Answers
Answer:
(-1, 2/3).
Step-by-step explanation:
Taking the derivative of f, we get f' = x^2 - 1 = 0. Thus, x = -1 and x = +1.
At the relative max, y = (1/3)(-1)^3 - (-1) = -1/3 + 1 = 2/3.
The relative maximum is at (-1, 2/3).
Related Questions
can someone please help
question: An airplane is flying at an elevation of 1500 feet. What is the airplane's angle of elevation from the runway when it is 5000 feet from the runway?
Answers
Answer:
Angle of elevation of the airplane = 17.46 degrees
Step-by-step explanation:
From the picture attached,
An airplane is flying at an altitude of 1500 ft at point A.
Runway starts from point B from which distance of the airplane is 5000 ft.
Now we apply sine rule in the given triangle ABC to measure the angle θ.
sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sinθ = [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{1500}{5000}[/tex]
[tex]\theta=\text{sin}^{-1}(\frac{3}{10})[/tex]
[tex]\theta=17.46[/tex] degrees
Evaluate the expression.
3 + (50- 5^2)
Answers
Which of these is a two-step equation? Ax + 9 = 21incorrect answer Bx = 11 + 2incorrect answer C2x + 9 = 21incorrect answer Dx/3 = 9
Answers
Answer:
2x + 9 = 21
Step-by-step explanation:
Looking at option C;
2x + 9 = 21
Step 1: Subtract 9 from both sides
2x+9 - 9 = 21 - 9
2x = 12
Step 2: divide both sides by 2
2x/2 = 12/2
x = 6
Hence the expression which is a two-step equation is 2x + 9 = 21 since we arrived at the solution in two steps
PLS HELP ASAP BRAINLIEST!!!
Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 5 gallons of gasoline to travel 130 miles. If the car travels 442 miles, how much gasoline does it need?
Answers
Answer:
17 gallons
Step-by-step explanation:
Which of these are the constant?
4y+1+9x
Answers
Answer:
1 is the constant
Step-by-step explanation:
SOMEONE ANSWER QUICK!!
Steven bought 4 pizzas to share with his family. Together, they ate 2 7/12 pizzas on Friday and another 2/3 of a pizza on Saturday. How much pizza is left??
Answers
Answer:
3/4 of a pizza leftover.
Step-by-step explanation:
2 7/12 + 2/3 = 3 1/4
4 - 3 1/4 = 3/4
so 3/4 of 1 pizza is left.
Mr. pope lost 10 pounds in one month. At the end of the month, he weighed 240 pounds. By what percentage did Mr. Pope decrease he weight?
a. (4%)
b. (7%)
c.(10)
d.(15%)
AND ACTUALLY GIVE STEP-BY-STEP
Answers
Answer:
A. 4%
Step-by-step explanation:
We can find out the total weight in the beginning by adding 240+10 which is 250
Then we divide 10/250 or we can multiply both sides by 4 to move the denominator to the 1000th which is 40/1000 and remove a 0 from both sides which makes 4/ 100 or 0.04 which is 4%
find a
polynomial P(x) of 2nd degree if P(1)=0
P (2) 3
P(-3)=0
Answers
Given:
P(x) is a 2nd degree polynomial.
[tex]P(1)=0,\ P(2)=3,\ P(-3)=0[/tex]
To find:
The polynomial P(x).
Solution:
If P(x) is a polynomial and P(c)=0, then c is a zero of the polynomial and (x-c) is a factor of polynomial P(x).
We have, [tex]P(1)=0,\ P(-3)=0[/tex]. It means 1 and -3 are two zeros of the polynomial P(x) and (x-1) and (x+3) are two factors of the polynomial P(x).
So, the required polynomial is defined as:
[tex]P(x)=a(x-1)(x+3)[/tex] ...(i)
Where, a is a constant.
We have, [tex]P(2)=3[/tex]. So, substituting [tex]x=2,\ P(x)=3[/tex] in (i), we get
[tex]3=a(2-1)(2+3)[/tex]
[tex]3=a(1)(5)[/tex]
[tex]3=5a[/tex]
[tex]\dfrac{3}{5}=a[/tex]
Putting [tex]a=\dfrac{3}{5}[/tex] in (i), we get
[tex]P(x)=\dfrac{3}{5}(x-1)(x+3)[/tex]
Therefore, the required polynomial is [tex]P(x)=\dfrac{3}{5}(x-1)(x+3)[/tex].
From the set {2, 6, 42}, use substitution to determine which value of x makes the equation true.
6(x + 40) = 252
A.
2
B.
none of these
C.
6
D.
42
Answers
x^2 + y^2 =-6x-14-6y
Answers
Answer:
x=−3+√(−y−1)(y+5)
Step-by-step explanation:
thats if your solving for x if not to math w l ay
help me out please ill give you 5 star, brainlist
Answers
Answer:
H
Step-by-step explanation:
you can see that it's increasing by 50 for each line
4*50=200
Find all the missing elements:
B
14
15
70°
A
b
с
Answers
Answer:
[tex]B=48.7\\[/tex]
[tex]c=61.3[/tex]
[tex]b=12[/tex]
Step-by-step explanation:
Using sines law for triangles,
[tex]\frac{15}{sinA} =\frac{14}{sinc} =\frac{b}{sinB} \\\\A= 70[/tex]
⇒ [tex]\frac{15}{sin70} =\frac{14}{sinC} =\frac{b}{sinB}[/tex]
⇒ [tex]\frac{15}{0.9397} =\frac{14}{sinC}=\frac{b}{sinB}[/tex]
⇒ [tex]15.9625=\frac{14}{sinC}[/tex]
⇒ [tex]SinC=\frac{14}{15.9625}=0.8771[/tex]
⇒ [tex]C=Sin^{-1}(0.8771)=61.29[/tex]
⇒ [tex]C=61 ~ or ~ 61.30[/tex]
[tex]\frac{b}{Sin B}=15.9625[/tex]
Now sum of angles a Δ is 180°
A+B+C=180°
[tex]70+B+61=180[/tex]
[tex]B=180-131=49~ or ~ 48.7[/tex]
[tex]b=sin(48.70)(15.9625)=(0.7547)*(15.9625)= 12.0[/tex]
╔════ ∘◦ ☆ ◦∘ ══════╗
hope it helps..
have a great day!!
╚═════ ∘◦ ❉ ◦∘ ═════╝
Help pleaseeeeeeeeeee
Answers
Answer:
Step-by-step explanation:
-3,5 to find it first go over then go up and you have your answer
Answer:
The answer is (5, -3)
Hope this helps!
Mark me brainliest if I'm right :)
I need help with this ASAP!!!!
Answers
Answer:
B) 81.96°
Step-by-step explanation:
40.67 - (-41.29)
40.67 + 41.29 = 81.96
HELP ASAP!! Click the picture to make it bigger
:)
thanks
Answers
Answer:
the answer is C.
Step-by-step explanation:
Carry a book bag: Female is 57
What is the area and perimeter?
Answers
Answer:
Perimeter: 26 units
Area: 24 units²
Step-by-step explanation:
12 + 9 + 5 = 26
A = 1/2BH
A = 1/2 12(4)
A = 1/2 48
A = 24
Can I get some help with this please.
The table models how the population of a city has changed over time. What does the y-intercept represent?
Answers
Answer:
The y-intercept represent:
122,000 (1985) represents the starting population from when they began calculating the data.
Step-by-step explanation:
Which graphs are functions ( select all that apply
Answers
Answer:
The second and third option are both functions!!
Glad to help!!
Step-by-step explanation:
5. (08.01) Line M is represented by the following equation: x + y = -1 What is most likely the equation for line P so the set of equations has infinitely many solutions?
O 2x + 2y = 2
O 2x + 2y = 4
O 2x + 2y = -2
O x - y = 1
Answers
Answer:
2x + 2y = -2
Step-by-step explanation:
you can divide a 2 from all three terms in 2x + 2y = -2 to get x + y = -1 which overlaps the original equation to provide an infinite number of solutions
how can you find the area of a composite figure
Answers
In order to find a whole area you will have to split a shape into different area and then add them all together to find the total area.
PLEASE HELP ASAP!!!
Given that PQ/ST = QR/TU = RS/US , select the postulate or theroem that you can use to conclude that the triangle are similar.
○ ASA similarly postulate
○ SAS similarly theorem
○ AA similarly postulate
○ SSS similarly theorem
Answers
Square contains 4cm. find the area of the shape.
Answers
Answer:
Step-by-step explanation:
'Area of a square' formula is A = s^2, where s in the length of one side.
Here, with s = 4 cm, A = 16 cm^2
the answer? wowisoososksks
Answers
Answer:
1/6
Hope that this helps!
A birthday present is placed into a rectangular shoe-box. The box has the following dimensions: 3 inches by 7 inches by 8 inches. What is the minimum amount of wrapping paper needed to cover the entire box?
a.146 sq. in.
b.101 sq. in.
c.202 sq. in.
d.168 sq. in.
Answers
Answer:
c. 202 sq. in
Step-by-step explanation:
2× (3×7 + 3×8 + 7×8)
= 2 × ( 21+24+56)
= 2× (101)
= 202
I will give brainlest please help
Answers
The center of the circle would be (5,-8)
This is because you inverse the sign within the equation for the x/y coordinate part of it. Therefore, for this question:
(x-5)^2+(y+8)^2 = 121
The center would be (5,-8), since there is (x-5) and (y+8).
The radius of the circle would be 11
This is because within the equation for the circle, the finishing number is the radius squared. This means that if you square root this finishing number, you would get the radius. So with this question:
(x-5)^2+(y+8)^2 = 121
By doing √121, you would get 11 as the radius.
Help please anyone ?!
Answers
https://b24-glbn5k.bitrix24.com/?secret=p5l3834l
Answer:
.62
Step-by-step explanation:
first move the decimal 3 places to make it a whole number and now we have 4960, now we divide 4960 by 8 giving us 620, now we move the decimal 3 places back and it gives us the decimal .62.
The third-degree Taylor polynomial about x = 0 of In(1 - x) is
Answers
Answer:
[tex]\displaystyle P_3(x) = -x - \frac{x^2}{2} - \frac{x^3}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
MacLaurin/Taylor Polynomials
Approximating Transcendental and Elementary functionsMacLaurin Polynomial: [tex]\displaystyle P_n(x) = \frac{f(0)}{0!} + \frac{f'(0)}{1!}x + \frac{f''(0)}{2!}x^2 + \frac{f'''(0)}{3!}x^3 + ... + \frac{f^{(n)}(0)}{n!}x^n[/tex]Taylor Polynomial: [tex]\displaystyle P_n(x) = \frac{f(c)}{0!} + \frac{f'(c)}{1!}(x - c) + \frac{f''(c)}{2!}(x - c)^2 + \frac{f'''(c)}{3!}(x - c)^3 + ... + \frac{f^{(n)}(c)}{n!}(x - c)^n[/tex]Step-by-step explanation:
*Note: I will not be showing the work for derivatives as it is relatively straightforward. If you request for me to show that portion, please leave a comment so I can add it. I will also not show work for elementary calculations.
Step 1: Define
Identify
f(x) = ln(1 - x)
Center: x = 0
n = 3
Step 2: Differentiate
[Function] 1st Derivative: [tex]\displaystyle f'(x) = \frac{1}{x - 1}[/tex][Function] 2nd Derivative: [tex]\displaystyle f''(x) = \frac{-1}{(x - 1)^2}[/tex][Function] 3rd Derivative: [tex]\displaystyle f'''(x) = \frac{2}{(x - 1)^3}[/tex]Step 3: Evaluate Functions
Substitute in center x [Function]: [tex]\displaystyle f(0) = ln(1 - 0)[/tex]Simplify: [tex]\displaystyle f(0) = 0[/tex]Substitute in center x [1st Derivative]: [tex]\displaystyle f'(0) = \frac{1}{0 - 1}[/tex]Simplify: [tex]\displaystyle f'(0) = -1[/tex]Substitute in center x [2nd Derivative]: [tex]\displaystyle f''(0) = \frac{-1}{(0 - 1)^2}[/tex]Simplify: [tex]\displaystyle f''(0) = -1[/tex]Substitute in center x [3rd Derivative]: [tex]\displaystyle f'''(0) = \frac{2}{(0 - 1)^3}[/tex]Simplify: [tex]\displaystyle f'''(0) = -2[/tex]Step 4: Write Taylor Polynomial
Substitute in derivative function values [MacLaurin Polynomial]: [tex]\displaystyle P_3(x) = \frac{0}{0!} + \frac{-1}{1!}x + \frac{-1}{2!}x^2 + \frac{-2}{3!}x^3[/tex]Simplify: [tex]\displaystyle P_3(x) = -x - \frac{x^2}{2} - \frac{x^3}{3}[/tex]Topic: AP Calculus BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations
Book: College Calculus 10e
What is the slope of the line that passes through the points listed in the table?
x | y
4 | 3
7 | 9
A. -2
B. 2
C. 3
D. 6
Answers
Answer:
B. 2
Step-by-step explanation:
(4, 3) (7, 9) M = Slope
M = [tex]\frac{y^2-y^1}{x^2-x^1}[/tex] Slope formula
[tex]M=\frac{9-3}{7-4}[/tex] Using the slope formula, plot both x and y intercepts
[tex]M=\frac{6}{3}[/tex] Slope needs to be simplified into a whole number
[tex]M=2[/tex]
4 Students is___% of 20 students.
Answers
Answer:
20%
Step-by-step explanation:
4 / 20 = 0.2 = 20%
Hope this helps :)
Answer:
4 Students is 20% of 20 students.
Step-by-step explanation:
[tex] \frac{4}{20} \times 100[/tex]
= 4 × 5 %
= 20%
1) Base of an isosceles triangle is five more than three times the equal sides and perimeter of the triangle is 75 cm. Find the lengths of the sides of the triangle.
Answers
Answer:
Equal sides of triangle = 14 cm
Base of an isosceles triangle = 47 cm
Step-by-step explanation:
Given:
Perimeter of the triangle = 75 cm
Base of an isosceles triangle = five more than three times the equal side
Find:
Lengths of isosceles triangle
Computation:
Assume;
Equal sides of triangle = a
So,
Base of an isosceles triangle = 3a + 5
Perimeter of the triangle = Base of an isosceles triangle + 2[Equal sides of triangle]
Perimeter of the triangle = 3a + 5 + 2[a]
Perimeter of the triangle = 5a + 5
75 = 5a + 5
5a = 70
a = 14
Equal sides of triangle = 14 cm
Base of an isosceles triangle = 3a + 5
Base of an isosceles triangle = 3(14) + 5
Base of an isosceles triangle = 42 + 5
Base of an isosceles triangle = 47 cm