf \dashrightarrow \: \frac{1}{2} (5 + 13) - 4.5[/tex]
[tex]\qquad \sf \dashrightarrow \: \frac{1}{2} (18) - 4.5[/tex]
[tex]\qquad \sf \dashrightarrow \: 9 - 4.5[/tex]
[tex]\qquad \sf \dashrightarrow \:4.5[/tex]
Expression 2[tex]\qquad \sf \dashrightarrow \:(5 + 11) - (24 - 15) \times 3[/tex]
[tex]\qquad \sf \dashrightarrow \:16 - (9 \times 3)[/tex]
[tex]\qquad \sf \dashrightarrow \:16 - 27[/tex]
[tex]\qquad \sf \dashrightarrow \: - 11[/tex]
Expression 3[tex]\qquad \sf \dashrightarrow \: {6}^{2} + (3 \times 7) - (9 \div 3)[/tex]
[tex]\qquad \sf \dashrightarrow \:36 + 21 - 3[/tex]
[tex]\qquad \sf \dashrightarrow \:57 - 3[/tex]
[tex]\qquad \sf \dashrightarrow \:54[/tex]
What is the relationship between the ratios? 10/24 and 5/12 Proportional Not proportional (the numbers are fractions)
Answers
Answer:
Proportional
Step-by-step explanation:
[tex]\frac{10}{24}= \frac{5}{12}[/tex] the ratio is 2:1
5 x 2 = 10
12 x 2=24
The ratios are proportional.
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!
Stay Brainy!
−Kallmekrish
Answer:
The given ratios are proportional
Step-by-step explanation:
To consider the fractions as "proportional", they must be equivalent. Let us assume that the fractions are equivalent. Then, we get;
[tex]\implies \dfrac{10}{24} = \dfrac{5}{12}[/tex]
When using cross multiplication, we get;
[tex]\implies \dfrac{10}{24} = \dfrac{5}{12}[/tex]
[tex]\implies 10 \times 12 = 24 \times 5[/tex]
When simplified, we get;
[tex]\implies 10 \times 12 = 24 \times 5[/tex]
[tex]\implies 120 = 120 \ \checkmark[/tex]
Therefore, the relationship is proportional.
PLEASE HELP ASAP
(answer as many as you can please)
a. write the first four terms of the series
b. does the series diverge or converge?
c. if the series has a sum, find the sum
Answers
Answer:
A) -4,-4/3,-4/9,-4/27
B) converge
C) no idea
I’m not entirely sure with this question, anyone can please help?
Answers
Step-by-step explanation:
3x + 4 = 72 - x
3x - x = 72 - 4
2x = 68
x = 39