find f(a), f(a h), and the difference quotient f(a h) − f(a) h , where h ≠ 0. f(x) = 5 − 3x 4x2
Answers
The difference quotient (f(a + h) - f(a)) / h = 8a + 4h.To find f(a), f(a + h), and the difference quotient f(a + h) - f(a) / h, we substitute the given function f(x) = \(5 - 3x + 4x^2\) into the expressions.
1. f(a):
To find f(a), we substitute 'a' into the function:
f(a) = \(5 - 3a + 4a^2\)
2. f(a + h):
To find f(a + h), we substitute 'a + h' into the function:
f(a + h) = \(5 - 3(a + h) + 4(a + h)^2\)
Expanding the terms:
f(a + h) =\(5 - 3a - 3h + 4(a^2 + 2ah + h^2)\)
Simplifying further:
f(a + h) =\(5 - 3a - 3h + 4a^2 + 8ah + 4h^2\)
3. Difference quotient (f(a + h) - f(a)) / h:
To find the difference quotient, we subtract f(a) from f(a + h) and divide by 'h':
(f(a + h) - f(a)) / h =\([5 - 3a - 3h + 4a^2 + 8ah + 4h^2 - (5 - 3a + 4a^2)] / h\)
Simplifying further:
(f(a + h) - f(a)) / h =\((5 - 3a - 3h + 4a^2 + 8ah + 4h^2 - 5 + 3a - 4a^2) / h\)
Combining like terms:
(f(a + h) - f(a)) / h =\((8ah + 4h^2) / h\)
Canceling out the 'h' terms:
(f(a + h) - f(a)) / h = 8a + 4h
Therefore, the expressions are:
- f(a) = \(5 - 3a + 4a^2\)
- f(a + h) = \(5 - 3a - 3h + 4a^2 + 8ah + 4h^2\)
- The difference quotient (f(a + h) - f(a)) / h = 8a + 4h
To know more about quotient visit:
https://brainly.com/question/16134410
#SPJ11
Related Questions
What is the inverse of the logarithmic function f x log2x?
Answers
The inverse of the logarithmic function f(x) = log2x is the exponential function f(x) = 2^x
The inverse of a logarithmic function is an exponential function. To find the inverse of the logarithmic function f(x) = log2x, we need to switch the x and y values of the function and solve for the y. This will give us the inverse function in the form y = 2^x.
The inverse of the logarithmic function f(x) = log2x is the exponential function f(x) = 2^x.
The inverse of a logarithmic function is an exponential function, which is a function of the form y = b^x, where b is a constant. To find the inverse of the logarithmic function f(x) = log2x, we need to switch the x and y values of the function and solve for the y. This will give us the inverse function in the form y = 2^x, where 2 is the constant. This inverse exponential function expresses the relationship between the x and y values of the logarithmic function in reverse, with the x values now being the exponents and the y values being the result of the exponential function.
Learn more about logarithm here
brainly.com/question/28596588
#SPJ4
Which expressions are equivalent to 3^4•3^x
A. (3 • x)^4
B. 3^4 + x
C. 81•3^x
D. 9^4x
E. 3^4x
F. 3^4-x
Answers
119 is 0.7% of what number
Answers
Answer:
17,000
Step-by-step explanation:
0.7% × 17,000 =
(0.7 ÷ 100) × 17,000 =
(0.7 × 17,000) ÷ 100 =
11,900 ÷ 100 =
119
Answer:
1700??
Step-by-step explanation:
I set up a proportion with fractions. My first fraction is 7 over 100 and my second fraction is 119 over x. Is over of!!!!! BTW I don't know if this is correct
Can someone help solve question 12 and 13 please
Answers
13. zero slope
answer:
the answers are undefined and zero ( and in that order )
step-by-step explanation:
for question 12,
x = 10
since that equation is just a vertical line, the slope is undefined!
but for question 13
y = -5
the equation is just a horizontal line rather then a vertical line, the slope is zero ( since it is not moving )
i hope this helps you and if you need anymore help then please feel free to ask me! :)
show all work
7. A conical tank with equal base and height is being filled with water at a rate of 2 m/min. How fast is the height of the water changing when the height of the water is 7m. As the height increases,
Answers
When the water is 7 meters high, it is changing height at a rate of about 0.019 meters per minute.
To find how fast the height of the water is changingWe need to use related rates and the volume formula for a cone.
V as the conical tank's water volume
h is the measurement of the conical tank's water level
The conical tank's base has a radius of r
The volume of a cone can be calculated using the formula: V = (1/3)πr²h.
Given that the base and height of the conical tank are equal, we can write r = h.
Differentiating the volume formula with respect to time t, we get:
dV/dt = (1/3)π(2rh dh/dt + r² dh/dt).
Since r = h, we can simplify the equation to:
dV/dt = (1/3)π(2h² dh/dt + h² dh/dt)
= (2/3)πh² dh/dt (Equation 1).
Assuming that the rate of water filling is 2 m/min, dh/dt must equal 2 m/min.
Finding dh/dt at h = 7 m is necessary because we want to know how quickly the water's height is changing.
Substituting the values into Equation 1:
2 = (2/3)π(7²) dh/dt
2 = (2/3)π(49) dh/dt
2 = (98/3)π dh/dt
dh/dt = 2 * (3/(98π))
dh/dt ≈ 0.019 m/min.
Therefore, When the water is 7 meters high, it is changing height at a rate of about 0.019 meters per minute.
Learn more about volume of cone here: brainly.com/question/28109167
#SPJ4
You have been asked to cut a 1.5m roll of bubble wrap into 30 cm lengths, which are used to wrap CDs before posting to clients. How many pieces of bubble wrap will you end up with?
a. 3
b. 4
c. 5
d. 6
Answers
Answer:
c. 5
Step-by-step explanation:
1.5m = 1.5*100 cm = 150 cm
Divide 150 cm by 30 cm,
150/30 = 5
if the correlation between two variables in a sample is r=1, then what is the best description of the resulting scatterplot?
Answers
If the correlation between two variables in a sample is r=1, the best description of the resulting scatterplot is that the points lie perfectly on a straight line with a positive slope.
A correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. When the correlation coefficient is 1,
it indicates a perfect positive linear relationship between the variables. In this case, every data point in the scatterplot falls precisely on a straight line with a positive slope.
The scatterplot represents the relationship between the two variables, with each data point plotted based on its corresponding values for the two variables.
With a correlation coefficient of 1, all the data points in the scatterplot align exactly on a straight line. This implies that as one variable increases, the other variable also increases in a consistent and proportional manner.
The scatterplot will exhibit a tight, upward-sloping pattern, where there is no variability or scatter around the line.
This indicates a strong and predictable relationship between the variables. Each point in the scatterplot will have the same x and y values, resulting in a perfect positive correlation.
To know more about linear click here
brainly.com/question/30444906
#SPJ11
The graph of a proportional relationship is shown. Describe the real world situation that could be represented by the graph. Be sure to include the meaning of the constant of proportionality
Answers
The real world situation that could be represented by a graph is Given that y varies proportionally with x, with a constant of proportionality k=13 , find y when x=12.
How to illustrate the information?The graph of the proportional relationship equation is a straight line through the origin.
The real-world situation that could be represented by a graph is Given that y varies proportionally with x , with a constant of proportionality k=13 , find y when x=12.
The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant
Learn more about graph on:
https://brainly.com/question/19040584
#SPJ1
PLEASE HELP ME FAST!! I am close to a 100 so please don't give me a wrong answer.
Answers
Answer:
y = 8x
Step-by-step explanation:
1. First, we need to know what slope-intercept form is. The slope-intercept form of any linear equation is y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.
2. To find the slope, let's take the two points (0,0) and (10,80) and plug their values into this formula: \(\frac{y_2-y_1}{x_2-x_1}\)
\(\frac{80-0}{10-0}\) \(\frac{80}{10}\) \(8\\\)3. Now that we know our slope, our equation should look like this so far: y = 8x + b.
4. Since b is the y-intercept, we can say that b = 0 because the line intersects with the y-axis at (0,0).
5. Therefore, we get an equation of y = 8x or y = 8x + 0.
ten more than a number is 3 times the sum of the number and 4
Answers
Answer:
Step-by-step explanation:
x + 10 = 3(x + 4)
x + 10 = 3x + 12
10 - 12 = 3x - x
- 2 = 2x
x = - 1
If the elasticity of labor is 0.60, a 15 percent increase in the wage rate will induce a a. 4.0 percent decrease in the quantity of labor supplied. b. 9.0 percent increase in the quantity of labor supplied. c. 9.0 percent decrease in the quantity of labor supplied. 4. 4.0 percent increase in the quantity of labor supplied.
Answers
The elasticity of labor refers to the responsiveness of the quantity of labor supplied to changes in the wage rate. If the elasticity of labor is 0.60, a 15 percent increase in the wage rate will induce a decrease in the quantity of labor supplied, but the extent of this decrease will depend on the magnitude of the elasticity. The correct option is c.
In this case, a 0.60 elasticity implies that a 15 percent increase in the wage rate will result in a 9.0 percent decrease in the quantity of labor supplied. This can be calculated using the formula for elasticity, which is the percentage change in quantity divided by the percentage change in price (or wage rate, in this case):
Elasticity of labor = percentage change in quantity / percentage change in wage rate
0.60 = percentage change in quantity / 15 percent
Percentage change in quantity = 0.60 x 15 percent = 9.0 percent
Therefore, the correct answer is (c) a 9.0 percent decrease in the quantity of labor supplied. This means that as the wage rate increases, workers may be less willing to supply labor, resulting in a decrease in the number of workers willing to work at that wage rate.
To know more about elasticity, refer to the link below:
https://brainly.com/question/30610639#
#SPJ11
A particular disease is tested for and the results determine that it occurs in about 1 of every 275 Hispanic baby births and about 1 of every 184,000 non Hispanic baby births. Find the empirical probability that a randomly selected Hispanic baby will have this disease.
Answers
Since the selected baby is Hispanic, we can use the probability given for Hispanic babies, which is 1 of 275.
\(P=\frac{1}{275}\approx0.0036=0.36\text{ \%}\)You start at (9, 5). You move right 1 unit. Where do you end? y x 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 0 ( , )
Answers
Answer:
(10, 5)
Step-by-step explanation:
Starting coordinate : (9, 5)
x = 9 ; y = 5
Vertical distance (up and down) = y
Horizontal distance (left and right) = x
Movement to the right = positive
Movement to the left = negative
Hence, 1 unit moved to the right ; x + 1
Therefore ;
(9 + 1, 5)
= (10, 5)
om 3: Linear Regression
FINAL PROJECT: DAY 3
he manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee salm
ne days this past fall are shown in the table below
Day 1 Day 2 Day 3 Day 4 Day 5 Day & Day 7 Day 8 Day 9
High Temperature, t 54
Coffee Sales, f(t)
50
70
58
52
48
$2900 $3080 $2500 $2580 $2200 $2700 $3000 $3620 $372
e linear regression function, f(t), that estimates the day's coffee sales with a high temperature
Answers
A linear regression function, f(t), that estimates the day's coffee sales with a high temperature is f(t) = -58t + 6,182.
The correlation coefficient (r) is -0.94.
Yes, r indicates a strong linear relationship between the variables because r is close to -1.
How to find an equation of the line of best fit and the correlation coefficient?In order to determine a linear regression function and correlation coefficient for the line of best fit that models the data points contained in the table, we would have to use an online graphing tool (scatter plot).
In this scenario, the high temperature would be plotted on the x-axis of the scatter plot while the y-values would be plotted on the y-axis of the scatter plot.
From the scatter plot (see attachment) which models the relationship between the x-values and y-values, the linear regression function and correlation coefficient are as follows:
f(t) = -58t + 6,182
Correlation coefficient, r = -0.944130422 ≈ -0.94.
In this context, we can logically deduce that there is a strong linear relationship between the data because the correlation coefficient (r) is closer to -1;
-0.7＜|r| ≤ -1.0 (strong correlation)
Read more on scatter plot here: brainly.com/question/28605735
#SPJ1
Missing information:
State the linear regression function, f(t), that estimates the day's coffee sales with a high temperature of t. Round all values to the nearest integer. State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong linear relationship between the variables? Explain your reasoning.
need the answers please
Answers
Answer:
8
sqrt(7)
1/2
20
Step-by-step explanation:
4sqrt(2) * sqrt(2) = 4 * sqrt(4) = 4 * 2 = 8
3sqrt(7) - 2sqrt(7) = sqrt(7)
sqrt(7)/(2sqrt(7)) = 1/2
2sqrt(5) * 2sqrt(5) = 2 * 2 * sqrt(25) = 4 * 5 = 20
answer choices:
37
74
16
20
Answers
Answer:
∠ BDC = 37°
Step-by-step explanation:
the central angle BAC is twice the angle on the circumference subtended on the same arc.
∠ BDC = \(\frac{1}{2}\) ∠ BAC = \(\frac{1}{2}\) × 74° = 37°
Which of the following statements is TRUE? Select ALL that apply. ln( y
x
)= ln(y)
ln(x)
log 5
(xy)=log 5
(x)⋅log 5
(y)
log 2
( y
x
)=log 2
(x)−log 2
(y)
log 4
(xy)=log 4
(x)+log 4
(y)
log b
( 4
1
)=−log b
(4)
log(x+y)=log(x)+log(y)
Answers
The correct statements are:
ln( yx)= ln(y)ln(x)
log 5(xy)=log 5(x)⋅log 5(y)
log 2( yx)=log 2(x)−log 2(y)
log 4(xy)=log 4(x)+log 4(y)
How to determine the correct statementsThe true statements from the given options are:
1. ln( yx) = ln(y)ln(x) (This is the property of logarithms known as the power rule for natural logarithms.)
2. log 5(xy) = log 5(x)⋅log 5(y) (This is the product rule for logarithms with base 5.)
3. log 2( yx) = log 2(x)−log 2(y) (This is the quotient rule for logarithms with base 2.)
4. log 4(xy) = log 4(x)+log 4(y) (This is the product rule for logarithms with base 4.)
Therefore, the true statements are:
ln( yx)= ln(y)ln(x)
log 5(xy)=log 5(x)⋅log 5(y)
log 2( yx)=log 2(x)−log 2(y)
log 4(xy)=log 4(x)+log 4(y)
Learn more about logarithms at https://brainly.com/question/30340014
#SPJ1
PLEASE HELP! BRAINLIEST TO WHOEVER CORRECTLY ANSWERS THE QUESTION BELOW!
Answers
Answer:
Your answer is -3
Step-by-step explanation:
Set the functions equal to each other, then solve for the variable.
what is the answer to the following questions 32 − 14
Answers
Answer:
Step-by-step explanation:
18
what is 4 time x-4 ?
Answers
Answer:
Answer :16
hope this helps
Answer:
4(x-4)=0
4x-16=0
4x=0+16
x=4
Simplify the given equation.
5x + 2(x-3) = -2(x - 1)
A. 7x-3 -2x - 1
B. 7x-6=-2x + 2
C. 7x-6 -2x - 2
Pls help
Answers
Answer:
B
Step-by-step explanation:
5x + 2(x-3) = -2(x - 1)
1. Distribute 2 through the parentheses:
5x + 2x - 6 = -2 (x - 1)
2. Distribute -2 through the parentheses:
5x + 2x - 6 = -2x + 2
3. Collect like terms:
7x - 6 = -2x + 2
What is the value of m in the m + 3/4 = − 3/8
Answers
Answer:
M=-9/8
Step-by-step explanation:
-3/8-3/4=-3/8-6/8=-9/8
Answer:
m = -9/8
Step-by-step explanation:
First, let's get m by itself by subtracting 3/4 from both sides:
m = -3/8 - 3/4
The least common denonimator between our two fractions is 8, so we can turn 3/4 into the equivalent fraction 6/8 to subtract our two fractions:
m = -3/8 - 6/8 = -9/8
Let f(x)=(x^2)+2
Let g(x)=1-3x
(fg)(-1)
Find the Value of each Function.
Answers
f[g(x)]=(g(x))² +2 —(2)
substitute the function g(x) into (2)
f[g(x)]= (1-3x)² +2
now x=-1
fg(-1)=(1-3(-1))² +2
=(1+3)² +2
= 16+2
= 18
For the problem -4(-5)(9), will the answer be positive or negative?
Answers
Answer:
Positive
Step-by-step explanation:
-4(-5)(9)
Negative cancels out negative, so it makes a positive:
20(9)
Simplify normally to get 180 as your final answer.
Question is in image
Answers
The radius of the spherical part is 3 inches and the length of the tube is 21 cm.
What is the volume of a cylinder?The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.
Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.
The two equations can be formed as below:-
4554 / 7 = πr²l + (2/3)πr³
396 = πr²( l - 9 ) + (2/3)πr³
Subtract the second equation from the first,
( 4554 / 7 ) - 396 = 9πr²
9πr² = 254.5
r² = 9
r = 3 cm
The length will be calculated as:-
4554 / 7 = πr²l + (2/3)πr³
4554 / 7 = π( 3 )²l + (2/3)π(3)³
l = 21 cm
Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.
To know more about volume follow
https://brainly.com/question/22716418
#SPJ1
Find the inequality represented by the graph
Answers
Answer:
y<or equal to 5/2x + 5
Step-by-step explanation:
when graphing inequalities, the line is solid when the inequality is also "or equal to". also, the less than sign indicates that the area below the line will be shaded. the y intercept is the y value when x is 0, so + 5. the slope, calculated with rise over run, is 5/2x
for a field trip 12 students rode in cars and the rest filled six buses how many students were in each bus if 342 students were on the trip
Answers
Answer:
55
Step-by-step explanation:
we have 342 students, subtract 12 because we need only kids riding the bus, now we have 330 kids, we divide the 330 kids between 6 buses 330/6, our answer is 55.
Estimate. 110×298
30,000
3,000
40,000
2,000
Answers
Answer:
it's acually 107,800
Answer:
30,000 yes this is correct
Step-by-step explanation:
5√27-2√48-5√3-√(3-2√3)2
Answers
Answer:
4√3
Step-by-step explanation:
5√27-2√48-5√3-(√3-2√3)2
= 5√(3x9)-2√(3x16)-5√3-2√3+4√3
= 5(3)√3-2(4)√3-5√3-2√3+4√3
= 15√3-8√3-5√3-2√3+4√3
= 4√3
2. The following set of count readings was made in a gradient-free γ-ray field, using a suitable detector for repetitive time periods of one minute: 18,500;18,410; 18,250;18,760;18,600;18,220;18,540;18,270;18,670;18,540. (a) What is the mean value of the number of counts? (b) What is its standard deviation (S.D.)? (c) What is the theoretical minimum S.D. of the mean? (d) What is the actual S.D. of a single reading? (e) What is the theoretical minimum S.D. of a single reading?
Answers
The inflection point of f(t) is approximately t = 3.73.
(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.
Taking the derivative of f(t), we have:
f'(t) = -1.275t^2 + 9.516t + 6.741
To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:
-1.275t^2 + 9.516t + 6.741 = 0
Using the quadratic formula, we find two possible values for t:
t ≈ 0.94 and t ≈ 6.02
Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).
For t < 0.94, choose t = 0:
f'(0) = 6.741 > 0
For 0.94 < t < 6.02, choose t = 1:
f'(1) ≈ 14.982 > 0
For t > 6.02, choose t = 7:
f'(7) ≈ -5.325 < 0
From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).
(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.
Taking the second derivative of f(t), we have:
f''(t) = -2.55t + 9.516
Setting f''(t) = 0 and solving for t, we find:
-2.55t + 9.516 = 0
t ≈ 3.73
Therefore, The inflection point of f(t) is approximately t = 3.73.
Learn more about inflection point here:
https://brainly.com/question/29249123
#SPJ11