This is for AP CALCULUS. I really need help on this. I’m trying to find the first and second derivative of these three functions.
Answers
Review Material:
[tex]\sqrt[n]{x^m} = x^{\frac{m}{n}}[/tex]
[tex]\frac{d}{dx}[x^n]=nx^{n-1}\\[/tex]
[tex]\frac{d}{dx}[\sin(x)]=\cos(x)\\[/tex]
[tex]\frac{d}{dx}[\cos(x)]=-\sin(x)\\[/tex]
[tex]\frac{d}{dx}[constant]=0\\[/tex]
Step-by-step explanation:
(a)
[tex]F(x) = -2\cos(x) +x^{\frac{4}{3}} -3e\\ \text{Note: 3e is a constant}\\F'(x) = 2\sin(x) + \frac{4}{3}x^{\frac{1}{3}}\\F''(x) = 2\cos(x) + \frac{4}{9}x^{-\frac{2}{3}}[/tex]
(b)
[tex]F(x) = x^{-3} + \frac{1}{2}x^2-\sin(x)\\F'(x)=-3x^{-4} + x - \cos(x)\\F''(x) = 12x^{-5} + 1 + \sin(x)[/tex]
(c)
[tex]F(x) = 2x^{-3}+x^{\frac{3}{4}}-4x\\F'(x) = -6x^{-4} + \frac{3}{4}x^{-\frac{1}{4}}-4\\F''(x)= 24x^{-5} - \frac{3}{16}x^{-\frac{5}{4}}[/tex]
Related Questions
Rita has a circular hot tub. the hot tub has a circumference of 25.12 feet. it is 3.5 feet deep.
how much water can the hot tub hold?
Answers
Volume is a three-dimensional scalar quantity. The amount of water that the tub can hold is 4,981.75 litres.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the circumference of the tub is 25.12 feet, therefore, the radius of the circumference of the tub will be,
Circumference = 2πr
25.12 = 2×π×r
r = 3.9979ft ≈ 4ft
Now, the volume of the tub will be,
Volume = πr²h = π×(4²)×3.5 = 175.929 ft³
Since 1 ft³ is equal to 28.3168 litres, therefore, the amount of water that a tub can store is
Volume of water = 175 × 28.3168 = 4,981.75 litres
Hence, the amount of water that the tub can hold is 4,981.75 litres.
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find x - and - y intercepts of the following equation. a. 4x - 3y = 12 b. y = 1/3x c. y = 2x + 5 d. y = 6
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✒️ Equation
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A. To find the x - intercept, let y = 0.
[tex]\tt \: \: \large \tt \: \begin{array}{|c|} \hline \tt \: 4x \: - \: 3y \: = \: \tt\underline{\green{ 12 }} \\ \tt 4x \: - \: 3(0) \: = \: \tt\underline{\blue{ 12 }} \\ \tt4x \: - \: 0 \: = \: \tt\underline{\pink{ 12 }} \\ \tt \tt\underline{\red{ \: x \: = \: 3 }} \\ \\ \tt \: x ↬\: the \: intercept\\ \tt\\ \hline\end{array} \: \\ [/tex]
[tex] \\ [/tex]
To find the y - intercept, let x = 0
[tex]\large \tt \: \begin{array}{|c|} \hline \tt 4x \: - \: 3y \: = \: \tt\underline{\green{ 12 }} \\ \tt 4(0) \: - \: 3y \: = \: \tt\underline{\blue{ 12 }} \\ \tt \: 0 \: - \: 3y \: = \: \tt\underline{\pink{ 12 }} \\ \tt \tt\underline{\red{ y \: = \: - 4 }} \\ \\ \tt \: x ↬\: the \: intercept \\ \ \\ \hline\end{array} \: [/tex]
[tex] \\ [/tex]
B. Replace x with 0 and solve for y. Then replace y with 0 and solve for x.
[tex]\large \tt \: \begin{array}{|c|} \hline \tt y \: - \: intercept: \: y \: = \: \frac{1}{3}(0) \\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \tt = \tt\underline{\red{ 0 }} \\ \\ \tt \: x \: and \: y ↬ intercepts: (0,0)\\ \\ \tt \: x \: ↬ \: intercepts: \: 0 = \: \frac{1}{3} x \\ \quad\quad \quad \quad\quad\quad\quad\quad\quad \: \tt \tt\underline{\red{ \: 0 \: = \: x }} \ \\ \\ \hline\end{array} \\ [/tex]
[tex] \\ [/tex]
The equation in b is a linear equation in the form y = mx, where m is any real number. the graph of any equation in the form y = mx is always a line that passes through the origin, which means that both the x - and - y - intercepts are (0,0).
[tex]\large \tt \: \begin{array}{|c|} \hline \tt intercept \: for \: m \: of \: y \: = \: \tt\underline{\red{ mx }} \\ \hline\end{array}[/tex]
[tex] \\ [/tex]
C. Replace y with 0, then solve for the x.
[tex]\large \tt \: \begin{array}{|c|} \hline \tt x ↬ \: intercept : \: 0 \: = \: 2x \: \ + 5 \\ \\ \tt - 5 \: = \: 2x\\ \\ \tt \: \frac{ - 5}{2} \: = \: x\\ \\ \tt \: x \: ↬ \: intercept \ \\ \hline\end{array}[/tex]
Now, replace x with 0, and then solve for y.
[tex]\large \tt \: \begin{array}{|c|} \hline \tt y ↬ \: intercept: \: y \: = \: 2(0) \: + \: 5 \\ \\ \tt \: y \: = \: 0 \: + \: 5 \\ \\ \tt \: y \: = \: 5 \\ \\ \tt y ↬ \: intercept \ \\ \\ \hline\end{array}[/tex]
The equation in 11c is written in the form y = mx + b. note than in the form, when x is replaced by 0 to find the y↬intercept. you are left with the constant b.
[tex]\large \tt \: \begin{array}{|c|} \hline \tt \: the \: y ↬ intercept \: of \: y \: = \: mx \: + \: b \\ \hline\end{array}[/tex]
If the equation is in the form y = mx + b, where m and b are real numbers, then the y ↬intercept is b.
[tex] \\ [/tex]
D. Remember that the graph of y = 6 is horizontally line parallel to the x axis that passes through the y axis at (0,6). since the line is parallel to x axis, it will not incest tha x-axis. Hence, there is no x ↬ intercept.
[tex] \\ \\ \\ [/tex]
[tex]\pmb{(ノ‥)ノ}\qquad\qquad\qquad\qquad\boxed{\tt{[05-12-2022]}} \\ \qquad\qquad\qquad\qquad\qquad\qquad\boxed{\tt{[03:11 \: am]}}[/tex]
A train left a station at noon going at 40 mph. A second train left at 3 pm going in thte same direction at 6o mph. At what time iwll the second train catch up with the first
Answers
Answer:
9PM
Step-by-step explanation:
3pm - 40x3=120 Miles Travelled (Noon Train)
3pm - 60x0=0 Miles Travelled (3pm Train)
4pm - 40x4=160 Miles Travelled (Noon Train)
4pm - 60x1=60 Miles Travelled (3pm Train)
5pm - 40x5=200 Miles Travelled (Noon Train)
5pm - 60x2=120 Miles Travelled (3pm Train)
6pm - 40x6=240 Miles Travelled (Noon Train)
6pm - 60x3=180 Miles Travelled (3pm Train)
7pm - 40x7= 280 Miles Travelled (Noon Train)
7pm - 60x4=240 Miles Travelled (3pm Train)
8pm - 40x8 = 320 Miles Travelled (Noon Train)
8pm - 60x5=300 Miles Travelled (3pm Train)
9pm - 40x9 = 360 Miles Travelled (Noon Train)
9pm - 60x6= 360 Miles Travelled (3pm Train)
4.
Suppose events A and B are independent and P(A and B) is 0.2
Which statement could be true?
(1) P(A) = 0.4, P(B) = 0.3, P(A or B) = 0.5
(2) P(A) = 0.8, P(B) = 0.25
(3) P(A/B) = 0.2, P(B) = 0.2
(4) P(A) = 0.15, P(B) = 0.05
Answers
Answer: answer choice 2) P(A) = 0.8, P(B) = 0.25
Step-by-step explanation:
The True statement is P(A) = 0.8, P(B) = 0.25.
The correct option is (B).
What is Conditional Probability?Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
1. 0.4 ·0.3≠ 0.2,
2. 0.8 · 0.25 = 0.2
3. P(A|B)= P(A)= 0.2
0.2 ≠ 0.2 · 0.2
4. 0.2 ≠ 0.15 · 0.05
Hence. the only condition is satisfied is (B).
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please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answers
Answer:
6.5
Step-by-step explanation:
9.1^2-6.4^2 is 41.85
square root of that is 6.469...
Solve the following...
[tex]1 \cfrac{1}{5} \times 2\cfrac{1}{3} [/tex]
Answers
Let's see
[tex]\\ \rm\Rrightarrow 1\dfrac{1}{5}\times2\dfrac{1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6}{5}\times \dfrac{7}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6(7)}{5(3)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{42}{15}[/tex]
[tex]\\ \rm\Rrightarrow2 \dfrac{12}{15}[/tex]
A prism has a volume of 125 cubic inches. The base measures 5 in x 5 in What is the height? a. 10 inches b. 25 inches c. 5 inches d. 125 inches
Answers
Answer:C
Step-by-step explanation:First multiply 5*5=25 then divide 125/5 = 5
What is the volume of a sphere with a radius of 6 mm? sphere v = four-thirds pi r cubed v = 216pi mm3 v = 288pi mm3 v = 512pi mm3 v = 648pi mm3
Answers
Answer:
[tex]V =288 \pi \ mm^3[/tex]
Step-by-step explanation:
[tex]V =\frac{4}{3} \pi r^{3}[/tex]
[tex]=\frac{4}{3} \pi \left( 6\right)^{3}[/tex]
[tex]=\left( \frac{4}{3} \right) \times \pi \times 216[/tex]
[tex]=\left( \frac{4}{3} \right) \times 216\times \pi[/tex]
[tex]=288\times \pi[/tex]
Answer:
IT IS B
Step-by-step explanation:
SOURCE: TRUST ME BRO
What is the value of x in the equation 2/3(1/2x+12)=1/2(1/3x+14)-3
A.-24
B.-6
C.-2/3
D.0
Answers
The cosine of an angle a is 0.8. what is the value of sin (a)
Answers
Sine is opposite side over hypotenuse
You need 2 values to solve this.
The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. the linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. according to the model, for what price is each comb being sold? startlayout enlarged left-brace 1st row y = startfraction x over 2 endfraction 2nd row y = negative 0.03 (x minus 95) squared 550 $0.03 $0.50 $0.95 $2.00
Answers
The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
The linear equation y = x/2 models the income, in dollars, from selling x plastic combs. Hence:
Price of each comb = (x/2) / x = 0.5
The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2
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Answer: B. $0.50
Step-by-step explanation:
Took the Test/Exam
if there was 9/15 of leftover pizza, and jimmy ate 5/15 of the leftover pizza, how much of the original pizza did he eat
Answers
Answer:
— Work in pizza slices, assuming a dozen per pizza. If I buy 36 slices, and eat 5 slices, and Joe eats 15 slices, there should be 36 - 5 - 15 = 16 slices left.
Step-by-step explanation:
8. In the diagram, the measure of the arc from A to B not
passing through C is 80 degrees. What is the measure of
angle ACB?
A. 20 degrees
B. 40 degrees
C. 80 degrees
D. 160 degrees
Answers
Step-by-step explanation:
for the same arc, the angle at the circumference of the circle is half of the angle at the center of the circle.
and the arc angle is normally representing the angle at the center of the circle.
therefore, the
angle ACB = arc angle AB / 2 = 80/2 = 40°
so, B is the right answer.
divide 9 by 2, then subtract 4 from the result
Answers
Answer:
9 / 2 = 4.5
4.5 - 4 = 0.5
Cavalieri’s principle states that if two solids of equal height have equal cross-sectional areas at every level parallel to the respective bases, then the two solids have equal volume. the two shaded solids both have a height of 2r units. at every level, the areas of the cross sections of both solids equal π(r2 – b2). a cylinder and a sphere are shown. 2 cones are cut out of the cylinder. the cones have a radius of 4. the cylinder has a height of 2 r. the sphere has a radius of 4. the sphere has a height of 2 r. cross-sectional areas are shown on each figure. therefore, the formula for the volume of the sphere can be derived by writing an expression that represents the volume of one cone within the cylinder. the two cones within the cylinder. the solid between the two cones and the cylinder. the cylinder.
Answers
Therefore, the formula for the volume of the sphere can be derived by writing an expression that represents the volume of C. The solid between the two cones and the cylinder
What is the Volume of a Sphere?
This refers to the capacity of a sphere, which is the maximum that can be contained in the sphere. This is denoted as V=4/3πr3
Hence, we can see that based on Cavalieri’s principle that states that if two solids of equal height have equal cross-sectional areas, then the two solids have equal volume.
Therefore, the two shaded solids both have a height of 2r units, and thus, to derive the function, we would have to write an expression that represents the volume of the solids between the two cones and the cylinder
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Answer: B
Step-by-step explanation: just did it
evauleate 150-(2+x)^3 when x is 2
Answers
Answer:
Down below
Step-by-step explanation:
150 - (2 + x)^3
150 - (2 + 2)^3
150 - (4)^3
150 - 64
= 86
I would check my math but I believe this is correct.
Answer:
86
150-(2+x)^3
⇒ x = 2
2 + 2 = 4
4^3(4 • 4 • 4) = 64
150 - 64 = 86
Determine the equation of the circle graphed below.
Answers
Answer:
(x-6)^2+(y-5)^2=16
Step-by-step explanation:
Focus on the center point ONLY and change the signs of those numbers to negative for your equation. Count how much the outer circle moves back (which is 4) and times that as your radius
Someone please helppp
your friend house is 6.4 miles north and 12 miles west of your bank. how far is your friends house from your bank
Answers
Answer:
the answer is 76.8
Step-by-step explanation:
multiple of the number
What is the area,in square meters,of the isosceles trapezoid?
Answers
Step-by-step explanation:
the area of a trapezoid is
(base1 + base2)/2 × h = (18.6 + 9.2)/2 × 7.2 =
= 27.8/2 × 7.2 = 13.9 × 7.2 =
= 100.08 m²
An invoice shows a net purchase price of $1809.13 after the subtraction of discounts of 12.5%, 25%, 8.3%. What was the list price?
Answers
Answer:
I hope this helps................
If you live in a state that needs to collect $18 million in property taxes and has a tax rate of 2.77%, what is that state's
taxable value?
O $650 million
O $65 million
O $6 million
O $499,000
Answers
Answer:
la respuesta es 65 millones
If YV = 23 ft, find the length of VYX to the nearest tenth.
Answers
The length of EC shown in the diagram is 66.2.
"To understand the calculation, check below."
TrianglesΔBE - ΔAE = ΔAB
ΔAB = 180°- 117°
ΔAB = 63°
Δ[tex]BE-[/tex] Δ[tex]AB-[/tex] Δ[tex]BC[/tex] = Δ[tex]CD[/tex] (Congruent angles)
Δ[tex]CD= 180 - 63 - 15[/tex]
Δ[tex]CD=102[/tex]
[tex]EC = 102 + 63[/tex]
[tex]EC=165[/tex]
[tex]L = 165[/tex] • [tex]2\pi23/360[/tex]
[tex]L = 66.2[/tex]
Therefore, EC = 66.2
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Double tap to add title • AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC? A 1200 B w c D 85
Answers
Answer:
Step-by-step explanation:
Find (qor)(x).
q(x) = 3x
r(x) = 6x + 5
Write your answer as a polynomial in simplest form.
Answers
Answer: 18x + 15
Step-by-step explanation:
(qor)(x)
q(r(x))
q(6x+5)
3(6x+5)
⇒18x + 15 This is your answer I believe
if we were solving for x then..
⇒x = [tex]-\frac{15}{18}[/tex]
There are 2022 kangaroos and some koalas living across seven parks. in each park the number of kangaroos is equal to the number of koalas in all the other parks. how many koalas live in the seven parks in total
Answers
Answer:
337
Step-by-step explanation:
I remember this from UKMT maths challenge.
Let the number of kangaroos in each of the seven parks be , , , , , and with the
corresponding number of koalas being , , , , , and . The question tells us that the
number of kangaroos in any park is equal to the sum of the numbers of koalas in the other six
parks. Therefore we have
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + .
Adding these equations, we obtain
+ + + + + + = 6( + + + + + + ).
The total number of kangaroos in the seven parks is 2022. Hence
+ + + + + + = 2022.
Therefore
2022 = 6( + + + + + + )
and hence the total number of koalas in the seven parks is
+ + + + + + = 2022 ÷ 6 = 337.
If the dimensions of a rectangular prism are 10 cm x 5 cm x 7 cm, what is
the surface area?
Answers
Answer:
310
Step-by-step explanation:
Multiply the l/w/h x 2
the food bill for meal at a restaurant is $12. THe sales tax is 6.5%, and you leave 15% tip. Wat is the total cost of the meal? PLEASE ANSWER FAST
Answers
Answer:
Step-by-step explanation:
12*6.5%=0.72
12+15%=13.8
0.72+13.8=14.52
How do I find the domain range and function of the graph
Answers
Answer:
D = {-3, -2, -1, 1, 4}
R = {-5, -1, 0, 2}
Step-by-step explanation:
You have correctly described the process of finding the domain and range by the way you filled in the blanks at the top of the sheet.
__
The domain is the set of x-values of the points on the graph:
D = {-3, -2, -1, 1, 4}
The range is the set of (unique) y-values of the points on the graph:
R = {-5, -1, 0, 2}
Rectangle ABCD is going to be reflected over the x-axis. Which of the following will not be one of the new coordinates? Group of answer choices (6, -6) (-6, 2) (-3, 2) (-3, 6)
Answers
Using translation concepts, it is found that the following rule is applied to each point:
(x,y) -> (x,-y).
The point that is does not result from this transformation will not be one of the new coordinates.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
When a function is reflected over the x-axis, it's output is multiplied by -1, hence the rule is given by:
(x,y) -> (x,-y).
Thus, this rule is applied to all points, which are A, B, C and D, and the point that is does not result from this transformation will not be one of the new coordinates.
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What is the average rate of change in f(x) over the interval [4,13]? on a coordinate plane, a function has four points that are connected by lines. the points are (0, 0), (4, 8), (10, 5), and (13, 12). one-third four-thirteenths eleven-thirteenths eleven-eighths
Answers
Using it's concept, it is found that the average rate of change of the function over the interval [4,13] is given by:
[tex]\frac{4}{9}[/tex]
What is the average rate of change of a function over an interval?It is given by the change in the output divided by the change in input.
In this problem, we have points (4,8) and (13,12), hence the rate of change is given by:
r = (12 - 8)/(13 - 4) = 4/9.
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Answer:
B
Step-by-step explanation:
4/13
