Answer:
[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]
Step-by-step explanation:
We want to find the maximum and minimum values of the function:
[tex]\displaystyle f(x) = \sqrt{x + x^2} - 2\sqrt{x}[/tex]
On the interval [0, 4].
First, evaluate its endpoints:
[tex]\displaystyle \begin{aligned} f(0) &= \sqrt{(0)+(0)^2} - 2\sqrt{0} \\ &= 0 \\ \\ f(4) &= \sqrt{(4)+(4)^2} - 2\sqrt{(4)} \\ &= 2\sqrt{5} -4 \end{aligned}[/tex]
Recall that the extrema of a function occurs at its critical points; that is, where its derivative equals zero (or is undefined).
Take the derivative of both sides:
[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ \sqrt{x + x^2} - 2\sqrt{x}\right][/tex]
Differentiate:
[tex]\displaystyle \begin{aligned} f'(x) &= \frac{1}{2\sqrt{x + x^2}} \cdot (1 + 2x) - 2\left(\frac{1}{2\sqrt{x}}\right) \\ \\ &= \frac{2x+1}{2\sqrt{x+x^2}} - \frac{1}{\sqrt{x}} \\ \\\end{aligned}[/tex]
Note that the derivative is undefined at x = 0. Hence, x = 0 is a critical point.
Solve for the zeros of the derivative:
[tex]\displaystyle\begin{aligned} \frac{2x+1}{2\sqrt{x + x^2}} - \frac{1}{\sqrt{x}} &= 0\\ \\ \frac{2x+1}{2\sqrt{x}\sqrt{1 + x }} - \frac{1}{\sqrt{x}} &= 0 \\ \\ \frac{2x+1}{2\sqrt{1+x}} - 1 &= 0\\ \\ 2x + 1 &= 2\sqrt{1+x} \\ \\ 4x^2 + 4x + 1 &= 4 + 4x \\ \\ x^2 &= \frac{3}{4} \\ \\ x= \frac{\sqrt{3}}{2} \end{aligned}[/tex]
Therefore, our only two critical points are at x = 0 and x = √3/2:
Evaluate the function at x = √3/2:
[tex]\displaystyle \begin{aligned} f\left(\frac{\sqrt{3}}{2}\right) &= \sqrt{\left(\frac{\sqrt{3}}{2} \right)+ \left(\frac{\sqrt{3}}{2}\right)^2} - 2 \sqrt{\left(\frac{\sqrt{3}}{2}\right)} \\ \\ &= \frac{\sqrt{3+2\sqrt{3}}}{2}- \frac{2\sqrt[4]{3}}{\sqrt{2}} \\ \\ &\approx -0.5900\end{aligned}[/tex]
In conclusion: the exact maximum and minimum values of f on the interval [0, 4] is:
[tex]\displaystyle \text{min} = \frac{\sqrt{3+2\sqrt{3}}}{2} - \frac{2\sqrt[4]{3}}{\sqrt{2}} \text{ at } x = \frac{\sqrt{3}}{2}\text{ and } \\ \\ \text{max} = 2\sqrt{5} -4 \text{ at } x = 4[/tex]
Alguien me ayuda con esto?
Answer:
x=10
Step-by-step explanation:
10 a 8 son dos, entonces 14 ax es 4
Answer:
La explicación sería:
//////////////////////////
=> 9 * 2 + 4/2 = 20
=> 18 +2 =20
=> 20 =20
//////////////////////////
=> 5*2 + 8/2 = 14
=> 10 +4 =14
=> 14 =14
//////////////////////////
=> 3*2 + 10/2 = x
=> 6 + 5 = x
=> 11 = x
Find the value of x.
9514 1404 393
Answer:
x = 6
Step-by-step explanation:
The angle bisector divides the sides proportionally.
(6x -1)/42 = (10x +5)/78
13(6x -1) = 7(10x +5) . . . . . . . multiply by 546 = LCM(42, 78)
78x -13 = 70x +35 . . . . . . . . eliminate parentheses
8x = 48 . . . . . . . . . . . . . . . . add 13-70x
x = 6 . . . . . . . . . . . . . . . . . divide by 8
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?
Answer:
6(3) - 4 - 3²
Step-by-step explanation:
(g - f) = 6x - (4 - 2x²)
= 6x - 4 - 2x²
and when we replace x with 3 ,it will be
6(3) - 4 - 3²
hope this helps
Answer:
Basically what the person on top of me said
Step-by-step explanation:
Got it right !
On the first day of December, 34,789 people went to the mall. On the second day 63,587 people went to the mall. How many people went to the mall over the two days
Answer:
98376
Step-by-step explanation:
What the answer I don’t get Mary at all
Answer:
1
Step-by-step explanation:
By order of operations, we first evaluate the parentheses, which is 2 * 1 = 2. We then evaluate the brackets, which are 3 / 2 = [tex]\frac{3}{2}[/tex]. Finally, [tex]\frac{3}{2}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{6}{6}[/tex] or 1.
Define a variable and write an inequality for each problem. Then solve.
15. Nineteen more than a number is less than 42.
16. The difference of three times a number and 16 is at least 8.
17. One half of a number is more than 6 less than the same number.
18. Five less than the product of 6 and a number is no more than twice that same number.
Answer:
15) n+19<42
16) 3n-16 (less or equal) 8
17) n/2 > n-6
18) 6n-5<2n
Step-by-step explanation:
Plsssssssssssss help me
Find the linear function f if f^-1(2)=-1 and f^-1 (-9)=3
Answer:
[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]
Step-by-step explanation:
We want to find the linear function given that:
[tex]f^{-1}(2) = -1\text{ and } f^{-1} (-9) = 3[/tex]
Recall that by the definition of inverse functions:
[tex]\displaystyle \text{If } f(a) = b\text{ then } f^{-1}(b) = a[/tex]
In other words, f(-1) = 2 and f(3) = -9.
This yields two points: (-1, 2) and (3, -9).
Find the slope of the linear function:
[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(-9) - (2)}{(3) -(-1)} = -\frac{11}{4}[/tex]
From point-slope form:
[tex]\displaystyle y - (2) = -\frac{11}{4}( x- (-1))[/tex]
Hence:
[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]
We can simplify if desired:
[tex]\displaystyle f(x) = -\frac{11}{4}x -\frac{3}{4}[/tex]
simplify 5 p - 3 - (1 + p) +( 2 - p)
Answer:
3p-2
Step-by-step explanation:
................
Answer:
3p - 2
Step-by-step explanation:
[tex]5p - 3 - (1 + p) + (2 - p)[/tex]
[tex]5p - 3 - 1 - p + (2 - p)[/tex]
[tex]5p - 3 - 1 - p + 2 - p[/tex]
[tex]5p - 1p - p[/tex][tex]5p - 1p - 1p[/tex][tex](5 - 1 - 1)p[/tex][tex] = 3p[/tex][tex] - 3 - 1 + 2[/tex]➡️ [tex] - 4 + 2[/tex]
➡️ [tex] = - 2[/tex]
[tex] = 3p - 2[/tex]
What is the volume of the rectangular solid?
12 cubic feet
15 cubic feet
5 ft
25 cubic feet
50 cubic feet
2 ft
5 ft
Mark this and retum
Save and Exit
Next
Submit
Answer:
I need to see the rectangular solid
what is the zero turn for the arithmetic sequence 128,96,64,32
You are falling by [tex]32[/tex],
[tex]128, 128 - 32, 128 - 32\cdot2,\dots[/tex]
In general your sequence is defined as,
[tex]a_n=128-32\cdot n[/tex] where [tex]0\leq n \lt\infty[/tex].
The question is at which [tex]n[/tex] does the value [tex]a_n=0[/tex].
If you divide [tex]128[/tex] with [tex]32[/tex] you get the number of steps needed to stuff [tex]128[/tex] with [tex]32[/tex], [tex]4[/tex].
If you plug in [tex]n=4[/tex], you get [tex]a_4=128-32\cdot4[/tex], since [tex]32\cdot4=128[/tex] you get [tex]a_4=0[/tex].
The zero turn of the arithmetic sequence is thus at [tex]n=4[/tex].
Hope this helps :)
How do Curves A and B compare to each other with respect to f and f ′?
The answer cannot be determined.
f: Curve B, f ′: Curve A
f: Curve A, f ′: Curve B
Neither Curve A nor Curve B are derivatives of each other.
It's likely that curve A is f and curve B is f '.
The points where curve B crosses the horizontal axis correspond to the extrema of curve A at around 0 and 0.45, and the extremum of curve B corresponds to the inflection point of curve A at around 0.2. These observations are consistent with the first and second derivative tests.
Find the differential of the function w=x^(4)sin(y^(4)z^3)
Step-by-step explanation:
[tex]w = x^4\sin(y^4z^3)[/tex]
The differential [tex]dw[/tex] is
[tex]dw = 4x^3\sin(y^4z^3)dx [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(4y^3z^3)dy [/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+ x^4\cos(y^4z^3)(3y^4z^2)dz[/tex]
Are these answers correct? Thxxx
Which of the following is equivalent to?
Answer:
Answer is 1/6
Step-by-step explanation:
[tex] {36}^{ - \frac{1}{2} } \\ = \frac{1}{ {36}^{ \frac{1}{2} } } \\ \\ = \frac{1}{ \sqrt{36} } \\ \\ = \frac{1}{6} [/tex]
Jaya's mother is 5 years more than three times her age. Find Jaya's age if her mother is 44 years old.
Answer:
Jaya is 13 years old.
Step-by-step explanation:
Let's assume Jaya's age to be x years old.
Jaya's mothers age is (3*x)+5.
3x+5=44
3x=39
x=13.
Two jets leave an airbase at the same time and travel in opposite directions, One jet travels 71mi/h faster than the other. If two jets are 7014 miles apart after 6 hours what is the speed of each jet?
jet1 = 549 mi/h
jet2 = 620 mi/h
x= jet1
x + 71 = jet2
6 hours
6 * x
6 * x + 71
6x + 6x + 426 = 7014
12x = 7014 - 426
12x = 6588
x = 6588/12
x= 549
x + 71 = 620
wyzant
Help with this please now
Answer:
ok dude
Step-by-step explanation:
Wʜᴇʀᴇ ɪs ǫᴜᴇsᴛɪᴏɴ?
Answer:
what help l don't understand please sorry I didn't help you explain your problem l will help you
Critical Thinking Point M is the midpoint of AB. The coordinates of point A are
(-8, 3) and the coordinates of Mare (–2, 1). What are the coordinates of point B?
Answer:-1,4
Step-by-step explanation:
Use the diagram to the right.
If AD = 17 and AC = 2y - 6, find the value of y. Then find AC
and DC.
Step-by-step explanation:
if AD =17,then Dc is also 17 because from the diagram,it is given that AD=DC.
And because AD and DC are equal,it means AC = AD +DC,therefore AC = 17+17,AC =34
AC=2y-6
therefore
34=2y-6
28=2y and y=14
Answer:
Step-by-step explanation:
A perpendicular bisector runs through the middle of a line segment and splits into
Answer:
B two congruent pieces
Step-by-step explanation:
Perpendicular means at a 90 degree angle
bisector means it divides in it half, into two equal pieces
The width of a rectangle measures (2p - 9q) centimeters, and its length measures
(7p - 10q) centimeters. Which expression represents the perimeter, in centimeters,
of the rectangle?
Given Data : Length = (7p - 10q) and Breadth = (2p - 9q)
Calculation :
⟹ Perimeter = 2(Length + Breadth)
⟹ Perimeter = 2(7p - 10q + 2p - 9q)
⟹ Perimeter = 2(9p - 19q)
⟹ Perimeter = 18p - 38q centimetres
Answer : 18p - 38q centimetresThe required perimeter of the rectangle is 18p - 38q centimeters.
It is required to find the required perimeter of the rectangle.
What is rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
Given:
width of a rectangle = (2p - 9q) centimeters,
length measures= (7p - 10q) centimeters.
We know that
⟹ Perimeter = 2(Length + Breadth)
By put the value width and length in perimeter we get,
⟹ Perimeter = 2(7p - 10q + 2p - 9q)
⟹ Perimeter = 2(9p - 19q)
⟹ Perimeter = 18p - 38q centimeters
Therefore, the required perimeter of the rectangle is 18p - 38q centimeters.
Learn more about rectangle here:
brainly.com/question/24437900
#SPJ2
Solve the following inequality: |x – 4|> 6
Answer:
x>10 or x< -2
Step-by-step explanation:
There are two solutions, one positive and one negative, remembering to flip the inequality for the negative
x-4 >6 or x-4 < -6
Add 4 to each side
x-4+4 > 6+4 or x-4+4 < -6+4
x>10 or x< -2
Jerimiah can type 300 words in 1/5 of an hour. How many words can he type in 2/3 of an hour
Answer:
Answer:
If: 153 words = 3 minutes :
Then: 1 minute = 153 3 = 51 words
10 minutes is:
10 × 51 = 510
Ben can type 510 words in 10 minutes
What is 12 divided by 2/5?
Answer:30
Step-by-step explanation:
Need help!!!!
Will earns $6.50 per hour and time-an-a-half for all hours over 40.
Find his weekly pay if he worked 47 hours.
a. $305.50
b. $328.25
c. $269.75
d. $68.25
Answer:
b
Step-by-step explanation:
In the following expression, both A and B are variables that can take positive values.
A+2/B
Which of these actions will cause the expression's value to increase?
Choose 2 Answers
A.
Keeping A constant and increasing B
B.
Keeping A constant and decreasing B
C.
Increasing A and keeping B constant
D.
Decreasing A and keeping B constant
I think the answer is A and C!
Answer:
B) Keeping A constant and decreasing B
C) Increasing A and keeping B constant
Step-by-step explanation:
I did it on Khan Academy :)
If f(x)= 2|x|+3x, then the value of f(-1) is
Answer:
-1
Step-by-step explanation:
f(-1) = 2|-1| + 3(-1)
|-1| = 1
=> f(-1) = 2(1) - 3
=> f(-1) = 2 - 3
=> f(-1) = -1
Supplementary angles are pairs of angles whose measures total 180º. Determine the measure of
supplementary to an angle with a measure of 92°
Hi there!
»»————- ★ ————-««
I believe your answer is:
88°
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
As mentioned in the question, supplementary angles add up to 180°.⸻⸻⸻⸻
[tex]\boxed{\text{Setting Up An Equation...}}\\\\a + 92 = 180\\----------\\ a - \text{Unknown angle measure.}\\----------\\\rightarrow a + 92 - 92 = 180 - 92\\\\\rightarrow \boxed{ a = 88}[/tex]
⸻⸻⸻⸻
The unknown angle measurement should be 88°.
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
7/9+6/8+6/3=
I really need the answer
Answer:
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:
Take it in steps. First, find 7/9+6. Then we'll find 8+6/3, and, finally, we'll divide the two answers.
1:
7/9+6 = 7/15
2:
8+6/3 = 14/3
3:
[tex]\frac{\frac{7}{15}}{\frac{14}{3}}[/tex] or [tex]\frac{7/15}{14/3}[/tex]
Then take that in chunks: 7/14 and 15/3.
7/14 = 1/2
15/3 = 5/1
Use those to rewrite it as [tex]\frac{1/5}{2/3}[/tex].
1/5 = .2
2/3 ≈ .6667 so we'll keep writing it as 2/3
[tex]\frac{\frac{.2}{2}}{3}[/tex]
.2/2 = .1, so:
[tex]\frac{.1}{3}[/tex] = [tex]\frac{1}{30}[/tex]
