Find the area of the sector of a circle with diameter 30 feet and an angle of 3Pi/5 radians. Round your answer to four decimal places.
Answers
half the diameter is the radius, so
[tex]r=15[/tex]now we can calculate the total area of the circle , and then will calculate the area for the angle
[tex]\begin{gathered} A=\pi\times r^2 \\ A=\pi\times15^2 \\ A=225\pi \end{gathered}[/tex]the area of the circle is 225pi, this is the corresponding area for the complete angle of the circle, therefore it is equivalent to 2pi
now we create a relation to find the area corresponding to the indicated angle
if 225pi is equal to 2pi how much is 3pi / 5
[tex]\begin{gathered} 225\pi\longrightarrow2\pi \\ x\longrightarrow\frac{3}{5}\pi \end{gathered}[/tex]where x is the area covered by the angle
we solve ussing cross multiplication, x is equal to: multiply the values that are found diagonally and make them equal
[tex]\begin{gathered} x\times2\pi=\frac{3}{5}\pi\times225\pi \\ \end{gathered}[/tex]and solve for x
[tex]\begin{gathered} x=\frac{\frac{3}{5}\pi\times225\pi}{2\pi} \\ \\ x=\frac{135\pi^2}{2\pi} \\ \\ x=67.5\pi\approx212.0575 \end{gathered}[/tex]The rounded area is 212.0575 square feet
Related Questions
A direct variation includes the points (3, 12) and (n, 8). Find n.
Answers
For a direct variation between each point (x, y),
[tex]\begin{gathered} x\propto y \\ x=ky \\ k=\frac{x}{y} \end{gathered}[/tex]For (x₁, y₁) = (3, 12),
[tex]\begin{gathered} k=\frac{3}{12} \\ k=0.25 \end{gathered}[/tex]To find n, consider (n, 8) = (x, y)
[tex]\begin{gathered} x=ky \\ \end{gathered}[/tex]Substituting,
[tex]\begin{gathered} n=0.25\times8 \\ n=2 \end{gathered}[/tex]Therefore, the value of n is 2
Sanya's car can drive 300 miles in 6 hours. How many miles can she drive in 14 hours?
Answers
Assuming that these variables behave proportionally, we can solve this problem through proportional relationships:
[tex]\begin{gathered} \frac{300}{6}=\frac{x}{14} \\ x=\frac{300\times14}{6} \\ x=\frac{4200}{6} \\ x=700 \end{gathered}[/tex]She can drive 700 miles in 14 hours
5. How much must be deposited now at 5% compounded semi-annually to yield an annuity payment of ₱30,000 at the beginning of each 6-month period for 6 years?
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to calculate the amount to be deposited
STEP 1: Write the formula for Future value annuity
[tex]FV=P\times\frac{(1+r)^n-1}{r}[/tex]Where:
FV = present value of an ordinary annuity
P=value of each payment
r=interest rate per period
n=number of periods
STEP 2: Write the given parameters
[tex]\begin{gathered} FV=30000,r=5,n=12,r=\frac{5}{100}=0.05,P=? \\ n=12\text{ because }6\text{months period for 6 years will be 2}\times6=12 \end{gathered}[/tex]STEP 3: Calculate the P
[tex]\begin{gathered} FV=P\times\frac{(1+r)^n-1}{r} \\ 30000=P\times\frac{(1+0.05)^{12}-1}{0.05} \\ 30000=P\times\frac{(1.05)^{12}-1}{0.05} \\ 30000=P\times\frac{(1.05)^{12}-1}{0.05} \\ 30000=P\times\frac{1.795856326^{}-1}{0.05} \\ 30000=P\times\frac{0.795856326^{}}{0.05} \\ 30000=\frac{0.795856326P^{}}{0.05} \\ By\text{ cross multiplication,} \\ 30000\times0.05=0.795856326P \\ 1500=0.795856326P \\ \frac{0.795856326P}{0.795856326}=\frac{1500}{0.795856326} \\ P=1884.762301 \\ P\approx1884.76 \end{gathered}[/tex]Hence, the amount that must be deposited now is approximately 1884.76 to the nearest cents
11. A cylinder and a sphere both have the same radius, 4. The height of the cylinder isequal to the diameter of the sphere. Select the expression that describes thevolume of the cylinder that is not occupied by the sphere. (Use 3.14)A. 39.67B. 85.33T1 - 128TTC. 124.560D. 128TT – 85.33TT
Answers
Given that :
the radius of the cylinder and sphere = 4 units
the height of the cylinder (h) is equal to the diameter (d) of the sphere
the diameter of the sphere = 2 x radius = 2 x 4 = 8 units
also, the height of the cylinder = 8 units
The volume of the cylinder can be calculated using the formula:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi\times4^2\times8 \\ V=128\pi \end{gathered}[/tex]The volume of the Cylinder
[tex]\begin{gathered} V=128\times3.14 \\ V=401.92uits^3 \end{gathered}[/tex]Answer:
Given that :
the radius of the cylinder and sphere = 4 units
the height of the cylinder (h) is equal to the diameter (d) of the sphere
the diameter of the sphere = 2 x radius = 2 x 4 = 8 units
also, the height of the cylinder = 8 units
The volume of the cylinder can be calculated using the formula:
The volume of the Cylinder
Step-by-step explanation:
Kaira's gross pay is $6,820. Her deductions total $917.27. What percent of her grosspay is take-home pay?Round to the nearest whole percent.
Answers
Answer:
87%
Explanation:
• Kaira's gross pay = $6,820
,• Deductions = $917.27
First, determine her take-home pay.
[tex]\begin{gathered} \text{Take}-\text{home Pay}=\text{Gross Pay-Deductions} \\ =6,820-917.27 \\ =\$5902.73 \end{gathered}[/tex]Next, determine what percent of her gross pay is her take-home pay.
[tex]\begin{gathered} \text{Percent}=\frac{\text{Take}-\text{Home Pay}}{\text{Gross Pay}}\times100 \\ =\frac{5902.73}{6820}\times100 \\ =86.55\% \\ \approx87\% \end{gathered}[/tex]87% of her gross pay is her take-home pay.
A Factor with the distributive property Apply the distributive property to factor out the greatest common factor, 56+32 Stuck? Watch a video or use a hint.
Answers
the greatest commmon factor of 56 and 32 is 8
so in order to use the distributive property
8(7+4)=56+32=88
Find the value of the expression. 07-2 . (131 alw The value is I I
Answers
Determine the signs of given trigonometric function of an angle in standard position with given measure.cos (-302°) and sin (-302°)
Answers
Exercise: Calculate the sign of cos(-302°) and sin(-302°).
We can know the sign of the trigonometric value of an angle depending on which quadrant the angle is located. In the case of cosine and sine, we have the following rules:
Let's calculate the sign of cos(-302°) first. Note that the angle within the cosine is negative; this means that it must be measured from the x-axis clockwise. Now, every quadrant has a total measure of 90°; then, dividing 302 by 90 we obtain
[tex]\frac{302}{90}\approx3.4,[/tex]which means that -302° goes through two complete quadrants and a partial part of a third one. Since we must measure the angle clockwise, -302 lies in the first quadrant.
By the diagram above, the sign of -302° is +.
On the other hand, looking at the sine diagram, we see that the sign of sine(-302°) is + as well.
AnswerThe signs of cos(-302°) and sin(-302°) are both +.
Write a variation equation for the following situation. Use k as the constant of variation.R varies inversely as the square of h.The variation equation is ______
Answers
Given
R varies inversely as the square of h
Find
Equation for the given statement
Explanation
[tex]\begin{gathered} R\propto\frac{1}{h^2} \\ \\ R=\frac{k}{h^2} \end{gathered}[/tex]Final Answer
The equation for given statement is
[tex]R=\frac{k}{h^2}[/tex]( 5/13 Marie made a $4,500 down payment on a car. The total cost of the car was $19,000. She made 50 equal monthly payments to pay the car in full. How much did Marie pay per month? Equation: Solution:
Answers
The total cost is $19,000, but Marie already did a payment of $4,500, so the remaining cost is:
[tex]19000-4500=14500[/tex]Now, this remaining cost was paid in 50 equal monthly payments, so in order to find the value of this monthly payment, we just need to divide the remaining cost by 50:
[tex]\frac{14500}{50}=\frac{1450}{5}=290[/tex]So Marie paid $290 per month.
Please help with this question: I have attached the image A survey was done where males and females were asked if they would prefer to eat chicken or steak. The results of the survey are shown in the two-way frequency table. ChickenSteakMale0.2380.216Female0.3110.235What percent of the males surveyed prefer chicken?Enter your answer to the nearest tenth of a percent in the box. __%
Answers
23.8%
Explanation:
Since 0.238 represent the frequency of male who eats chicken
0.238 / 100 = 23.8%
Answer: 52.4%
Step-by-step explanation: I took the test and that was the correct answer.
am I supposed to x all this together I need help with the answer please thank you
Answers
The volume of the tank can be calculated using the Volume of a cylinder formula, which is:
[tex]V=\pi\cdot r^2\cdot h[/tex]Where:
v = volume;
r = radius;
h = height.
In this exercise:
r = Diameter/2 = 12/2 = 6 ft
h = 16 ft
So, substituting the values:
[tex]\begin{gathered} V=\pi\cdot6^2\cdot16 \\ V=\pi\cdot36\cdot16 \\ V=576\pi \end{gathered}[/tex]Using π = 3.14:
[tex]\begin{gathered} V=576\cdot3.14 \\ V=1808.64 \\ V=1809ft^3 \end{gathered}[/tex]Answer:
The volume of the tank is 1809 ft³.
cambio siete decimos a una fracción igual Común denominador de 100
Answers
Answer:
70/100
Explicación:
2 fracciones son iguales si una de ellas puede ser calculada multiplicando el numerador y el denominador de la otra por el mismo número.
Por lo tanto, 7/10 es equivalente a:
[tex]\frac{7}{10}=\frac{7\cdot10}{10\cdot10}=\frac{70}{100}[/tex]Multiplicamos por 10 arriba y abajo para que el denominador fuera 100. De este modo obtemos que 7/10 es igual a 70/100.
I need help w this question for geometry Find the total area
Answers
Explanation
We are asked to find the total area of the figure
To do so, we will split the area into 2 as shown below
For figure A
We have a trapezoid
The area of a trapezoid is
[tex]\begin{gathered} Area=\frac{1}{2}(a+b)\times height \\ b=13 \\ a=3 \\ height=8 \\ area=\frac{1}{2}(13+3)\times8 \\ area=\frac{26}{2}\times8 \\ area=13\times8 \\ area=104yd^2 \end{gathered}[/tex]For figure B
The figure is a parallelogram
The area of a parllelogram is given by
[tex]base\times height=13\times(15-8)=13\times7=91yd^2[/tex]Therefore, the total area is the sum of the areas of the two figures which will be
[tex]104+91=195yd^2[/tex]Thus, the area is 195 yd²
The ages of grandparents of students in Mr. Keyes' third period class are listed below.52 54 57 61 56 6167 64 63 57 60 50A. Create the five-number summary that represents the data set.B. Create a box plot that represents the data set.
Answers
Given the data set (ages of grandparents):
52, 54, 57, 61, 56, 61, 67, 64, 63, 57, 60, 50
Let's create a five-number summary that represents the given data set and also create a box plot.
A) A five number summary of a data set consists of the following:
• Minimum value
,• First quartile
,• Median
,• Third quartile
,• Maximum value
Let's determine the five-number summary of the given data set.
• Minimum value:
The minimum value is the smallest number from the given data set.
Thus, the minimum is = 50
• First quartile:
The first quartile is also called the lower quartile. It is the median of the lower half of the data set.
To find the first quartile, list out the lower half of the data set after arranging the data in acsending order.
Arrange in ascending order: 50, 52, 54, 56, 57, 57, 60, 61, 61, 63, 64, 67
Lower half: 50, 52, 54, 56, 57, 57
Median of lower half:
[tex]\frac{54+56}{6}=\frac{110}{2}=55[/tex]Therefore, the first quartile is = 55
• Median:
Median is the middle term of the data set.
50, 52, 54, 56, 57, 57, 60, 61, 61, 63, 64, 67
The middle terms are = 57 and 60
To find the median, divide the sum of the middle terms by 2.
Thus, we have:
[tex]\frac{57+60}{2}=\frac{117}{2}=58.5[/tex]Therefore, the median of the data set is 58.5
• Third Quartile:
The third quartile is also called the upper quartile. It is the median of the upper half of the data set.
Upper half of data set = 60, 61, 61, 63, 64, 67
Median of upper half =
[tex]\frac{61+63}{2}=\frac{124}{2}=62[/tex]Therefore, the third quartile is 62
• Maximum value:
The maximum value is the greatest number in the given data set.
The greatest number in the data set is 67.
Therefore, the maximum value is 67.
We have the five-number summary that represents the data set below:
• Minimum = 50
,• First quartile = 55
,• Median = 58.5
,• Third quartile = 62
,• Maximum = 67
b) Let's create a box plot that represents the data set.
We have the box plot below:
In an electrical circuit with resistors placed in parallel, thereciprocal of the total resistance is equal to the sum of thereciprocals of each resistance:
Answers
Answer:
C
[tex]R_2=16.16\Omega[/tex]Explanation:
Given the below equation;
[tex]\frac{1}{R_c}=\frac{1}{R_1}+\frac{1}{R_2}[/tex]We're also given;
[tex]\begin{gathered} R_1=25\Omega \\ R_c=10\Omega \end{gathered}[/tex]Let's substitute the given values into the equation, we'll have;
[tex]\frac{1}{10}=\frac{1}{25}+\frac{1}{R_2}[/tex]Let's subtract 1/25 from both sides of the equation;
[tex]\begin{gathered} \frac{1}{10}-\frac{1}{25}=\frac{1}{R_2} \\ \frac{5-2}{50}=\frac{1}{R_2} \\ \frac{3}{50}=\frac{1}{R_2} \end{gathered}[/tex]Let's cross multiply;
[tex]\begin{gathered} 3R_2=50 \\ R_2=\frac{50}{3} \\ R_2=16.16\Omega \end{gathered}[/tex]what the closest volume of a cylinder with a height of 10 and a circumference of 8
Answers
In order to calculate the volume of a cylinder, we can use the following formula:
[tex]V=\pi r^2h[/tex]Where r is the base radius and h is the height.
If the circumference is 8, we have:
[tex]\begin{gathered} C=2\pi r \\ 8=2\pi r \\ r=\frac{4}{\pi} \end{gathered}[/tex]Now, calculating the volume, we have:
[tex]\begin{gathered} V=\pi(\frac{4}{\pi})^2\cdot10 \\ V=\frac{160}{\pi} \\ V=50.93 \end{gathered}[/tex]So the correct option is the second one.
Use the graph of f to find the value of f(0)
Answers
Solution:
The expression f(0) represents the y-intercept on the graph of f(x). The y-intercept of a graph is the point where the graph crosses the y-axis.
Thus, from the graph;
[tex]f(0)=0[/tex]Solve for x.
√x+3 = 2√x-1
Answers
Answer:
x = 16
Step-by-step explanation:
sqrt x + 3 = 2 sqrt x - 1 subtract sqrt x from both sides
3 = sqrt x -1 add 1 to both sides
4 = sqrt x square both sides
16 = x
Jan makes four claims about the twopolynomials Any 6x + 1 and 2x. The claims arelisted belowClaim 1 states that when 2x is added to 4xy + 5x +1 the sum is a polynomial.Claim 2 states that when 2x is subtractedfrom xy + 6x + 1 the difference is a polynomial.Claim 3 states that when 4xy + 5x + 1 is multipliedby 2x the product is a polynomial.Claim 4 states that when xy + 6x + 1 is divided by2x the quotient is a polynomialSelect all claims by Jan that are correct.
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A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division but is never division by a variable.
Therefore claim 4 is false.
When 2x is added, the resultant will be a polynomial.
when 2x is subtracted, the resultant will be a polynomial.
When multiplied by 2x also, the resutant will be a polynomial.
Use the table of values for f and g below to find the indicated compositions.f(g(8))=Answerg(f(5))=Answerf(f(4))=Answerg(g(2))=Answer
Answers
Starting from the first question, we want:
[tex]f(g(8))[/tex]Let's start from the inside part:
[tex]g(8)[/tex]Since the inside of "g" is 8, this means we need to check for the row with x = 8, thay is, "8" in the column "x". Finding this row, we check the value in this row and column "g", which is "4".
This means that:
[tex]g(8)=4[/tex]Now, we can substitute this back in:
[tex]f(g(8))=f(4)[/tex]And we can do similarly. We check the row which has "4" in the "x" column and see the corresponding value in column "f". We can see that it is also "4", so, the answer for the first is:
[tex]f(g(8))=f(4)=4[/tex]Lastly, for the second, we do the same thing, the inside part is:
[tex]f(5)[/tex]So, we got to line x = 5 and check column "f". It is 0, so:
[tex]\begin{gathered} f(5)=0 \\ g(f(5))=g(0)_{} \end{gathered}[/tex]Now, we check row x = 0 and column "g" to find "9", so:
[tex]g(0)=9[/tex]Thus, the answer for the second is:
[tex]g(f(5))=g(0)=9[/tex]Between 10 P.M and 7:20 A.M., the water level in a swimming pool decreased by 7/12 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour? PLEASE HELP I DONT GET THIS AT ALL!
Answers
Answer:
0.0625 or [tex]\frac{1}{16}[/tex]
Step-by-step explanation:
Interpreting the ProblemIf the water level decreases at a constant rate, then that just means that the relationship between the water level and time is linear or is a straight line if graphed.
Calculating Constant Rate:let's just say that: [tex]C = \text{ contant rate the water level dropped at each hour}[/tex]
this means if we added C by how many hours passed, we should get the amount the water level dropped: [tex]C+C+C+C\text{...how many hours passed} =\frac{7}{12}[/tex]
let's also just say that: [tex]H = \text{ amount of hours that passed}[/tex]
from here we can rewrite the equation using multiplication: [tex]CH = \frac{7}{12}[/tex]
we can now divide both sides to isolate C: [tex]C = \frac{\frac{7}{12}}{H}[/tex], so now all we have to do is find how many hours passed.
From 10 P.M to 12 A.M, 2 hours pass. From 12 A.M to 7 A.M, 7 hours pass and from 7 A.M to 7:20 A.M, 20 minutes pass
So we have: [tex]2 \text{ hours} + 7 \text{ hours} + 20 \text{ minutes} = 9\text{ hours} + 20\text{ minutes}[/tex]
We want to represent this as one value and also in hours, so we'll need to convert the minutes to hours. To see how many 20 minutes is to one hour, we simply divide this 20 minutes by how many minutes are in an hour, which is 60 minutes: [tex]\frac{20}{60} = \frac{1}{3}[/tex]
It's actually super useful to keep this in fraction form, and even convert the 9 hours to fraction form: [tex]9 + \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3}[/tex]
Now from here, we know that: [tex]H = \frac{28}{3}[/tex]
so let's plug this into the expression we made! [tex]C = \frac{\frac{7}{12}}{\frac{28}{3}}\implies \frac{7}{12} * \frac{3}{28}[/tex]
before multiplying, we can rewrite 12 as (4 * 3) so we can cancel out the 3 in the numerator and denominator making the simplification process a bit easier. We can also rewrite 28 as (4 * 7) to cancel out the 7 in the numerator and denominator: [tex]C = \frac{7 * 3}{(4 * 3) * (7 * 4)} = \frac{1}{16} = 0.0625[/tex]
This means if we multiplied the 1/16 or 0.0625 by the 9.33333 hours that passed we would get the total amount that decreased: 7/12
What is the axis of symmetry for f(x) = x2 + 4x + 6? A. x= -4B. X= -2C. X = 2D X = 3
Answers
Answer:
Step by step explanation:
In order to find the axis of symmetry, we will have to find the x-value of the vertex
[tex]\text{Vertex = }\lbrack\frac{-b}{2a},\text{ f(}\frac{-b}{2a})\rbrack[/tex][tex]x^2\text{ + 4x +6}[/tex]a = 1
b = 4
c = 6
[tex]\text{Vertex = }\lbrack\frac{-4}{2},f(\frac{-4}{2})\rbrack[/tex][tex]Vertex=\lbrack-2,f(-2)\rbrack\text{ }[/tex]We have found the x-value of the vertex which is -2
Line/axis of symmetry is x=-2
Distribute [tex]( - 5a + 2a {}^2 - 2)(2a - 4)[/tex]distribute
Answers
The given expression is
[tex](-5a+2a^2\text{ - 2)(2a - 4)}[/tex]To distribute, we would multiply the terms in each bracket individually and add or subtract where necessary. It becomes
[tex]\begin{gathered} -\text{ 5a}\times2a\text{ + (-5a}\times-4)+(2a^2\times2a)+(2a^2\times-4)+(-2\times2a)+(-2\times-4) \\ -10a^2+20a+4a^3-8a^2-4a+8 \\ 4a^3-10a^2-8a^2+20a-4a+8 \\ 4a^3-18a^2+16a\text{ + 8} \end{gathered}[/tex]Which of the following is graphed below?
Answers
The function that is graphed here is option A;
y = {x³ - 3, x ≤ 2 and x² + 6, x > 2
Given,
The graph
Function;
A function is a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
We have to find the function that is graphed here from the given options.
Here,
The function that is graphed here is option A;
y = {x³ - 3, x ≤ 2 and x² + 6, x > 2
Learn more about function here;
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The 32 students in Mrs. Colby's class will share 80 slices of pizza equally. How many slices will each student get? Enter the correct answer to complete the statement. The students will each get slices. Explain how to get the fraction after you find the remainder. The slices leftover can each be cut in ? giving everyone another? v of a slice.
Answers
The 32 students in Mrs. Colby's class will share 80 slices of pizza equally. How many slices will each student get? Enter the correct answer to complete the statement. The students will each get slices. Explain how to get the fraction after you find the remainder. The slices leftover can each be cut in ? giving everyone another? v of a slice.
step 1
Divide 80 by 32
80/32=40/16=20/8=10/4=5/2=2.5=2 1/2
each student get 2 1/2 slices
2 1/2=2+0.5=2+1/2
the fraction is 5/2
so
5/2=4/2+1/2=2+1/2=2 1/2
we have 32 students by 2 1/2
so
32 students by 2
32*2=64 slices
the remainder is
80-64=16 slices
divide 16 by 32
16/32=1/2
therefore
2+1/2=2 1/2
the answers part 2 are
The 16 slices leftover can each be cut in 2 half........giving everyone another (1/2) of a slice
Transformation (x + 2, y - 3) is applied to triangle ABC.What are the coordinates of B’ (the transformation of point B)?A) (-5, 3)B) (2, - 1)C) (0, - 2)D) (2, - 3)
Answers
Transformation:
[tex](x+2,y-3)[/tex]The coordinate of B in (x, y) we can get from the graph, which is (-2, 1):
Thus, the transformation based on the information given is:
[tex](-2+2,1-3)[/tex]Simplifying:
[tex](0,-2)[/tex]Answer: C) (0, -2)
In the diagram above <3 = 135 degrees find the measure of <4
Answers
First, let's draw the picture and write some information that we already know about it
Remember that a line that passes throw two parallel lines will make the same angles, so if we already know that the angle <3=135º (which is alpha in the draw) we can find the supplementary angle which is <4 (the angle that we want to know), lets do it:
Finally, the angle <4=45º
an elevation on the tenth floor goes down 9 floors then it goes up 19 floors down three and finally down 12 what floor does it end up on write an equation to show how you found your answer
Answers
onIn order to solve this, we have to add the number of floors the elevator goes up and subtract the number of floors the elevator goes down, like this:
Initially, it goes down 9 floors since it was at the 10th floor we get:
10 - 9 = 1
Then, after it goes down 9 floors it gets to the first floor, then it goes up 19 floors , now we get:
1 + 19 = 20
After it goes up to the 19th floor from the fits one, it gets to the 20th floor, then it goes down 3 floors, now we get:
20 - 3 = 17
After it goes down 3 floors it gets to the 17th floor, then it goes 12 floors down from the 17th floor:
17 - 12 = 15
At the end, the elevator ends up in the 15th floor
Let f(x) = 4x^3-5x^2Then f(x) has a local minimum at x= ____a local maximum at x= ____and inflection point at x= ____ write inflection points (if any) in numerical order smallest first
Answers
Given:
[tex]f\mleft(x\mright)=4x^3-5x^2[/tex]Find-: Local minimum and local maximum and inflection point.
Sol:
Derivative of function.
[tex]\begin{gathered} f\mleft(x\mright)=4x^3-5x^2 \\ f^{\prime}\left(x\right)=12x^2-10x \\ f^{\prime}\left(x\right)=2x\left(6x-5\right) \end{gathered}[/tex]The critical point is:
[tex]\begin{gathered} f^{\prime}\left(x\right)=0 \\ 2x\left(6x-5\right)=0 \\ 2x=0;6x-5=0 \\ x=0;x=\frac{5}{6} \end{gathered}[/tex]Local minima is:
[tex]\left(x,f\lparen x\right))=\lparen\frac{5}{6},-1.157)[/tex]Local minima at x=5/6
Local maxima at x=0
Inflection point.
[tex]\begin{gathered} f=4x^3-5x^2 \\ \text{ Inflection point} \\ x=\frac{5}{12} \end{gathered}[/tex]