Answers
Given:
[tex]C=\frac{x^4}{4}-\frac{4}{3}x^3-\frac{35}{2}x^2+150x[/tex]Let's solve for the following:
• (a). Find C'(x).
Here, we are to find the derivative of C(x).
Apply the sum rule:
[tex]\begin{gathered} C^{\prime}=\frac{d}{dx}(\frac{x^4}{4})+\frac{d}{dx}(-\frac{4}{3}x^3)+\frac{d}{dx}(-\frac{35}{2}x^2)+\frac{d}{dx}(150x) \\ \\ C^{\prime}=x^3-4x^2-35x+150 \end{gathered}[/tex]• (b). The critical numbers of C(x).
The critical numbers will be the points where the graph changes direction.
Using the derivative, let's solve for x.
[tex]x^3-4x^2-35x+150=0[/tex]Factor the left side using the rational root test:
[tex](x-5)(x^2+x-30)=0[/tex]Now factor using the AC method:
[tex]\begin{gathered} (x-5)((x-5)(x+6))=0 \\ \\ (x-5)(x-5)(x+6)=0 \end{gathered}[/tex]Equate each factor to zero and solve for x:
[tex]\begin{gathered} x-5=0 \\ \text{ Add 5 to both sides:} \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x-5=0 \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x+6=0 \\ x+6-6=0-6 \\ x=-6 \end{gathered}[/tex]Therefore, the critical numbers of C(x) are:
x = -6, 5
• (C). Increasing interval.
Use the critical points to find the increasing and decreasing intervals.
Using interval notation, the increasing interval is:
[tex](-6,5)\cup(5,\infty)[/tex]• D. Decreasing interval:
Using interval notation, the decreasing interval is:
[tex](-\infty,-6)[/tex]ANSWER:
(a). C'(x) = x³ - 4x² - 35x + 150
(b). x = -6, 5
(c). Increasing: (-6, 5) U (5,∞)
Decreasing: (-∞, -6)
Related Questions
Find the average rate of change of
refer to the image please
Answers
The average rate of change of the function f(x) = -2x² - 2 from x = 2 to x = 6 is -16
How to solve an equationAn equation shows the relationship between two or more numbers and variables.
The average rate of change of a function f(x) over the interval x = a to x = b is given by:
A(x) = [f(b) - f(a)]/[b - a]
Given that function f(x) = -2x² - 2 from x = 2 to x = 6, hence:
f(2) = -2(2)² - 2 = -10
f(6) = -2(6)² - 2 = -74
The average rate of change is:
A = [f(b) - f(a)]/[b - a]
Substituting:
A = [-74 - (-10)] / [6 - 2] = -16
The average rate of change is -16
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Instructions: Solve the system. Enter your answer as an ordered pair.
Answers
Given the system:
[tex]\begin{gathered} 3x-9y=12\text{ Eq. 1} \\ 3x+4y=-1\text{ Eq. 2} \end{gathered}[/tex]First, we solve for 3x on both equations, as follows:
[tex]\begin{gathered} 3x=12+9y \\ 3x=-1-4y \end{gathered}[/tex]Equating both equations:
[tex]\begin{gathered} 12+9y=-1-4y \\ 13=-4-9y \\ 13=-13y \\ y=-1 \end{gathered}[/tex]Substituting y on equation 2:
[tex]\begin{gathered} 3x+4y=-1\text{ Eq. 2.} \\ 3x+4\times(-1)=-1 \\ 3x=-1+4 \\ 3x=3 \\ x=1 \end{gathered}[/tex]ANSWER
(1, -1)
Find the time (in years) for the investment to double. (Round your answer to two decimal places)
Answers
Solution
Step 1
Write the compound interest formula
[tex]\text{A = P\lparen1 + }\frac{r}{n})^{nt}[/tex]Step 2
n = 4 (quarterly)
[tex]\begin{gathered} \text{P = x} \\ \text{A = 2x} \\ r\text{ = 7}\frac{3}{4}\text{ = 7.75\% = 0.0775} \end{gathered}[/tex]Step 3:
Substitute in the formula to find t.
[tex]\begin{gathered} 2x\text{ = x\lparen 1 + }\frac{0.0775}{4})^{4t} \\ \text{2 = \lparen1 + 0.019375\rparen}^4t \\ \text{2 = 1.019375}^{4t} \\ Take\text{ natural logarithm of both sides} \\ In(2)\text{ = 4t In\lparen1.019375\rparen} \\ 4t\text{ = }\frac{ln(2)}{ln(1.019375)} \\ 4t\text{ = 36.12080351} \\ t\text{ = }\frac{36.12080351}{4} \\ t\text{ = 9.03 years} \end{gathered}[/tex]Final answer
t = 9.03
patterns in proportional relationships, need help with the graph and the process table, i need to find a algebraic rule that represents the relationship between the number of pizzas, x, and the total cost, y.
Answers
Since the cost of each medium pizza is $7, then
Assume that the number of pizzas is x and the total cost is y, then
Multiply x by x to find y
The algebraic rule is
[tex]y=7x[/tex]a) Let us complete the table
x: Process: y
0 0 x 7 = 0 0
1 1 x 7 = 7 7
2 2 x 7 = 14 14
3 3 x 7 = 21 21
4 4 x 7 = 28 28
a) We need to find the cost of 10 pizzas, then
Substitute x by 10 in the algebraic rule
[tex]\begin{gathered} y=7(10) \\ y=70 \end{gathered}[/tex]The cost of the 10 pizzas is $70
b) If you have exactly $84, then substitute y by 84 to find x
[tex]\begin{gathered} y=84 \\ 84=7x \end{gathered}[/tex]Divide both sides by 7 to find x
[tex]\begin{gathered} \frac{84}{7}=\frac{7x}{7} \\ 12=x \end{gathered}[/tex]You can buy 12 pizzas buy $84
c) If you buy 0 pizza, then the cost of it is
[tex]\begin{gathered} x=0 \\ y=7(0) \\ y=0 \end{gathered}[/tex]Since zero multiplied by any number give zero
The cost of zero pizza is zero
Because 0 x $7 = $0
Solve 3 < 2x + 1 ≤9 I’m so confused
Answers
Answer:
1 < x ≤4
Step-by-step explanation:
3 < 2x + 1 ≤9
Solve for x
Subtract 1 from all sides
3-1 < 2x + 1-1 ≤9-1
2 < 2x ≤8
Divide by 2
2/2 < 2x/2 ≤8/2
1 < x ≤4
Two bicyclists, 44 miles apart, begin riding toward each other on a long straight avenue. One cyclist
travels 16 miles per hour and the other 17 miles per hour. At the same time, Spot (a greyhound), starting
at one cyclist, runs back and forth between the two cyclists as they approach each other. If Spot runs 39
miles per hour and turns around instantly at each cyclist, how far has he run when the cyclists meet?
Answers
The Greyhound has run to a distance equal to 50.7 miles.
This question can be solved using the distance, speed and time relation. The Distance, Speed and time are related to each other by the relation
Speed = Distance/Time, Let the time travelled be equal to t.
Distance travelled by first bicyclist is equal to 16t and Distance travelled by second bicyclist is equal to 17t. The total distance is equal to 44 miles. So, we get
44 = 17t + 16t
44 = 33t
=> t = 44/33
=> t = 1.3 hours
At this time a greyhound starts running back and forth around each cyclist. The speed of Greyhound is equal to 39 miles per hour. Distance will be given by
Distance = Speed × Time
Distance = 39 × 1.3
Distance = 50.7 miles
Learn more about Distance at:
brainly.com/question/12356021
#SPJ9
An object is dropped from a height of 144 feet off the ground. The height
h
of the object after
t
seconds can be found using the function
h
(
t
)
=
144
−
16
t
2
When will the height be 128 feet?
seconds
When will the object reach the ground?
seconds
Answers
Answer:
The height will reach 128 feet after 1 second.
The object will reach the ground after 3 seconds.
Step-by-step explanation:
Plug in the height into the equation: h(t)=144-16t^2
Solve for t.
Ex:
128=144-16t^2, subtract 144 on both sides
-16=-16t^2, divide -16 on both sides
1=t^2, find the square root of both sides
1=t
how the absolute value is never negative
Answers
Answer:
absolute value is a distance from 0; distance cannot be negative
Step-by-step explanation:
the def of absolute value is a numbers distance from 0
distances cannot be negative no matter what you are talking about
Answer: The point of absolute value is to find the distance from a number to 0, which can never be less than 0.
Step-by-step explanation:
The point of absolute value is to find the distance from a number to 0.
For example, if a number line has a -3 point on it, how far away will it be to 0.
<=====o=======o======>
-3 0
The answer is 3! Just like the absolute value
|-3| = ?
3 = ?
Evaluate the expression |2x – 5| for x = –3 and for x = 3.
Answers
Answer:
9 and 1 respectively
Step-by-step explanation:
|2(-3)-5| = |-9| = 9
|2(2)-5| = |1| = 1
the vertical lines represents absolute value, this just mean that any negative values are then turned into their positive counterparts.
What is the area of the triangle shown below?131310units2
Answers
SOLUTION
We want to find the area of the triangle in the image.
To do this, we will make use of the Heroes formula which states
[tex]\begin{gathered} A=\sqrt{s(s-a)(s-b)(s-c)} \\ where\text{ s =}\frac{a+b+c}{2} \\ a,b\text{ and c are the sides of the triangle } \end{gathered}[/tex]applying this, we have
[tex]\begin{gathered} s=\frac{13+13+10}{2} \\ s=\frac{36}{2} \\ s=18 \end{gathered}[/tex]The area A becomes
[tex]\begin{gathered} A=\sqrt{18(18-13)(18-13)(18-10)} \\ =\sqrt{18\times5\times5\times8} \\ =\sqrt{3,600} \\ =60\text{ units}^2 \end{gathered}[/tex]Hence the answer is 60 square units
The adult daily dosage for a certain medicine is 90 mg (milligrams) of medicine for every pounds of body weight.
At this rate, find the daily dose for a man who weighs 175 pounds.
Answers
A daily dose of 15750 mg is required of a certain medicine for a man weighing 175 pounds
An adult daily dose of a certain medicine = 90 mg for every pound of body weight
Daily dose: The adult daily dose specifies the amount of drug dose in mg that must be taken within 24 hours as per the body weight of the person. The body weight of the person determines how much dose is required for the medicine to be effective in the body.
Weight of the man = 175 pounds
The daily dose for a man is given:
Weight of man*Daily dose per pound of body weight
= 175*90
= 15750
Learn more about weight:
https://brainly.com/question/23312072
#SPJ1
That's the value of x, but you need to evaluate the expression x + 26 for
X = 28.5.
Answers
The answer to the expression is 54.6
How to solve variable related problems?1. Switch the positions of the variables in the equation. Starting with "solving for x" (or any other variable) in one of the equations, this "substitution" approach begins. [2] Say your equations are, respectively, 4x + 2y = 8 and 5x + 3y = 9.
2. To "solve for x," divide both sides of the equation.
3. Reconnect this to the other equation. Don't use the equation you just employed; rather, return to the other one.
When a particular variable's value is given to you
we just have to substitute that value in the required equation.
For instance in this question
x= 28.5
And the given equation is x + 26
Therefore the answer is 28.5 + 26 = 54.6 .
To know more about variable visit:
https://brainly.com/question/10462869
#SPJ13
How much solute is in each Percent Solution below
How many grams of KOH are in a 25% w/w solution?
Answers
25% w/w solution has 25 grams of solute.
The expression w/w stands for weight by weight. This expression indicates the amount of solute present in solution. Concerning this, 25 gram of KOH or potassium hydroxide is present in 100 gram of solution.
Further elaborating, the amount of solvent will be calculated by the formula -
Amount of solution = amount of solute + amount of solvent
Amount of solvent = 100 - 25
Performing subtraction to find the amount of solvent
Amount of solvent = 75 grams
Thus, the 100 gram of solution has 25 grams solute and 75 grams of solvent.
Learn more about percentage solution -
https://brainly.com/question/23520050
#SPJ9
Find the area of the figure (Please respond I need help)
Answers
Answer: 32 unit squared
Step-by-step explanation:
To find the area you multiply the amount of unit squares on one side of the shape and multiply it by the amount of unit squares at the top of the shape.
Answer:
to find the area of a shape you want to use the formula A=wl which is area is equal to width multiplied by length.
for this exact problem you want to count the squares on one short side and one long side. when you get the two numbers you multiply them
answer is: 4x8=32hope this helped!
1. There is a two digit number where the difference in the units digit and the tens digit is 5. If the digits are reversed, the
new number is the sum of twice the original number and seven. Find the number.
Answers
Answer:
38
Step-by-step explanation:
Let x = the ones digit, and let y = the tens digit.
The number looks like yx.
The value of the original number is
10y + x
"the difference in the units digit and the tens digit is 5."
x - y = 5 Equation 1
When you reverse the digits, you have xy.
The value of the new number is
10x + y
"If the digits are reversed, the new number is the sum of twice the original number and seven."
10x + y = 2(10y + x) + 7 Equation 2
We have a system of 2 equations.
x - y = 5
10x + y = 2(10y + x) + 7
Simplify the second equation.
10x + y = 2(10y + x) + 7
10x + y = 20y + 2x + 7
8x - 19y = 7
x - y = 5
8x - 19y = 7
Solve the first equation for x. Substitute that value for x in the second equation.
x = 5 + y
8(5 + y) - 19y = 7
40 + 8y - 19y = 7
-11y = -33
y = 3
x = 5 + y
x = 5 + 3
x = 8
The digits are:
ones digit: 8
tens digit: 3
The number is 38.
The price p and the quantity x sold of a small flat-screen television set obeys the demand equation below.
a) Express the revenue R as a function of x. Use the formula R=px
b) How much should be charged for the television set if there are 70 television sets in stock?
c) How much should be charged for the television set if there are 1250 television sets in stock?
d) What is the revenue when there are 1250 sets in stock?
p= .14x +350
Answers
a. The revenue R as a function of x will be R = px.
b. The amount that charged for the television set if there are 70 television sets in stock is R / 70.
c. The amount that charged for the television set if there are 1250 television sets in stock is R / 1250
d. The revenue when there are 1250 sets in stock is 1250p
How to illustrate the information?1. From the information, the price p and the quantity x sold of a small flat-screen television is.
given. The revenue will be:
= Price × Quantity
= p × x.
= px
b. The amount that charged for the television set if there are 70 television sets in stock will be:
R = px
R = 70p
p = R / 70
c. The amount that should be charged for the television set if there are 1250 television sets in stock will be:
R = px
R = 1250p
p = R / 1250
d. The revenue when there are 1250 sets in stock will be:
= Price × Quantity
= p × 1250
= 1250p
Learn more about revenue on:
brainly.com/question/25623677
#SPJ1
Cuál es la cantidad de divisores en 2121?
Answers
Answer:
2121 tiene 8 divisores respuesta B
Which property is shown -2x1/-2=1
Answers
Answer:
Multiplicative inverse
Step-by-step explanation:
1. AI = 400 ft2. Calculate the distance MI for the length of the zipline cable. 3. Calculate the angle at which our zipliners will be descending toward the island . Safety regulations state that the angle at which a zipline cable meets the launching point cannot be smaller than 68 degrees . Please determine if we are in compliance with these regulations
Answers
2. The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Applying this theorem to triangle AMI (where AI and MA are the legs and MI is the hypotenuse), we get:
[tex]\begin{gathered} MI^2=AI^2+MA^2 \\ MI^2=400^2+100^2 \\ MI^2=160000+10000 \\ MI^2=170000 \\ MI=\sqrt[]{170000} \\ MI\approx412.31\text{ ft} \end{gathered}[/tex]3. By definition:
[tex]\tan (angle)=\frac{\text{opposite}}{\text{adjacent}}[/tex]Applying this definition to triangle AMI, considering the angle M, we get:
[tex]\begin{gathered} \tan (\angle M)=\frac{AI}{MA} \\ \tan (\angle M)=\frac{400}{100} \\ \tan (\angle M)=4 \\ \angle M=\arctan (4) \\ \angle M\approx76\text{ \degree} \end{gathered}[/tex]This angle is greater than 68°, then it satisfies the regulation.
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Answers
please hellppp!!!!!!!!!
Answers
C. 3/10
Answer:
C
Step-by-step explanation:
the volume of a cube is 125 cubic centimeters. How many centimeters long is each edge of the cube?
Answers
Answer:
Each edge of the cube is 5 cm
Explanation:
The volume of a cube can be calculated using the formula;
[tex]V=l^3[/tex]Where;
V = volume of the cube
l = length of each side (since all the sides are equal)
Making length l the subject of formula by cube rooting both sides of the formula;
[tex]\begin{gathered} \sqrt[3]{V}=\sqrt[3]{l^3} \\ \sqrt[3]{V}=l \\ l=\sqrt[3]{V} \end{gathered}[/tex]Next, let's substitute the value of volume given;
V = 125 cubic centimeters
[tex]\begin{gathered} l=\sqrt[3]{V} \\ l=\sqrt[3]{125} \\ l=5\text{ cm} \end{gathered}[/tex]Each edge of the cube is 5 cm
If the formular-(X-X|Y-Xwere used to find the r-value of the5x буfollowing data, what would be the value of x?XY8496101811912|13A. 8B. 10C. 6D. 4
Answers
The value of x⁻, is the mean of the x values of the table.
The mean of x is obtained by adding all values of x, and divided the result by the total number of data, which is 5.
Then, you have:
[tex]\bar{x}=\frac{8+9+10+11+12}{5}=\frac{50}{5}=10[/tex]Hence, the mean of x, which is used in the formula to calculate the r-value, is 10
Laura won a charity raffle. Her prize will be randomly selected from the 9 prizes shown below. The prizes include 4 rings, 3 cameras, and 2 headsets. Find the odds against Laura winning a camera. Find the odds in favor of Laura winning a camera.
Answers
The odds in favor of Laura winning a camera 1/3.
What are the odds in favor?
The ratio of favorable outcomes to bad outcomes is known as the odds of the probability of a specific event.
The ratio of positive outcomes to unfavorable outcomes determines the odds in favor of a specific event.
Odds against are determined by dividing the number of unfavorable results by the number of favorable results.
9 prizes consist of 4 rings, 3 cameras, and 2 headsets.
Odds in favor = ( Number of favorable outcomes/ Number of unfavorable outcomes)
The odds in favor of Laura winning a camera = 3/9= 1/3
To learn more about the odds in favor here:
https://brainly.com/question/14350753
#SPJ1
Can you do the graph please I left some notes on the yellow sticky notes
Answers
The equation is a linear one, therefore its graph will be a line on the plane.
To completely define a line we need two points.
We can use the information about the y-intercept and use it as one of the points we need. (0, -3)
As for the second point, we can get the x-intercept by setting y=0 and evaluating the function for x:
[tex]\begin{gathered} y=0 \\ \Rightarrow\frac{1}{2}x-3=0 \\ \Rightarrow\frac{1}{2}x=3 \\ \Rightarrow x=6 \\ \Rightarrow(6,0) \end{gathered}[/tex]Then, we have the points we need: (0, -3) and (6,0).
Now, we only need to mark those points on the plane and draw a line through both of them.
Since the plane in the image only reaches the point (5,0), we need to calculate another point to specifically draw the graph on that grid.
Let set y=-1, then:
[tex]\begin{gathered} y=-1 \\ \Rightarrow\frac{1}{2}x-3=-1 \\ \Rightarrow\frac{1}{2}x=2 \\ \Rightarrow x=4 \\ \Rightarrow(4,-1) \end{gathered}[/tex]Now, we will use the points (0,-3) and (4,-1)
Find the point-slope form of the equation given: g(5) = 10 and g(2) = 8
will give brainliest
Answers
Answer:
[tex]y -10=\cfrac{2}{3} (x -5 )[/tex]========================
Given Two points: (5, 10) and (2, 8)To findThe point-slope form of the equation representing this lineSolutionPoint-slope form is:
[tex]y -y_1=m(x - x_1)[/tex], where (x₁, y₁) is one of the points and m is the slopeFind the slope:
[tex]m=\cfrac{y_2-y_1}{x_2-x_1} =\cfrac{8-10}{2-5} =\cfrac{-2}{-3} =\cfrac{2}{3}[/tex]Use one of the points and the slope to determine the equation of the line:
[tex]y -y_1=m(x - x_1)[/tex], substitute the slope and [tex]y -10=\cfrac{2}{3} (x -5 )[/tex]Answer:
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given: g(5)=10, and g(2)=8.
The value inside the parentheses is the x value, and the value that it (g(x)) is equal to is the y value.
So, as points, the values are (5, 10), and (2, 8).
The equation wants to be written in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.
Solving SlopeWe first want to find the slope of the line.
The slope (m) can be found with two points using the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
We can label the values of the points we were given.
[tex]x_1=5\\y_1=10\\x_2=2\\y_2=8[/tex]
Now, substitute these values into the formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{8-10}{2-5}[/tex]
Subtract.
[tex]m=\frac{-2}{-3}[/tex]
Simplify.
[tex]m=\frac{2}{3}[/tex]
The slope is 2/3.
Since we now have the value of the slope, as well as [tex](x_1, y_1)[/tex], we can plug these values into the formula for point-slope form.
Point-Slope FormRecall that [tex]x_1=5[/tex] and [tex]y_1=10[/tex]; plug these in for [tex]x_1[/tex] and [tex]y_1[/tex] respectively.
[tex]y-10=m(x-5)[/tex]
We also just found the slope, which is 2/3. Plug that in for m.
[tex]y-10=\frac{2}{3} (x-5)[/tex]
Topics: Point-slope form, functions
See more: https://brainly.com/question/24217374
weiyr the coordinates of the two points on the line then find the slope
Answers
ANSWER:
two points are (3,4) and (3,0)
the slope is undefined or indeterminate
SOLUTION:
since the denominator of the slope (change in x) is 0, the slope, change in y over change in x is indeterminate
On August 31, 2024, Shocker borrows $57,000 from a local bank. A note is signed with principal and 9% interest to be paid on August 31, 2025. Record the adjusting entry for interest for Shocker at its year-end of December 31.
Answers
(a)Dr Unearned Revenue $1,400
Cr Service Revenue $1,400
(b)Dr Advertising Expense $880
Cr Prepaid Advertising $880
(c)Dr Salaries Expense $7,800
Cr Salaries Payable $7,800
(d)Dr Interest Expense $1,360
Interest Payable $1,360
Journal entry preparation
(a) According to the information provided, Shocker gets a $4,200 payment from a client for services done over the following three months, which implies the journal entry will be:
Unearned Dr. $1,400 in revenue
($4,200 x 1/3)
$1,400 in Cr Service Revenue
(a) Based on the information provided, we were told that the firm pays a local radio station $2,640 for radio advertisements throughout the months of December, January, and February, which implies that the Journal entry would be entered as:
Dr. Advertising Cost $880
($2,640 x 1/3)
$880 in Cr Prepaid Advertising
(c) According to the information provided, the corporation Employee salaries for the month of December were $7,800, which will be paid on January 7, 2022, implying that the Journal entry would be:
Dr Salaries Cost $7,800
$7,800 in Cr Salaries
(d) According to the facts provided, Shocker borrows $68,000 from a local bank, which implies the Journal entry will be:
$1,360 in Dr. Interest Expense
($68,000 x 6% x 4/12)
$1,360 in payable interest
Learn more about Business economics at
https://brainly.com/question/18272508
#SPJ1
A 4 1/2 bag of raisians must be divided equally into 1/4 bag portions
Answers
Answer:
18 portions
Step-by-step explanation:
1/4 x 4 1/2 = 18
Jaime's football has a mass of 0.435 kilograms. His football helmet has a mass of 2.57 kilograms. Estimate how much more the mass of the helmet is than the mass of the football. Explain your estimate. Show your work.
Answers
Mass of football = 0.435kg
Mass of football helmet = 2.57kg
To find how much more the mass of the helmet is than the mass of football, we have to find the difference
2.57kg - 0.435kg