Answers
Answer:
[tex]\displaystyle f'(x) = \frac{-3}{2\sqrt{2 - 3x}}[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Expanding/FactoringFunctions
Function NotationCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Differentiation
DerivativesDerivative NotationDefinition of a Derivative: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \sqrt{2 - 3x}[/tex]
Step 2: Differentiate
Substitute in function [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{\sqrt{2 - 3(x + h)} - \sqrt{2 - 3x}}{h}[/tex]Expand: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{\sqrt{2 - 3x - 3h} - \sqrt{2 - 3x}}{h}[/tex]Rationalize: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{\sqrt{2 - 3x - 3h} - \sqrt{2 - 3x}}{h} \cdot \frac{\sqrt{2 - 3x - 3h} + \sqrt{2 - 3x}}{\sqrt{2 - 3x - 3h} + \sqrt{2 - 3x}}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{2 - 3x - 3h - (2 - 3x)}{h(\sqrt{2 - 3x - 3h} + \sqrt{2 - 3x})}[/tex]Expand: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{2 - 3x - 3h - 2 + 3x}{h(\sqrt{2 - 3x - 3h} + \sqrt{2 - 3x})}[/tex]Combine like terms: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-3h}{h(\sqrt{2 - 3x - 3h} + \sqrt{2 - 3x})}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-3}{\sqrt{2 - 3x - 3h} + \sqrt{2 - 3x}}[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = \frac{-3}{\sqrt{2 - 3(0) - 3h} + \sqrt{2 - 3x}}[/tex]Simplify: [tex]\displaystyle f'(x) = \frac{-3}{2\sqrt{2 - 3x}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Related Questions
what is going on
I am confused
Answers
Answer:
What do you mean?
Step-by-step explanation:
I would suggest adding more info
How many bows can you make from 3 and 2/3 meters of ribbon if 1/4 of a meter of ribbon makes one bow
Answers
Answer:
14
Step-by-step explanation:
(11/3)/(1/4)=14 2/3 which means you can make 14 complete bows
SOMEONE HELP ME WITH THIS PLEASE IM STRUGGLING
Answers
Answer:
Final point (-4, 4) Original point (3, -4)
Answer:
Again, I can't move it for you but I can give you the points!
original: (3, -4)
final: (-4, 4)
The parallelogram shown below has an area of 140 units² .
Answers
Answer:
Step-by-step explanation:
140 = b * h
140 = b * 10
14 = b
Which expression is NOT equal to 28?
A (9 + 25 = 5) x 2
B. [(13 – 4x2) – 1] x 7
C. 42 = 6 + 28 = 4
D. 7 [8 - (12 - 4x 2)]

Answers
Answer:
aaaaa
Step-by-step explanation:
Answer:
I think it’s A
Step-by-step explanation:
A keyboard cost -P400.
On sale the price is
reduced to to P360.
calculate the percentage
decrease.
Answers
400-360=40/400=0.1 x100=10%
Find the value of the following by suitable rearrangement. Mention the
property used.
a. 25 x 679 x 4
b. 2917 x 102 - 2917 x 2
Answers
(a) 67900
(b) 291700
Step-by-step explanation:(a) 25 x 679 x 4
Rearrange the terms starting with the smallest
4 x 25 x 679
The property used here is the commutative property of multiplication which states that the order in which these numbers are multiplied does not matter.
Now solve
4 x 25 x 679 = 67900
(b) 2917 x 102 - 2917 x 2
Factor out the common terms
2917(102 - 2)
Using the distributive property which states that when a number is multiplied by the sum or difference of two numbers, the result is the same as multiplying each of the two numbers by the number and then adding or subtracting the products.
Now solve
2917(102 - 2) = 2917(100)
= 291700
PLEASE HELP ME IT'S MY LAST GRADE
Answers
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
-61=-3(1-5p)+4(-8-7p)
Answers
Answer: hello! have a good day! :)))
P = 2
The weights of running shoes are normally distributed with an unknown population mean and standard deviation. If a random sample of 31 running shoes is taken to estimate the mean shoe weight, what t-score should be used to find a 98% confidence interval estimate for the population mean
Answers
Answer:
The t-score is t = 2.457.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 31 - 1 = 30
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 30 degrees of freedom(y-axis) and a one-tailed confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.457.
The t-score is t = 2.457.
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 6 yards long, and the height of the equilateral triangle is 5.2 yards. The pyramid's slant height is 7 yards. What is its surface area?
Answers
Answer:
78.6 sq. yards
Step-by-step explanation:
SA = (½×6×5.2)+(3×½×6×7)
= 15.6 + 63 = 78.6 sq. yards
What is the area of the polygon?
Answers
Answer:
[tex]154m^{2}[/tex]
Step-by-step explanation:
8 · 7 = 56m (horizontal rectangle shape) the width was given by subtracting the total of the width (23m) minus (16m).
5 · 8 = 40m (square shape) Subtract 8m - 3m = 5m.
6 · 8 = 48m (square shape to the left of the polygon)
2 · 5 = 10m (small rectangle shape bottom left) 8 - 6 = 2 for the length and 5 for the width by 8 - 3 = 5
56m + 40m + 48m + 10m = 154 [tex]m^{2}[/tex]
Which inequality is represented by the graph below? Check all that apply. Ox>9 Ox
Answers
Answer:
The correct answers are [tex]x < 9[/tex] and any rational number less than 9.
Step-by-step explanation:
Since the inequality represented in the number line has the arrow going towards the left, and has a open/not highlighted circle on 9, that means the inequality represented by the number line is [tex]x < 9[/tex], which means the exact same as any rational number less than 9, so those two choices are the correct answer.
no links I can interpret numerical expressions without evaluating them.
A.
strongly agree
B.
agree
C.
disagree
D.
strongly disagree
Answers
B. Agree
I think
What is 12% of 125? Round each answer to the nearest WHOLE number.
Answers
Answer:
10
Step-by-step explanation:
Answer: 15
you do the whole number (125) times the percentage in decimal for (.12)
so its 125 x 0.12 = 15
x>-2
Wyatt wants to spend no more than $25 at the grocery store. He bought a
pizza for $7.55 and a cake for $11.02 (including tax). Choose the inequality
that he can use to find how much money he can still spend.
Answers
Answer:
he spent $18.57 and he can spend $7.43 more
The solution is, he can still spend no more than $6.43.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
given that,
Wyatt wants to spend no more than $25 at the grocery store.
He bought a pizza for $7.55 and a cake for $11.02 (including tax).
now, we have to find the inequality that he can use to find how much money he can still spend.
let, we would spend = x
now, we have,
He bought a pizza for $7.55 and a cake for $11.02
so, he had = $ x - ( 7.55 + 11.02)
we have,
x ≥ 25
so, he can still spend ≥ 25 - ( 7.55 + 11.02)
or, he can still spend ≥ 6.43
i.e. he can still spend no more than $6.43
Hence, The solution is, he can still spend no more than $6.43.
To learn more on inequality click:
brainly.com/question/24853349
#SPJ2
If 35% of a number is 21 and 90% of the same number is 54, find 55% of that number.
Answers
the answer is on the picture
ifu={12345678},a={1234},b={5678},then find (a union b)`
Answers
Step-by-step explanation:
A union b is 12345678
So is prime then is empty set
John walks his dog home from the vet. The graph shows the remaining distance from his house as a linear function of x, the number of minutes he spent walking. Find the domain and range of the graph.
Answers
Answer:
Step-by-step explanation:
domain is the input, or the x values, range is the output, or y values
x goes from 0 to 40 so that's the domain
y goes from 0 to 4 so that the range
Answer:
Y is more than or equal to 0, but less than or equal to 4.
X is more than or equal to 0, but less than or equal to 40
Step-by-step explanation:
Medidas de tendencia central
Answers
Answer:
uhh hell? What does that mean?
Step-by-step explanation:
ILL GIVE BRAINLEST, please show work :D
Answers
answer is 4/9 in^2
2/3 * 2/3 = 4/9
4/9
Your answer is 4/9
Ica ingin membuat sebuah lampion
berbentuk kubus, panjang rusuknya 15
dm, maka volume lampion Ica adalah
... m?
a. 45
b. 3,375
c. 33,75
d. 3,375
Answers
Well the answer is 3,375
Simplify this expression by distributing: (p - 3)6.
Answers
Answer:
6p-18
Step-by-step explanation:
Answer:
6p -18
Step-by-step explanation:
(p - 3)6
Distribute
6*p - 6*3
6p -18
Can someone please help?
Answers
[tex]9 \times \frac{1}{4} = \frac{9}{4} [/tex]✅
Step-by-step explanation:Option A⤵
[tex]5 \times \frac{1}{2} = \frac{1}{10} \\ ⇢ \frac{5}{2} ≠ \frac{1}{10} [/tex]
Option B⤵
[tex]4 \times \frac{1}{3} = \frac{4}{12} \\ ⇢ \frac{4}{3} ≠ \frac{4}{12} [/tex]
Option C⤵
[tex]9 \times \frac{1}{4} = \frac{9}{4} \\ ⇢ \frac{9}{4} = \frac{9}{4} [/tex]
Option D⤵
[tex]8 \times \frac{1}{ 5} = \frac{9}{5} \\ ⇢ \frac{8}{5} ≠ \frac{9}{5} [/tex]
Hence, option C is correct.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
What is the area of the figure? Round to the nearest tenth.
10 m
5 m
4 m
개
A 20.0 m2
B. 40.0 m2
O c. 45.0 m2
OD 50.0 m2
Answers
PLEASE HELP 7TH GRADE MATH
BRAINLIEST-SHOWS WORK
PLEASE HELP
ANSWER 1 OR MORE AN WILL MARK BRAINLIEST 1 OR MORE
Answers
Answer:
well it cant start off in the middle of the graph most graphs you start from the very beginning like lets just say we start at 11 and go all the way to the end so kinda like a straight line
Step-by-step explanation:
match the graph shown with one of the following equations
A. y=x+2
B. y=-x-2
C. y=x-2
D. y=-x+2
E. y=-x
Answers
Answer:
A
Step-by-step explanation:
We need to find the correct options which represents the given equation . We can try it out by eliminating the given options , as
Since the graph Intersects the y axis above the origin ,the value of constant is > 0 .So , option A , and D are preferred choices .
Now the slope of the line is (-1) in option D and 1 in A . Since the graph is in 1st quadrant, so its slope will be positive .Option A is the correct option . ✔️
Option A is correct answer .How much does $3,000 earn in six months at an interest rate of 4 compounded quarterly?
Answers
Answer:
The final balance is ₹4,926.8.
The total compound interest is ₹3,926.8.
The amount of money that was earned in six months with an interest rate of 4 compounded quarterly will be $3184.6.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
[tex]\rm A = P \left (1 + \dfrac{r}{n} \right ) ^{nt}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.
The principal amount of $3,000 was earned in six months at an interest rate of 4 compounded quarterly. Then the value of n will be 4. Then we have
[tex]A = 3000 \left (1 + \dfrac{0.04}{4} \right )^6[/tex]
Simplify the equation, then we have
A = 3000 (1.01)⁶
A = 3000 x 1.062
A = $3184.6
The amount of money that was earned in six months with an interest rate of 4 compounded quarterly will be $3184.6.
More about the compound interest link is given below.
https://brainly.com/question/25857212
#SPJ2
find the area of the trapezoid in square inches.
Answers
Answer:
Hello! answer: 64
Step-by-step explanation:
I split this into a triangle and rectangle and did the appropriate formulas for each for square I did base × height and got 48 because 8 × 6 = 48 then for the triangle I did base × height ÷ 2 So I did 8 × 4 = 32 32 ÷ 2 = 16 now I just add these two numbers up! so... 48 + 16 = 64 HOPE THAT HELPS!
Answer:
A = 64 in²
Step-by-step explanation:
Step 1: Add the bases
[tex]10 + 6 = 16[/tex]
Step 2: Multiply that by the height
[tex]16 * 8 = 128[/tex]
Step 3: Divide the result by 2
[tex]\frac{128}{2} = 64[/tex]
Therefore, the area of the trapezoid is 64 in²
Estimate the line of best fit using two points on the line. (8, 80) 100 90 80 70 60 50 40 30 20 10 (2.20) 10 O A. y= 2x O B. y = 2x + 10 O c. y= 10x+ 2 OD. y= 10x
Answers
Answer:
[tex]y = 10x[/tex]
Step-by-step explanation:
Given
The attached plot
Required
The line of the best fit using [tex](8,80)[/tex] and [tex](2,20)[/tex]
We have:
[tex](x_1,y_1) = (8,80)[/tex]
[tex](x_2,y_2) = (2,20)[/tex]
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{20 - 80}{2- 8}[/tex]
[tex]m = \frac{-60}{-6}[/tex]
[tex]m = 10[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 10(x - 8) + 80[/tex]
Expand
[tex]y = 10x - 80 + 80[/tex]
[tex]y = 10x[/tex]