The average rate of change of the function from t=1 to t=2.5 is given by:
[tex]\frac{h(2.5)-h(1)}{2.5-1}=\frac{h(2.5)-h(1)}{1.5}[/tex]It is given that:
[tex]\begin{gathered} h(t)=148-16t \\ h(2.5)=148-16\times2.5=108 \\ h(1)=148-6=142 \end{gathered}[/tex]Substitute the values to get:
[tex]\frac{h(2.5)-h(1)}{1.5}=\frac{108-142}{1.5}=\frac{-68}{3}\approx-22.6667[/tex]Hence the rate of change is -22.6667.
Solve the equation. f(x)=g(x) by graphing. f(x) = l x +5 l g(x) = 2x + 2 Select all possible solutions: No Solutions x=3 x=0 X=-1
As you can observe in the graph below, the given functions intercept at one point.
Hence, there is a unique solution and it's x = 3.You draw 7 cards from a standard deck of cards. What is the probability of drawing 3 diamonds and 2 clubs?
Solution
For this case we can do the following:
[tex]p=\frac{\text{possible}}{\text{total}}[/tex]and we can find the answer with this:
[tex]p=\frac{(13C3)(13C2)(26C2)}{52C7}=0.0541[/tex]In a cricket match, you have a squad of 15 players and you need to select 11 for a game. The two opening batsmans are fixed and the rest of the players are flexible. How many batting orders are possible for the game?
The number of batting orders that are possible for the game is 1365 orders.
What are combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!
n = the number of items.
r = how many items are taken at a time.
This will be:
15! / 11! (15 - 11)!
= 15! / 11! 4!
= 15 × 14 × 13 × 12 / 4 × 3 × 2
= 1365 orders
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es26. Name the relationship between the anglesand solve for x.12x + 417x + 2
From the given figure, we can see that the angle (12x+4) and the angle (17x+2) lie on the same straight line.
Theerfore, they are supplimentary to each other.
1. Caitlyn is going away to college and will need to rent a truck to helpmove. The cost of the truck is $35 plus $0.79 per mile. If her collegeis 85 miles away and she budgeted $100 for the rental, will she haveenough money?
1. Caitlyn is going away to college and will need to rent a truck to help
move. The cost of the truck is $35 plus $0.79 per mile. If her college
is 85 miles away and she budgeted $100 for the rental, will she have
enough money?
we know that
The equation in slope intercept form of this situation is
y=mx+b
where
m=$0.79 per mile
b=$35
y -----> is the total cost
x -----> the number of miles
so
y=0.79x+35
so
For x=85 miles
substitute
y=0.79(85)=35
y=$102.15
we have that
102.15 > 100
therefore
she not have enough moneyGiven that XY = ZY, WX = 6x-3 and WZ= 4x + 9, find ZX
In the Given Figure,
There are two right triangles, ΔWXY and ΔWZY,
So, according to Pythagoras' theorem,
XW^2 + YW^2 = XY^2
And WZ^2 + YW^2 = ZY^2
Now, Since XY = ZY, their squares are also equal
⇒XW^2 + YW^2 = WZ^2 + YW^2
⇒ XW^2 = WZ^2 ................(YW^2 is the common term on both sides)
⇒ (6x-3) ^2 = (4x + 9) ^2
⇒ 36x^2 - 36x + 9 = 16x^2 + 72x + 81
⇒36x^2 - 16x^2 - 36x + 72x = 81-9
⇒20x^2 - 108x = 72
⇒ 5x^2 - 27x = 18
⇒ 5x^2 - 27x - 18 = 0
⇒ (5x+3) (x-6) = 0
⇒ x = 6 or x = -3/5
Since, the distance cannot have a negative value,
⇒ x = 6
So, WX = 6x - 3 = 6(6) - 3 = 36-3 = 33
WZ = 4x + 9 = 4(6) + 9 = 24 + 9 = 33
ZX = WX + WZ = 33 + 33 = 66 units.
Also, since all the three sides of ΔWXY and ΔWZY are equal, ΔWXY and ΔWZY are congruent to each other.
What are Congruent Triangles?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.Formally, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. This indicates that either object may be precisely aligned with the other object by moving and reflecting it, but not by resizing it. So, if we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are congruent.If the matching sides and angles of two triangles are the same length, then the triangles are said to be congruent.To learn more about Congruent Triangles, refer to:
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Solve the quadratic equation by completing the square.x^2+18x+75=0First choose the appropriate form and fill in the blanks with the with the correct numbers. Then solve the equation. If there is more than one solution, separate them with commas.
we have the quadratic equation
x^2+18x+75=0
complete the square
x^2+18x=-75
x^2+18x+81=-75+81
x^2+18x+81=6
rewrite as perfect squares
(x+9)^2=6
Find out the solutions
square root both sides
[tex]x+9=\pm\sqrt[\square]{6}[/tex][tex]x=-9\pm\sqrt[\square]{6}[/tex]The first solution is
[tex]x=-9+\sqrt[\square]{6}[/tex]The second solution is
[tex]x=-9-\sqrt[\square]{6}[/tex]Which of the following is only true sometimes? A. The sum of a rational number and a rational number is rational. B. The sum of a rational number and an irrational number is irrational. C. The product of an irrational number and an irrational number is irrational. D. The product of a nonzero rational number and an irrational number is irrational.
The sum of a rational number and a rational number is rational. ALWAYS
The sum of a rational number and an irrational number is irrational.
The product of an irrational number and an irrational number is irrational. SOMETIMES
For example, the product of multiplicative inverses like √2 and 1/√2 will be 1
The product of a nonzero rational number and an irrational number is irrational.
We have a box with a circular base (diameter 20 cm) and height 4 cm.Calculate the volume.
We can calculate the volume as the product of the area of the base and the height.
The area of the base is function of the square of the diameter, so we can write:
[tex]\begin{gathered} V=A_b\cdot h \\ V=\frac{\pi D^2}{4}\cdot h \\ V\approx\frac{3.14\cdot(20\operatorname{cm})^2}{4}\cdot4\operatorname{cm} \\ V\approx\frac{3.14\cdot400\operatorname{cm}\cdot4\operatorname{cm}}{4} \\ V\approx1256\operatorname{cm}^3 \end{gathered}[/tex]Answer: the volume of the box is 1256 cm^2.
The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?
The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?
we have that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube.
so
Find the scale factor
ratio volumes=40.5/12=3.375
3.375=(scale factor)^3
[tex]\text{scale factor=}\sqrt[3]{3.375}[/tex]scale factor=1.5
To find out the diameter of the larger balloon multiply the scale factor by the diameter of the smaller balloon
so
1.5*(10)=15 inches
the answer is 15 inchesIn the matrix equation below, what are the values of x and y? 1/2 [4 8 x+3 -4] -3 [1 y+1 -1 -2]= [-1 -5 7 4]
Using the matrix equation, the value of x and y are 5 and 2 respectively.
Consider the 2 by 2 matrix equations,
1/2 [ 4 8 ( x + 3 ) - 4 ] - 3[ 1 y+1 -1 - 2 ] = [ - 1 -5 7 4 ]
[ 2 4 (x+3)/2 -2] + [ - 3 -3y -3 +3 + 6] = [ - 1 - 5 7 4]
[ -1 -3y + 1 (x + 9)/2 + 4] = [ - 1 - 5 7 4]
Therefore,
- 3y + 1 = - 5
Subtracting 1 from each side of the equation,
- 3y + 1 - 1 = - 5 - 1
- 3y = - 6
Dividing each side of the equation by - 3,
y = 2
And;
( x + 9 )/2 = 7
Multiplying each side by 2,
x + 9 = 14
Subtracting 9 from each side of the equation,
x + 9 - 9 = 14 - 9
x = 5
Therefore, the value of x and y is 5 and 2 respectively.
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to rent a van a moving company charges $40.00 plus $0.50per miles
The problem talks about the cost for renting a van, which can be calculated adding $40.00 plus $0.50 for each mile.
The problem asks to wirte an explicit equation in slope-intercept form which can represent the cost of renting a van depending on the amount of miles. Then, the problem asks to find the cost if you drove 250 miles.
ok my question is math algebra. consider the linear equation y-1=0 and grapthe two points
To find:
We need to find two points on the linear equation y-1=0 and to plot those points on graph.
Step by step solution:
We know that:
General coordinate of any two points on line y = 1:
= (x, 1)
So let us assume any two random points on the line:
= (1,1) and (2,1)
We will now mark them on the graph:
For lunch, Kile can eat a sandwich with either ham or a bologna and with or without cheese. Kile also has the choice of drinking water or juice with his sandwich. The total number of lunches Kile can choose isA. 12B. 8C. 4D. 6
Okay, here we have this:
She can eat the following options:
Sandwich with ham with or without cheese. Two choices.
Sandwich with bologna with or without cheese. Other two choices
This mean that she can eat:
Sandwich with ham with cheese with water or juice. Two options.
Sandwich with ham without cheese with water or juice. Two options.
Sandwich with bologna with cheese with water or juice. Two options.
Sandwich with bologna without cheese with water or juice. Two options.
Finally we obtain a total of: 2+2+2+2=8 options of lunches.
Thw
two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the second on a bearing of 145° at 22 knots. how far apart are they after 1.5 hours (round to the nearest nautical mile)
Given that one of the ships travels at 12 nautical miles per hour, then after 1.5 hours, it will travel 12*1.5 = 18 miles
The other ship will travel 22*1.5 = 33 miles
The angle of 145° is measured with respect to the positive x-axis. Then, respect the negative x-axis, its measure is 180° - 145° = 35°
We have to use trigonometric functions to find x1, y1, x2, and y2, as follows:
sin(55°) = y1/18
sin(55°) *18 = y1
14.7 = y1
cos(55°) = x1/18
cos(55°)*18 = x1
10.3 = x1
sin(35°) = y2/33
sin(35°)*33 = y2
18.9 = y2
cos(35°) = x2/33
cos(35°)*33 = x
-27 = x2 (the minus sign comes from the graph)
The distance between two points (x1, y1) and (x2, y2) is computed as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting with the values found,
[tex]\begin{gathered} d=\sqrt[]{(-27-10.3)^2+(18.9-14.7)^2} \\ d=\sqrt[]{(-37.3)^2+4.2^2} \\ d=\sqrt[]{1391.29+17.64} \\ d\approx38\text{ miles} \end{gathered}[/tex]Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.y²-3y - 18/y²-9y + 18Rational expression in lowest terms:Variable restrictions for the original expression: y
Given: The expression below
[tex]\frac{y^2-3y-18}{y^2-9y+18}[/tex]To Determine: The lowest term of the given rational fraction
Solution
Let simplify both the numerator and the denominator
[tex]\begin{gathered} Numerator:y^2-3y-18 \\ y^2-3y-18=y^2-6y+3y-18 \\ y^2-3y-18=y(y-6)+3(y-6) \\ y^2-3y-18=(y-6)(y+3) \end{gathered}[/tex][tex]\begin{gathered} Denominator:y^2-9y+18 \\ y^2-9y+18=y^2-3y-6y+18 \\ y^2-9y+18=y(y-3)-6(y-3) \\ y^2-9y+18=(y-3)(y-6) \end{gathered}[/tex]Therefore
[tex]\begin{gathered} \frac{y^2-3y-18}{y^2-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ y-6-is\text{ common} \\ \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{y+3}{y-3} \end{gathered}[/tex]Hence, the rational expression in its lowest term is
[tex]\frac{y+3}{y-3}[/tex]The variable for the original expression is as given as
[tex]\begin{gathered} \frac{y^{2}-3y-18}{y^{2}-9y+18}=\frac{(y-6)(y+3)}{(y-3)(y-6)} \\ y\ne3,y\ne6 \end{gathered}[/tex]Select the correct answer.Using long division, what is the quotient of 3r4 + 2023 + 1422 + 17= + 30 and I + 67
EXPLANATION
we are asked to use the long division method to solve the division
[tex]\frac{3x^4+20x^3+14x^2+17x+30}{x+6}[/tex]We will have
What is the value of the expression 4x−y2y+x when x = 3 and y = 3? −31918
7 ( 1 + 3 )
Solve the sum inside the parentheses ( 1 + 3 = 4 )
7 ( 4 )
multiply
7*4 = 28
Since the sum must equal 28
7 + 21 = 28
Correct option = 7+21
Ms wash investdd $22000 in two accounts, one yielding 8% interest and the other yielding 11%. if she recieved a total of $1910 in interest at the end of the year, how much did she invest in each accouny
Take into account the following formula for the simple interest:
[tex]I=P\cdot r\cdot t[/tex]where:
P: principal investment
r: interest rate
t: time
In order to determine the investments for both accounts, proceed as follow:
-Consider that both investments are represented by P1 and P2 respectively, then, you have:
[tex]\begin{gathered} P_1+P_2=22000 \\ P_2=22000-P_1 \end{gathered}[/tex]- Next, use the given values for parameters r and t for each investment:
8% = 0.08
11% = 0.11
t = 1 year
[tex]\begin{gathered} I_1=P_1\cdot0.08\cdot1=0.08P_1 \\ I_2=P_2\cdot0.11\cdot1=0.11P_2 \end{gathered}[/tex]- Next, consider that the sum of the total earnings is $1910, then:
[tex]I_1+I_2=1910[/tex]- Replace I1 and I2 by the expressions in terms of P1 and P2 and write down the resultant expression in terms of P1, as follow:
[tex]\begin{gathered} 0.08P_1+0.11P_2=1910 \\ 0.08P_1+0.11(22000-P_1)=1910 \\ 0.08P_1+2420-0.11P_1=1910 \\ -0.03P_1=-510 \\ P_1=\frac{510}{0.03}=17000 \end{gathered}[/tex]And for P2:
[tex]\begin{gathered} P_2=22000-P_1 \\ P_2=22000-17000=5000 \end{gathered}[/tex]Hence, the amount of money invested in each account was $5000 and $17000
12)If the legs of a right triangle are 6 cm and 5 cm, find the area of the triangle.A)11 cm2B)15 cm2C)30 cm2D)60 cm2
Find the surface area of the prism. 8 cm. 3 cm. 3 cm. 3 cm.) - 3 cm. Surface Area cm2
Surface area of a rectangular prism:
[tex]\begin{gathered} SA=2(l\cdot h+w\cdot h+l\cdot w) \\ l=\text{lenght} \\ w=\text{width} \\ h=\text{height} \end{gathered}[/tex]For the given prims:
l=8cm
w=3cm
h=3cm
[tex]\begin{gathered} SA=2(8\operatorname{cm}\cdot3\operatorname{cm}+3\operatorname{cm}\cdot3\operatorname{cm}+8\operatorname{cm}\cdot3\operatorname{cm}) \\ SA=2(24cm^2+9cm^2+24cm^2) \\ SA=2(57cm^2) \\ SA=114cm^2 \end{gathered}[/tex]Then, the surface area is 114 square centimetersCalculate the determinant of this 2x2 matrix. Provide the numerical answer. |2 -1 | |4 -5|
Given the matrix
[tex]\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}{}\end{bmatrix}[/tex]its determinant is computed as follows:
ad - cb
In this case, the matrix is
[tex]\begin{bmatrix}{2} & {-1} & \\ {4} & -5 & {}\end{bmatrix}[/tex]and its determinant is
2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6
3. Carlos Quintero, Treasurer of X Corp is analyzing an investment on two projects, C and D. The data to
consider are shown below
Initial Investment
Annual Rate of
Return
Pessimistic
Most Likely
Optimistic
Amount
$135,000
39%
27%
25%
Project C
Probability
.30
.45
.25
Amount
$145,000
25%
15%
30%
Project D
Probability
.35
.40
.25
A. Determine the rates of return for each of the two projects. (6 points)
The rates of return for each of the two projects for X Corp are as follows:
Project C = 30.1%Project D = 19.75%.What is the rate of return?The rate of return refers to the percentage gain or loss over the initial cost of the investment.
For this purpose, the rate of return is expressed as the percentage of the expected returns (which is a product based on the probability of different scenarios) over the initial investment cost.
Project C Project D
Amount Probability Amount Probability
Initial Investment $135,000 $145,000
Annual Rate of Return
Pessimistic 39% .30 25% .35
Most Likely 27% .45 15% .40
Optimistic 25% .25 30% .25
Returns from Project C:Pessimistic $15,795 ($135,000 x 39% x 30%)
Most likely $16,402.50 ($135,000 x 27% x 45%)
Optimistic $8,437.50 ($135,000 x 25% x 25%)
Total expected returns = $40,635
Rate of return = 30.1% ($40,635/$135,000 x 100)
Returns from Project D:Pessimistic $9,062.50 ($145,000 x 25% x 35%)
Most Likely $8,700 ($145,000 x 15% x 40%)
Optimistic $10,875 ($145,000 x 30% x 25%)
Total expected returns = $28,637.50
Rate of return = 19.75% ($28,637.50/$145,000 x 100)
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Pls help! No ive asked 5 tutors and they cant do it!
The sampling distribution can be approximated to follow the normal distribution if the sample size is large, and the values of 'np' and 'n(1-p)' are much greater than 10.
Consider option A,
[tex]\begin{gathered} np=30\times0.3=9 \\ n(1-p)=30\times(1-0.3)=21 \end{gathered}[/tex]Consider option B,
[tex]\begin{gathered} np=22\times0.4=8.8 \\ n(1-p)=22\times(1-0.4)=13.2 \end{gathered}[/tex]Consider option C,
[tex]\begin{gathered} np=30\times0.8=24 \\ n(1-p)=30\times(1-0.8)=6 \end{gathered}[/tex]Consider option D,
[tex]\begin{gathered} np=22\times0.5=11 \\ n(1-p)=22\times(1-0.5)=11 \end{gathered}[/tex]It is observed that only the values in option D, give that 'np' and 'n(1-p)' are greater than 10. Therefore, option D will be the correct choice.
The cost of 5 gallons of ice cream has a varianceof 36 with a mean of 36 dollars during the summer.What is the probability that the samplean would differ from the true mean by more than 0.6 dollars if a sample of 107 5-gallon pails is randomly selected? Roundyour answer to four decimal places.
Given:
[tex]\begin{gathered} Variance=36 \\ mean=36 \end{gathered}[/tex]To Determine: The samplean would differ from the true mean by more than 0.6 dollars
Solution
Please note that standard deviation is the square root of variance
[tex]\begin{gathered} SD=\sqrt{Variance} \\ SD=Standard-deviation \\ SD=\sqrt{36}=6 \end{gathered}[/tex][tex]\begin{gathered} S.E=\frac{SD}{\sqrt{n}} \\ S.E=Standard-Error \\ n=107 \\ S.E=\frac{6}{\sqrt{107}}=0.5800 \end{gathered}[/tex]Please note that Z is the number of SE(standard error away from the mean. Therefore
[tex]\begin{gathered} Z=\frac{0.6}{0.5800} \\ Z=1.0345 \end{gathered}[/tex][tex]P(|Z|<1.0345)[/tex][tex]P(|Z|<1.0345)=1-P(Z<-1.0345)=1-0.1515=0.8485[/tex]Hence the probability is 0.8485
Describe the association in the scatter plot below.----------------The scatter plot shows (positive linear, positive linear with one outlier, negative linear, negative linear with one outlier, nonlinear, or no) association because as the plotted values of x increase, the values of y generally (decrease, increase, show no pattern or follow a nonlinear pattern).
From the given figure
The given point can form a line with a negative slope, because when
the values of x increase the values of y decrease
Then the scatter plot shows a negative linear association because
as the values of x increase, the values of y generally decrease
The function f(x) = 6x represents the number of lightbulbs f(x) that are needed for x chandeliers. How many lightbulbs are needed for 7 chandeliers? Show your work
There are a total of 42 lightbulbs needed for 7 chandeliers
How to determine the number of lightbulbs needed?From the question, the equation of the function is given as
f(x) = 6x
Where
x represents the number of chandeliersf(x) represents the number of lightbulbs
For 7 chandeliers, we have
x = 7
Substitute x = 7 in f(x) = 6x
So, we have
f(7) = 6 x 7
Evaluate the product
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers is 42
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The number of lightbulbs needed for 7 chandeliers would be; 42
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the given problem, the equation of the function is;
f(x) = 6x
Where
x be the number of chandeliers and f(x) represents the number of lightbulbs.
For 7 chandeliers, x = 7
Now Substitute x = 7 in f(x) = 6x
Therefore, f(7) = 6 x 7
Evaluate the product;
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers would be; 42
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The probability distribution for arandom variable x is given in the table.-105101520Probability.2015051.25115Find the probability that -5 < x < 5
Answer:
P = 0.30
Explanation:
From the table, we see that:
When: x = -5, Probability = 0.15
When: x = 0, Probability = 0.05
When: x = 5, Probability = 0.1
Therefore, the probability of -5 ≤ x ≤ 5 is obtained by the sum of the probabilities from -5 to 5, we have:
[tex]\begin{gathered} P=0.15+0.05+0.10 \\ P=0.30 \end{gathered}[/tex]Therefore, the probability is 0.30
BUSINESS MATH calculate the state income tax owed on a 50,000 per year salary
Hello there. To solve this question, we have to remember some properties about income and taxes.
The following table shows the progressive tax rate for calculating individual income tax:
We want to calculate the state income tax owed on a $50,000 per year salary.
For this, notice this value is contained in the interval 17,001 and up, hence the progressive tax rate for this value is 5.75%.
In this case, the tax is simply given by the product between the value and the rate:
Don't forget to divide the percentage value by 100% before multiplying.
[tex]50000\cdot\dfrac{5.75}{100}=\$2,875[/tex]This is the state income tax owed by one whose salary is $50,000 per year.
consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?
Problem: consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?.
Solution:
Let the function f(x) whose second derivative is:
[tex]f^{\prime\prime}(x)\text{ = 4x+4sin(x)}[/tex]Now, the antiderivative (integral) of the above function would be:
EQUATION 1:
[tex]f^{\prime}(x)=\int f^{\prime\prime}(x)\text{ }dx\text{= }2x^2-4\cos (x)\text{ +C1}[/tex]where C1 is a constant because we have an indefinite integral. Now the antiderivative (integral) of the above function f´(x) is:
[tex]f(x)=\int f^{\prime}(x)\text{ }dx\text{=}\int \text{ (}2x^2-4\cos (x)\text{ +C1)}dx\text{ }[/tex]that is:
EQUATION 2:
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+C1x+\text{ C2}[/tex]where C2 is a constant because we have an indefinite integral.
Now using the previous equation, if f(0)= 3 then:
[tex]3=\text{ C2}[/tex]Now, using equation 1 and the fact that f ´(0) = 4, then we have:
[tex]4=f^{\prime}(0)\text{= }^{}-4\text{ +C1}[/tex]That is:
[tex]4=\text{ }^{}-4\text{ +C1}[/tex]Solve for C1:
[tex]8=\text{ }^{}\text{C1}[/tex]Now, replacing the constants C1 and C2 in equation 2, we have an expression for f(x):
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+8x+3[/tex]Then f(5) would be:
[tex]f(5)=\text{ }\frac{2(5)^3}{3}-4\sin (5)+40+3=\text{ }125.98[/tex]
then the correct answer is:
[tex]f(5)=\text{ }125.98[/tex]