Find F If F' (X) = 16x^3 + 14x + 7 And F(1) = -5. Answer: F(X) =
Answers
The value of function f (x) is,
⇒ F (x) = 4x⁴ + 7x² + 7x - 22
We have to given that;
Function is,
⇒ F' (x) = 16x³ + 14x + 7
Now, We get;
Integrate both side;
F (x) = 16 x⁴ / 4 + 14x²/2 + 7x
F(x) = 4x⁴ + 7x² + 7x + c
Since, F (1) = - 5
Hence,
F (x) = 4 (1)⁴ + 7 (1)² + 7 (1) + c
- 5 = 4 + 7 + 7 + c
c = - 22
Thus, The function f (x) is,
⇒ F (x) = 4x⁴ + 7x² + 7x - 22
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Related Questions
3 pounds of avocados costs $4.50. how many avocados do you get per dollar spent?
Answers
Answer:
You get 1.5 avacados per dollar.
Step-by-step explanation:
If you divide $4.50 by 3 you get 1.5 and that is the amount of avacados you get per dollar spent.
The nth term of a sequence is 2n²- 1.
Which term is closest to 100?
Answers
The 5th term.
Plug in 5 for n
2(5)^2-1=99
Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems. 1. 2. 3. maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0. maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0. maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.
Answers
The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.
1. Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems.
maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
Now, To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 3/4), (0, 0), and (3, 0).
z = x₁ + 2x₂ = (0) + 2(3/4)
= 1.5z = x₁ + 2x₂ = (0) + 2(0) = 0
z = x₁ + 2x₂ = (3) + 2(0) = 3
The maximum value of the objective function z is 3, and it occurs at the point (3, 0).
Hence, the optimal solution is (3, 0), and the optimal value of the objective function is 3.2.
maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
To find the optimal solution and the optimal value of the objective function,
evaluate the objective function at each corner of the feasible region:
(0, 0), (3, 0), and (2, 5).
z = x₁ + x₂ = (0) + 0 = 0
z = x₁ + x₂ = (3) + 0 = 3
z = x₁ + x₂ = (2) + 5 = 7
The maximum value of the objective function z is 7, and it occurs at the point (2, 5).
Hence, the optimal solution is (2, 5), and the optimal value of the objective function is 7.3.
maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 1), (2, 0), and (5, 1).
z = 3x₁ + 4x₂ = 3(0) + 4(1) = 4
z = 3x₁ + 4x₂ = 3(2) + 4(0) = 6
z = 3x₁ + 4x₂ = 3(5) + 4(1) = 19
The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.
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(56 points) This table represents the cups of coffee, c, a coffee shop has left after being open for h hours.
When graphed, all of the points in the table lie on the same line.
What is the slope and y-intercept of the line?
Drag and drop the slope and y-intercept into the corresponding boxes.
Answers
Step-by-step explanation:
The slope is the ratio of change in number of cups to change in hours:
m = (288 - 432)/(3 - 0) = - 48The y-intercept is the number of cups at zero hour:
b = 432The line would be:
c(h) = 432 - 48hEach pair of figures a similar find the missing length brown to the nearest 10th where necessary
Answers
Answer:
vygtvfgbhngfvvmjcfnjvhygnchjdhrfu
Step-by-step explanation:bghnjmhgbvfcfv
reciprocal of -2/3^6
Answers
Answer:
PLEASE GIVE BRAINLIEST AND THANKS
-0.00068587105
Step-by-step explanation:
Two classes are having pizza parties. Ms. Rodriguez’s class decides to order enough so that every 3 students will have 2 pizzas. Mr. Becker’s class decides to order enough so that every 5 students will have 3 pizzas. Complete the following statements. You can enter whole numbers, decimals rounded to the hundredths place, or simplified fractions.
Each student in Ms. Rodriquez’s class will get _____ of a whole pizza.
Each student in Mr. Becker’s class will get _____ of a whole pizza.
Answers
Answer:
2/3
3/5
Step-by-step explanation:
Consider the following two-period model with log utility functions: \[ \begin{aligned} \operatorname{Max}_{C_{1}, C_{2}} \ln \left(C_{1}\right)+\beta \ln \left(C_{2}\right) \\ \text { s.t. } C_{1}+\fr
Answers
The given model is a two-period model with log utility functions. The objective is to maximize the sum of log consumption in both periods, subject to a budget constraint.
In this model, the decision-maker wants to maximize their utility derived from consumption in two periods, denoted as C1 and C2, respectively. The utility function is logarithmic, implying that the marginal utility of consumption decreases as consumption increases. The objective is to maximize the sum of the logarithmic utility of both periods.
The budget constraint states that the total consumption in both periods cannot exceed the available resources or income. However, specific details about the budget constraint are not provided in the question.
To solve this optimization problem, we can use mathematical techniques such as the Lagrangian method or dynamic programming. The Lagrangian method involves setting up the Lagrangian function with the objective function, constraints, and a Lagrange multiplier. By taking derivatives and solving the resulting equations, we can find the optimal consumption levels in each period.
Overall, the goal is to allocate consumption between the two periods in a way that maximizes the total utility, given the budget constraint.
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-5x + 18 = 3x - 38
show steps please need this asap
Answers
Answer:
x = 7.
Step-by-step explanation:
-5x + 18 = 3x - 38
18 + 38 = 3x + 5x
56 = 8x
x = 7.
2. Identify the missing factors:
d) 20 = (4) (?)
e) -14x = (7) (?)
f) x3 =x2 (?)
Answers
Answer:
d) 20 = (4) (5)
e)-14x = (7) (0) = undefined
f) Every Real numbers are solutions, here.
Step-by-step explanation:
2) Identify the missing factors:-
d) 20 = 4(?)
Solved:
Let us assume that *?* = x here.
20 = 4x20/4 = x5 = xx =5e)-14x = (7) (?)
Assume *?* as x
-14x = 7x−14x−7x=7x−7x−21x=0x = 0/-21 = undefinedf) x^3=x^2(?)
Assume ? as x
x³=x²(x)x³−x³=x^3−x^30=0Real numbers are solutions.please help ill give brainliest answer
Answers
Answer:
MO=36
AG=23
Step-by-step explanation:
\(\frac{MO}{AT}=\frac{PM}{GT}\)
\(\frac{MO}{18} =\frac{62}{31}\)
\(31MO=1116\)
\(MO=36\)
\(\frac{OP}{AG} =\frac{MP}{TG}\)
\(\frac{46}{AG} =\frac{62}{31}\)
\(62AG=1426\)
\(AG=23\)
How many inches means 1 feet?
Answers
1 foot is equal to 12 inches. So one feet is equal to 12 inches. The conversion factor between feet and inches is 1 ft = 12 in.
Inches (in) and feet (ft) are both units of measurement for length, but they are not directly interchangeable. To convert a measurement of length from feet to inches, you will need to use a conversion factor.
To convert a measurement of length from feet to inches, you will multiply the number of feet by the conversion factor of 12.
For example,
if you have a measurement of 2 feet, you would multiply 2 x 12 to get 24 inches. So, 2 ft = 24 in.
It's important to note that when measuring length, it's important to use the same system of measurement as the requirement, as using the wrong measurements can greatly affect the outcome of the calculation. It's always good to know the conversion factors to make your calculations easier.
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Vertical and Horizontal Lines
Write the equation of the line graphed below.
Answers
Answer:
x=3
Step-by-step explanation:
Because the line lies on x =3
Answer:
x=3
Step-by-step explanation:
This is a vertical line ( up and down)
Vertical lines are of the form x=
x=3
need help finding area
Answers
Answer:
93.53
Step-by-step explanation:
HELP HELO
HELPPPPPP ASAP
On average, Leah's car gets 31.4 miles on every gallon of gasoline. If she fills up her tank for $2.18 per gallon, how much will it cost her to drive
358 miles?
Answers
Answer:
Step-by-step explanation:
Car drive 31.4 miles/gallon
for 358 miles, Leah needs 358/31.4 =~ 11.40 gallons
since it cost $2.18 / gallon, it will cost Leah 2.18 * 11.4 = $24.85
8
Henry earned 5 dollars for each lawn he mowed. If he had 12 lawns to mow, but forgot
to mow 7 of them, how much money did he actually earn?
A $10
B $49
C $24
D $8
Plz help
Answers
Answer:
huh that's weird there should be an answer for 25
Step-by-step explanation:
Which of the following is a univariate display of quantitative data? histogram mosaic plot bar chart scatterplot
Answers
A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.
A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.
Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.
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the price of firewood 4 years ago was $140 per cord. today, a cord of wood costs $182. what has been the annual rate of increase in the cost to the nearest tenth of a percent?
Answers
Using the formula for compound interest we find that the annual rate of increase in the cost of firewood is approximately 7.8%.
We can use the formula for compound interest to calculate the annual rate of increase:
A = P(1 + r)^n
where A is the final price, P is the initial price, r is the annual rate of increase, and n is the number of years.
We know that P = $140, A = $182, and n = 4, so we can solve for r:
182 = 140(1 + r)^4
(1 + r)^4 = 1.3
1 + r = 1.3^(1/4)
r ≈ 0.0777
The annual rate of increase is approximately 0.0777 or 7.8% to the nearest tenth of a percent.
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Vada places a box of toys and a box of books together. The box of toys has a length of 5 feet, a width of 3 feet, and a height of 2 feet. The box of books has a length of 6 feet, a width of 4 feet, and a height of 2 feet. What is the combined volume of the boxes?
Answers
Answer:
78 ft cubed
Step-by-step explanation:
First calculate the volume of the toys...
5 x 3 x 2 = 30
Now the book boxes...
6 x 4 x 2 = 48
30 + 48 = 78
The combined volume should be 78 feet cubed! hope this helps!!!
Answer:
78 ft³
Step-by-step explanation:
Volume of a rectangular prism = length × width × height
Toy Box
length = 5 ftwidth = 3 ftheight = 2ft⇒ volume = 5 × 3 × 2 = 30 ft³
Book Box
length = 6 ftwidth = 4 ftheight = 2 ft⇒ volume = 6 × 4 × 2 = 48 ft³
Total combined volume = 30 + 48 = 78 ft³
If the composite functions f(g(x)) and g(f(x)) both equal x, then the function g is the____function of f.
Answers
If the composite functions f(g(x)) and g(f(x)) both equal to x, then the function g is the Inverse function of f.
What is the inverse of a function?A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.
Let us take the Example.
Suppose f(x)= x/4 and g(x)=4x.
Let x=1
then f(g(x))= f(g(1))=f(4)=1
and g(f(x))=g(f(1))=g(1/4)=1
Here, f(g(x))=g(f(x))=1
Therefore , we can say that f(g(x)) and g(f(x)) are inverse of each other.
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Find the value of x in the triangle shown below.
O
X =
37°
56°
Answers
Answer:
x equals 87
Step-by-step explanation:
37 + 56 = 93
triangles always equal to 180
180 - 93 = 87
Find an LU factorization of the matrix A (with L unit lower triangular). A=
⎣
⎡
4
−8
10
−8
8
−4
3
5
−7
7
6
−7
0
3
−3
⎦
⎤
Answers
The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].
Let's go step by step to find the LU factorization of matrix A.
Matrix A:
A =
[4, -8, 10]
[-8, 8, -7]
[6, -7, 3]
Step 1:
Initialize the L matrix as an identity matrix of the same size as A.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 2:
Perform Gaussian elimination to obtain U.
- Multiply the first row of A by (1/4) and replace the first row of A with the result.
A =
[1, -2, 2.5]
[-8, 8, -7]
[6, -7, 3]
- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[6, -7, 3]
- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.
A =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Step 3:
Update the L matrix based on the operations performed during Gaussian elimination.
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
Step 4:
The resulting matrix A is the upper triangular matrix U.
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
Therefore, the LU factorization of matrix A is:
L =
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
U =
[1, -2, 2.5]
[0, 24, -27]
[0, 5, -12.5]
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Look at this set of 9 numbers:
2,2,5 ,2,2 ,2,8,4 ,2
By how much would the mode decrease if the number 7 were added to the set?
Answers
Please answer..I'll give the Banlist or how ever u spell it lol
Answers
Answer:
Step-by-step explanation:
What’s the answer to this?!!!!!
Answers
Answer:
a = 6.7
Step-by-step explanation:
a² + b² = c²
a² + 6² = 9²
a² + 36 = 81
a² = 45
\(\sqrt{a^2} =\sqrt{45}\)
a = 6.7
FRE-E POIN-TS........................................................................................got your at-tention we-ll no free poi-nts answer the question below and show work
Answers
If it is solving for e then e = -2
Step-by-step explanation:
First you have to add 7 to both sides of the equation. Next you simplify by adding the numbers. Then subtract 7e from both sides of the equation. After that you have to simplify again by combining like terms. Then divide both sides of the equation by the same term which is 2. Finally you have to cancel the terms that are in both the numerator and denominator divide the numbers and you would get -2
We have the given equation:
9e - 7 = 7e - 11
Our goal is to isolate the variable, e.
9e - 7 = 7e - 11
+7 +7
____________
9e = 7e - 4
-7e -7e
____________
2e = -4
/2 /2
____________
e = -2
What is the equation of the line that passes through the point (-7-1) and has slope of 1
Answers
Answer: y=-x+-8
Step-by-step explanation:
Proof is in the screenshot below
Answer:
19=b
Step-by-step explanation:
Hence the equation in the form y = mx + c can written as y = 1/7x + 33/7 which is the equation of the line with the slope of 1/7 passing through the point (2,5).
The function y = 40 – 2.5x can be used to determine the
amount of water in gallons remaining after x minutes
draining. What is the rate of change of the amount of
water in gallons with respect to the number of minutes
draining?
Answers
Answer: -2.5 gallons per minute
Step-by-step explanation:
To simple it out It's asking for the slope aka the rate of change so the water drains out of the bucket at -2.5 gallons per minute
Hope you've had a good day!! :)))
If the odds against debroah's winning first prize are 3 to 5, what is the probability that she will win 1st prize?
Answers
Answer:
See below
Step-by-step explanation:
Odds AGAINST are 3 to5 then odds FOR are 2 to 5
2/5 = .4 = 40% chance of winning
What is the area of the trapezoid below?
A. 36 square root of 3 c m squared
B. 44 square root of 3 c m squared
C. 65 c m squared
D. 88 c m squared
Answers
The area of the trapezoid is 72 cm².
To find the area of the trapezoid, we can use the formula:
A = [(a + b) / 2] * h
Given:
Length of one parallel side (a) = 7 cm
Difference between the lengths of the parallel sides (b - a) = 4 cm
Slant height (h) = 8 cm
To calculate the length of the other parallel side (b), we can use the difference between the lengths of the parallel sides:
b = a + (b - a) = 7 + 4 = 11 cm
Now we have all the values we need to calculate the area:
A = [(7 + 11) / 2] * 8
= [18 / 2] * 8
= 9 * 8
= 72 cm²
Therefore, the correct answer is not listed among the given options. The area of the trapezoid is 72 cm².
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