Find f. f ''(x) = 4 + 6x + 36x2, f(0) = 2, f (1) = 10
The function [tex]\( f(x) \)[/tex] is: [tex]\[ f(x) = 2x^2 + x^3 + 3x^4 + 5x + 4 \][/tex]
Given:
[tex]\[ f''(x) = 4 + 6x + 36x^2 \][/tex]
[tex]\[ f(0) = 2 \][/tex]
[tex]\[ f(1) = 10 \][/tex]
1. Integrate [tex]\( f''(x) \)[/tex] to find [tex]\( f'(x) \)[/tex]:
[tex]\[ f'(x) = \int (4 + 6x + 36x^2) \, dx = 4x + 3x^2 + 12x^3 + C_1 \][/tex]
2. Integrate [tex]\( f'(x) \)[/tex] to find [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = \int (4x + 3x^2 + 12x^3 + C_1) \, dx = 2x^2 + x^3 + 3x^4 + C_1x + C_2 \][/tex]
3. Use the initial condition [tex]\( f(0) = 2 \)[/tex] to find [tex]\( C_2 \)[/tex]:
[tex]\[ 2x^2 + x^3 + 3x^4 + C_1x + C_2 \text{ at } x=0 \][/tex]
[tex]\[ 2 = C_2 \][/tex]
[tex]\[ C_2 = 2 \][/tex]
4. Use the initial condition [tex]\( f(1) = 10 \)[/tex] to find [tex]\( C_1 \)[/tex]:
[tex]\[ f(1) = 2(1)^2 + (1)^3 + 3(1)^4 + C_1(1) + 2 = 10 \][/tex]
[tex]\[ 2 + 1 + 3 + C_1 + 2 = 10 \][/tex]
[tex]\[ 8 + C_1 = 10 \][/tex]
[tex]\[ C_1 = 2 \][/tex]
Thus, the function [tex]\( f(x) \)[/tex] is:
[tex]\[ f(x) = 2x^2 + x^3 + 3x^4 + 5x + 4 \][/tex]
The complete question is:
Find f(x). f ''(x) = 4 + 6x + 36x2, f(0) = 2, f (1) = 10
you have a part-time job that pays $4.75 an hour with tips allergy $4 and fifty an hour your deductions are fic a 7.65% federal tax withholding 12.5% in state tax withholding 6.85 % you work 20 hours per week you want to save $40 a week how much left in your discretionary income per week soon that all the income from your part time job is discretionary and the next one is
You decide to save 15% of your realized income how much do you save per month?
helppppp picture included
Suppose a population proportion is .40, and 80% of the time when you draw a random sample from this population you get a sample proportion of .35 or more. how large a sample were you taking?
Final answer:
To determine the sample size needed, use the formula for sample proportion: n = (z * sqrt(p * q)) / E. Plugging in the given values, the minimum sample size required is 178.
Explanation:
To determine the sample size needed, we can use the formula for sample proportion:
n = (z * sqrt(p * q)) / E
Where:
n is the sample size
z is the z-value corresponding to the desired confidence level (in this case, 80%)
p is the population proportion (0.4)
q is 1 - p
E is the maximum allowable error (0.05)
Plugging in the values, we have:
n = (z * sqrt(p * q)) / E = (0.84 * sqrt(0.4 * (1 - 0.4))) / 0.05 ≈ 177.6
Since we cannot have a fractional number of individuals, we round up to the next whole number. Therefore, we would need a minimum sample size of 178 to be 80% confident that the population proportion is estimated to within 0.05.
Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations.
PLEASE HELP ASAP!! NEED NOW! THANKS!
y=-4/3x+300 i hope this helps you
5.6 times what equals 19.04
To win at lotto in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50). the order in which the selections is made does not matter. how many different selections are possible?
This is a function whose domain is a set of consecutive integers. They are finite and infinite.
Answer:
the answer is sequence (usa test prep)
Step-by-step explanation:
Find the distance between the points (
-
10,12) and (15,12).
If output per worker is now nearly $120,000 per year, how much will the average worker produce 5 years from now if productivity improves by (use the compounding formula below to answer the question): fv1 = p(1 + r), fv2 = p(1 + r)(1 + r), fv3 = p(1 + r)(1 + r)(1 + r)… instructions: enter your responses rounded to two decimal places. (a) 2 percent per year? $ (b) 3 percent per year? $
Find the surface area of the cylinder. Round to the nearest whole number.
•1,359 cm^2
•730 cm^2
•553 cm^2
•1,790 cm^2
The table shows the number of boys and girls that have black, blonde, brown, or red hair color. What is the probability that a girl has black hair?
Answer:
O.25
Step-by-step explanation:
Trust me on this one the answer was in the comments :/
The probability of a girl having black hair is determined by dividing the number of girls who have black hair by the total number of girls. Without actual numbers from the table, a specific probability cannot be calculated.
Explanation:To find the probability that a girl has black hair, we have to first know the total number of girls, and then the number of girls who have black hair. Probability is determined by dividing the number of desired outcomes by the total number of outcomes. So in this case, if we let 'G' denote the total number of girls and 'B' be the number of girls with black hair, the formula for the probability would be P(B) = B / G. Without the actual numbers from the table, we cannot calculate the specific probability.
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the radius of a glass is 1.25 inches. What circumference? use 3.14 for pi
REALY NEED HELP Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By=C. (4,8) and (3,5)
If the total income generated from gasoline for AER was $408 million how much would be the cost for a barrel of gasoline, gasoline 34% kerosene 14% 60 million barrels total production crude oil
The correct answer is: $20
Explanation:
As we are interested in finding the cost for a barrel of gasoline, we need to read the percentage of gasoline from the pie-chart first—which is 34%.
Now number of barrels containing gasoline = 34% of 60 million barrels = [tex] \frac{34}{100} * 60 = 20.4 [/tex] million barrels
For all the barrels, the total income is $408 million; therefore, in order to find the per-barrel cost, we need to divide $408 by 20.4:
[tex] \frac{408}{20.4} = \$20 [/tex]
Hence the correct answer is $20.
The dance committee has a budget of $125 to decorate the gym for the spring dance. They have already spent $65. Some members want to buy helium balloons that cost $0.80 each. Write and solve an inequality to show the number of balloons that the dance committee could buy
The dance committee could buy up to 75 helium balloons with their remaining budget of $60, after already spending $65 from their total budget of $125.
To determine the number of helium balloons that the dance committee could buy with their remaining budget, we first need to calculate how much money they have left after already spending $65. Since their total budget is $125, the remaining budget is calculated as $125 - $65 = $60.
Let's let b represent the number of balloons they can buy. The cost per balloon is $0.80, so the inequality representing the situation is 0.80b \<= 60. To solve for b, we divide both sides of the inequality by 0.80, which gives us b \<= 60 / 0.80, or b \<= 75.
Therefore, the dance committee could buy up to 75 helium balloons with their remaining budget, staying within their financial limitations.
What is the probability of flipping a coin and it coming up heads four times in a row
The graph of the function y=x^2+2 is shown. Which equation will shift the graph of the function to the right 2 units?
A bag contains 7 blue, 12 red, and 6 orange marbles. Find each probability if you draw one marble at random from the bag. Write as a fraction. a) P (purple)
b) P (red or orange) Please
c)P(not blue) Help
describe the steps you would use to factor 2x ^ 3 + 5x ^ 2 - 8x - 20 completely then State the factored form. this isn't multiple choice btw
Answer:
2·x^3 + 5·x^2 - 8·x - 20 = 0
You see that the term will be 0 for x = 2
(2·x^3 + 5·x^2 - 8·x - 20) / (x - 2) = 2·x^2 + 9·x + 10 = 0
You can use the abc-formula to solve the quadratic equation.
x = -2.5 ∨ x = -2
So the factored form will be
2·x^3 + 5·x^2 - 8·x - 20 = 2·(x - 2)·(x + 2)·(x + 2.5)
Answer:
2·x^3 + 5·x^2 - 8·x - 20 = 0
You see that the term will be 0 for x = 2
(2·x^3 + 5·x^2 - 8·x - 20) / (x - 2) = 2·x^2 + 9·x + 10 = 0
You can use the abc-formula to solve the quadratic equation.
x = -2.5 ∨ x = -2
So the factored form will be
2·x^3 + 5·x^2 - 8·x - 20 = 2·(x - 2)·(x + 2)·(x + 2.5)
use similar triangles to solve. a person who is 5 feet tall is standing 140 ft from the base of a tree and the tree cast a 154 foot shadow. the person's Shadow is 14 ft in length what is the height of the tree
The home of Russell Slater is assessed at $140,000. The tax rate is 11.8 mills. The actual amount of tax on Russell's home is:
$1,652
$1,462
$1,362
None of these
$1,562
Eve is replacing the soil in her plant containers. How many cubic inches of soil will Eve need for the two rectangular containers?
A.45
B.216
C.648
D.864
Lisa drove 40 3/5 miles in one hour. At the same speed in how many hours could she drive in 121 4/5
priority question
The dot plots below show the test scores of sixth- and seventh-grade students: Dot plot for Grade 6 shows 6 dots on score 70, 4 dots on score 80, 6 dots on score 90, and 4 dots on score 100. Dot plot for Grade 7 shows 5 dots on score 50, 7 dots on score 60, 4 dots on score 70, and 4 dots on score 80. Based on visual inspection of the dot plots, which grade, if any, appears to have the higher mean score? Grade 6 Grade 7 Both groups show about the same mean score. No conclusion about mean score can be made from the data.
Answer:
Grade 6 i think
PLEASE HELP!!! REWRITE THE FOLLOWING LINEAR EQUATION IN SLOPE INTERCEPT FORM??
Toysrus is having a 38% off sale. If a backpack normally costs $22, how much will it cost on sale
The backpack will cost $13.64 during the 38% off sale at Toysrus, calculated by subtracting the discount ($8.36) from the original price ($22).
To calculate the discount amount, we multiply the original price by the discount percentage:
$22 * 0.38 = $8.36
Now, to get the sale price, we subtract the discount amount from the original price:
$22 - $8.36 = $13.64
Therefore, the backpack will cost $13.64 on sale.
Find the first term, a1, of an arithmetic sequence if a12 = 38 and a45 = 170.
–6
132/33
–5
6
The solution is: The starting term is -6
What is Arithmetic progression?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Standard formula for arithmetic sequence:
an = a0 + d(n-1)
if we use the two terms given, setting a12 as starting term and a45 as the end term an.
170 = 38 + 33d
170 - 38 = 33d
132 = 33d
132/33 = d
This is the common difference, use it to find the first term.
38 = a0 + (132/33)(12-1)
38 = a0 + (132/33)(11)
38 = a0 + 132/3
38 - 132/3 = a0
38 - 44 = a0
-6 = a0
The starting term is -6
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line L1, L2 and L3 are in the same plane, L1 is perpendicular to L2, and L3 is parallel to L1. which of the following statement must be true?
1. L3 is parallel to L2
2.L3 is perpendicular to L2
3.L3 intersects L2
The true statement will be
1. ''L3 is perpendicular to L2''
What is Parallel lines?
Parallel lines are straight lines that do not intersect at any point.
Given that;
Line L1, L2 and L3 are in the same plane,
L1 is perpendicular to L2, and L3 is parallel to L1.
Now,
Line L1 is perpendicular to L2.
And, L3 is parallel to L1.
Then, Line L3 is perpendicular to line L2
Thus, The true statements will be
1. ''L3 is perpendicular to L2'' and
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What is the y-intercept of the equation of the line that is perpendicular to the line y = 3/5x + 10 and passes through the point (15, –5)?