Hi there!
[tex]\large\boxed{f''(x) = 2 - \frac{4}{x^{3}}}[/tex]
[tex]f(x) = x^2 - \frac{2}{x}[/tex]
Recall the power rule:
[tex]\frac{dy}{dx} x^n = nx^{n-1}[/tex]
Rewrite the function for ease of differentiation:
[tex]f(x) =x^2 - 2x^{-1}[/tex]
Use the power rule:
[tex]f'(x) = 2x + 2x^{-2}[/tex]
Take the derivative once more:
[tex]f''(x) = 2 - 4x^{-3}[/tex]
Rewrite:
[tex]f''(x) = 2 - \frac{4}{x^{3}}[/tex]
Which inequality matches the graph?
X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on graph has positive slope and runs through negative 3, negative 8 and 1, negative 2 and 9, 10. Above line is shaded.
−2x + 3y > 7
2x + 3y < 7
−3x + 2y > 7
3x − 2y < 7
Given:
The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).
Above line is shaded.
To find:
The inequality for the given graph.
Solution:
Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)[/tex]
[tex]y+2=\dfrac{10+2}{8}(x-1)[/tex]
[tex]y+2=\dfrac{12}{8}(x-1)[/tex]
[tex]y+2=\dfrac{3}{2}(x-1)[/tex]
Multiply both sides by 2.
[tex]2(y+2)=3(x-1)[/tex]
[tex]2y+4=3x-3[/tex]
[tex]2y-3x=-3-4[/tex]
[tex]-3x+2y=-7[/tex]
Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.
[tex]-3x+2y>-7[/tex]
This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.
[tex](-3x+2y)(-1)<-7(-1)[/tex]
[tex]3x-2y<7[/tex]
Therefore, the correct option is D.
the cost of a popular toy is $19.99 , Due to a limited supply , the store manager marks the price of the toy up by 15%. what is the new price ? HURRY PLEASE .
$22.99
Step-by-step explanation:
19.99 increased by 15% ≈ 22.99
Absolute change (actual difference):
22.99 - 19.99 ≈ 3
The difference is $3
use the quadratic formula to solve x^2 + 3^x - 28 = 0
Step-by-step explanation:
x^2 + 3x - 28 = 0
x^2 - 7x + 4x - 28 = 0
x(x-7) + 4(x-7) = 0
(x+4)(x-7)= 0
x+4=0 or x-7=0
x= -4 or x=7
what is 0.7dm to nm is? please help asap
Step-by-step explanation:
0.7 decimeter =
70,000,000 nanometers
what is the average number of students who like cookies, chips, and crackers?
Cookies=10
Chips=3
Crackers=2
Answer:
m = 15/3 = 5 is the mean
Step-by-step explanation:
Answer:
5 Students But divide by 15/3 to 5
Step-by-step explanation:
What does Average mean?
1. a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number.
So, to find the answer just ADD 10 + 2 + 3 = ?
10 + 2 = 12 So put that to the side for now.
Now, 10 + 2 = 12 + 3 = 15
So the total number of students who like cookies, chips, and crackers are 15.
Now do 15/3 to get 5.
prime numbers that can be expressed as a sum and difference of 2 prime numbers
ASAP
Given:
Prime numbers can be expressed as a sum and difference of 2 prime numbers.
To find:
The prime numbers that can be expressed as a sum and difference of 2 prime numbers.
Solution:
Prime numbers are the positive integers which are greater than 1, divisible by only 1 and itself.
Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19,... .
Only 2 is the even prime number.
The sum and difference of two odd integers is always an even number. So, we need to take one even prime number and one odd prime number to add and subtract the numbers to get a prime number.
[tex]2+3=5[/tex]
[tex]7-2=5[/tex]
Therefore, 5 is the only prime number that can be expressed as a sum and difference of 2 prime numbers.
Select the correct answer.
The manager at a car dealership is tracking the selling prices of two different used car models. When the tracking began, the selling price of
model A was less than $8,000, and the selling price of model B was at most $10,000. The manager has determined that the price of model A is
decreasing at a rate of 12% each year, and the price of model B is decreasing at a rate of 15% each year.
Which system of inequalities can be used to determine after how many years, t, that the selling price, y, will be the same for both car models?
O A.
Ов.
Jy < 8,000(0.88)
y < 10,000(0.85)
Sy < 8,000(1.12)
y < 10,000(1.15)
9 < 8,000(0.88)
y < 10,000(0.85)
Sy < 8,000(1.12)"
1y 10,000(1.15)
Oc.
OD
Answer:it’s C
Step-by-step explanation:
The system of inequalities can be used to determine, if The selling price of model A was less than $8,000, The selling price of model B was at most $10,000, are x < 8000 × 0.88, and y < 1000 × 0.85.
What is the selling price?The selling price of a good or service is the final cost to the seller, or what the buyer actually pays. A commodity or service in a specific amount, weight, or measurement can be exchanged.
It is one of the most crucial things for a business to decide. It is significant since it determines whether it will survive. Sales of a product are directly impacted by its price.
Given:
The selling price of model A was less than $8,000,
The selling price of model B was at most $10,000,
The price of model A is decreasing at a rate of 12% each year,
The price of model B is decreasing at a rate of 15% each year,
Write the inequality as shown below,
Assume the selling price of A is x,
x < 8000
Assume the selling price of B is y,
y < 1000
The decreased selling price of A,
x < 8000 × (1 - 0.12) = x < 8000 × 0.88
The decreased selling price of B,
y < 1000 × (1 - 0.15) = y < 1000 × 0.85
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The equation of line a is y=3/4x-3 If line b runs parallel to line a and passes
through (-4,5), what would be the equation of line b?
Answer:
y = -4/3 x - 1/3
Step-by-step explanation:
y = -4/3 x + b
5 = -4/3 (-4) + b
15 = 16 + 3b
b = -1/3
y = -4/3 x - 1/3
The equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.
To find the equation of line b, which is parallel to line a and passes through the point (-4,5), we need to use the fact that parallel lines have the same slope.
Given that line a has the equation y = (3/4)x - 3, we can determine its slope. The slope of line a is the coefficient of x, which is 3/4.
Since line b is parallel to line a, it will also have a slope of 3/4.
Using the slope-intercept form of a linear equation (y = mx + b), we can substitute the slope and the coordinates (-4,5) into the equation to solve for the y-intercept, b.
5 = (3/4)(-4) + b
Simplifying, we have:
5 = -3 + b
Adding 3 to both sides, we find:
b = 8
Therefore, the equation of line b, parallel to line a and passing through the point (-4,5), is y = (3/4)x + 8.
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Determine the measure of ZA.
45.6°
57.7°
55.2°
32.3°
Step-by-step explanation:
Cos A = 40^2 + 25^2- 34^2 ÷ (2×40×25)
= 200+625-1156 ÷ (2000)
= 1069 ÷2000
Cos A = 0.5345
A= cos inverse 0.5345
A = 57.7
Answer:
57.7
Step-by-step explanation:
took the test
Find the highest common factor (HCF) for 36, 84 and 108
Answer:
Check your question one time
Inventor A had 630 inventions, 600% more than the number of inventions inventor B had. How many inventions did B have?
Answer:
105 inventions
Step-by-step explanation:
Find how many inventions Inventor B had by dividing 630 by 6:
630/6
= 105
So, Inventor B had 105 inventions
Which of the following shows 5x + 17 + 8x – 9 + 2y in simplest terms?
Answer:
5x+8x+17-9+2y
13x+8+2y
Answer:
13x+8+2y
Step-by-step explanation:
5x+8x=13x
17–9=8
2y=2y
What is the value of x?
1/2(x+6)=18
Answer:
30
Step-by-step explanation:
Multiply by 2 to 18, x+6=36
subtract 6 x=30
x=30
The temperature of a cup of coffee varies according to Newton's Law of Cooling: -"dT/dt=k(T-A), where is the temperature of the coffee, A is the room temperature, and k is a positive
constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25*C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes,
74
67
60
42
Answer:
B) 67°C.
Step-by-step explanation:
Newton's Law of Cooling is given by:
[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]
Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.
We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.
And we want to find the temperature of the coffee after four minutes.
First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:
[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]
Take the integral of both sides:
[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]
Integrate:
[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]
Raise both sides to e:
[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]
The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:
[tex]\displaystyle T=Ce^{kt}+A[/tex]
We are given that A = 25. Hence:
[tex]\displaystyle T=Ce^{kt}+25[/tex]
Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:
[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]
Hence:
[tex]T=75e^{kt}+25[/tex]
We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.
So, T = 90 given that t = 1. Substitute:
[tex]90=75e^{k(1)}+25[/tex]
Solve for k:
[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]
Therefore:
[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]
Then after four minutes, the temperature of the coffee will be:
[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]
Hence, our answer is B.
What is the solution of 5/2x-7=3/4x+14
Answer:
D. x = 12
Step-by-step explanation:
if you plug 12 in
the solutoon says 23 = 23 which is correct
Answer:D 12
Step-by-step explanation:
I took the test
I need help in these questions please !
Answer:
b,b.a
Step-by-step explanation:
The incubation time for Rhode Island Red chicks is normally distributed with mean of 22 days and standard deviation of approximately 3 days. Of 1000 eggs are being incubated, how many chicks do we expect will hatch in 19 to 28 days
Answer:
We should expect 818 chicks to hatch in 19 to 28 days
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 22 days and standard deviation of approximately 3 days.
This means that [tex]\mu = 22, \sigma = 3[/tex]
Proportion between 19 and 28 days:
p-value of Z when X = 28 subtracted by the p-value of Z when X = 19.
X = 28
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 22}{3}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.977.
X = 19
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22}{3}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.159.
0.977 - 0.159 = 0.818
Out of 1000:
0.818*1000 = 818
We should expect 818 chicks to hatch in 19 to 28 days
if <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO
Answer:
<BCO = <BAO = 20degrees
Step-by-step explanation:
If <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO
To get <BAO and <BCO, we need to get <AOC first.
From the figure, it can be seen that triangle ABC is an isosceles trinagle. Hence;
<BAC + <BCA + 100 = 180
Since <BAC = <BCA
<BAC + <BAC = 180 - 100
2<BAC = 80
<BAC = 80/2
<BAC = 40
Also;
<BAO = <BCO and <BAO = <BAC/2
<BAO = 40/2 = <BCO
Hence <BCO = <BAO = 20degrees
What is the constant of variation, k, of the direct variation, y = for, through (5,8)?
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.
Usually represented with the variable [tex]k[/tex], it is given by:
[tex]\frac{y}{x}=k[/tex] for coordinates (x, y).
This relationship can be written as [tex]y=kx[/tex] which is also the layout for a proportional relationship.
Since coordinates are written (x, y), for point (5, 8), substitute [tex]x=5, y=8[/tex] to get the constant of variation:
[tex]8=5k,\\k=\boxed{\frac{8}{5}}[/tex]
Answer:
8/5
Step-by-step explanation:
Given that y varies directly with x , therefore ,
[tex]\implies y \propto x[/tex]
Let k be the constant . Therefore ,
[tex]\implies y = k x[/tex]
When the point is (5,8) ,
[tex]\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =\dfrac{8}{5}}}}[/tex]
Hence the constant of variation is 8/5.
pplied for a job as a cashier at a hardware store. As part of her employment screening, she was asked to take an exam that had general mathematical aptitude questions in it. This type of selection test is referred to as a
Answer:
cognitive ability
Step-by-step explanation:
A plane gets an average of 25 miles per gallon when it is traveling 500 miles per hour. The plane has 15,000 gallons of gas at the beginning of a trip and travels at an average speed of 500 miles per hour. Which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?
(A) f = 15000 + (25t/500)
(B) f = 15000 - (25t/500)
(C) f = 15000 - (500t/25)
(D) f = 15000 - 25t
(E) f = 25t
Answer:
D; f = 15,000 - 25t
Step-by-step explanation:
From the question;
per gallon, the number of miles traveled is 25, given traveling speed is 500 miles per hour
So after t hours, if traveling at 500 miles per hour, the amount of fuel expended will be 25 * t = 25t gallons
So, to get the amount remaining, we subtract 25t from what we have at the start of the trip
Mathematically, we have this as;
f = 15,000 - 25t
someone help me for this algebra task please
Answer:
200
Step-by-step explanation:
Substitute 15 for y
[tex] \frac{1}{5} x - \frac{2}{3} (15) = 30[/tex]
[tex] \frac{1}{5} x - 10 = 30[/tex]
[tex] \frac{1}{5} x = 40[/tex]
[tex]x = 200[/tex]
What is the answer to 3/4 x 1/2
What is the answer to 3/4 x 1/2?
Answer : 0.375
Answer:
3/8
Step-by-step explanation:
What is the value of x?
[tex] \frac{4}{5} x - \frac{1}{10} = \frac{3}{10} [/tex]
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{5}[/tex] x - [tex]\frac{1}{10}[/tex] = [tex]\frac{3}{10}[/tex]
Multiply through by 10 ( the LCM of 5 and 10 ) to clear the fractions
8x - 1 = 3 ( add 1 to both sides )
8x = 4 ( divide both sides by 8 )
x = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
WILL GIVE 50 POINTS PLS RESPOND FAST!!!!
The table below shows the radius y, I’m centimeters, created by grouping algae in x days:
Time (x) 2 4 6 8
(Days)
Radius(y) 4 7 10 14
(cm)
Part A: what is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and radius of the algae. [choose the value of the correlation coefficient from 1, 0.97, 0.5, 0.2.]
Part B: what is the value of the slope of the graph of radius versus time between 6 and 8 days, and what does the slope represent?
Part C: does the data in the table represent correlation or causation? Explain your answer.
Answer:
wait whats your question
Step-by-step explanation:
Find the missing side of the right triangle if two sides are 6, and 10
Hey is there any chance anyone could help me with this question ASAP?? Tysm :)
Answer:
6
Step-by-step explanation:
A = π. r²
36π = π. r²
eliminate π, we get:
36=r²
r=√36
r = 6
Answer:
r = 6
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
Given A = 36π , then
πr² = 36π ( divide both sides by π )
r² = 36 ( take the square root of both sides )
r = [tex]\sqrt{36}[/tex] = 6
if you want to make some money and do my acellus academy math and science subject in 1 day ill pay $25 dollars
Answer:
no tHank you hope someone can help
Step-by-step explanation:
helpppp and explain///////////////////////////
Answer:
A
Step-by-step explanation:
The first thing we have to do here is to subtract g(x) from f(x)
We have this as;
2x + 4 -(3x-7)
= 2x + 4-3x + 7
= -x + 11
Now, we substitute the value of x for 5
We have -5+ 11 = 6
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $20 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month
The question is incomplete. The complete question is :
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $15 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month. Job B-1 used 82 direct labor hours and $3650 worth of direct material used. Job B-2 used 130 direct labor hours and $2,900 worth of direct material. What is the total cost of job B-2? Round to closest whole dollar (no cents).
Solution :
Particulars Job B-2
Direct material used $ 2,900
Add : Direct labor cost (130 hours x $15) $ 1,950
Add : overhead cost (130 hours x $ 42) $ 5,460
Total Cost of Job B-2 $ 10,310
Therefore, the total cost of the Job B-2 is $ 10,310.
