Answers
Answer:
given function has 2 minimums - [tex]\frac{9}{4}[/tex] and [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Step 1. g'(x) = 4x³ - 10x
Step 2. Find find the critical points:
4x³ - 10x = 2x(2x² - 5) = 0
[tex]x_{1}[/tex] = - [tex]\sqrt{\frac{5}{2} }[/tex] , [tex]x_{2}[/tex] = 0 , [tex]x_{3}[/tex] = [tex]\sqrt{\frac{5}{2} }[/tex]
Step 3. g'(x) > 0 : - [tex]\sqrt{\frac{5}{2} }[/tex] < x < 0 or x > [tex]\sqrt{\frac{5}{2} }[/tex]
g'(x) < 0 : x < - [tex]\sqrt{\frac{5}{2} }[/tex] or 0 < x < [tex]\sqrt{\frac{5}{2} }[/tex]
Step 4.
If x ∈ ( - ∞ , - [tex]\sqrt{\frac{5}{2} }[/tex] ) , g(x) is decreasing ;
If x = - [tex]\sqrt{\frac{5}{2} }[/tex] , g(x) has minimum value ;
If x ∈ ( - [tex]\sqrt{\frac{5}{2} }[/tex] , 0 ) , g(x) is increasing ;
If x = 0 , g(x) has maximum value ;
If x ∈ ( 0 , [tex]\sqrt{\frac{5}{2} }[/tex] ) , g(x) is decreasing ;
If x = [tex]\sqrt{\frac{5}{2} }[/tex] , g(x) has minimum value ;
If x ∈ ( [tex]\sqrt{\frac{5}{2} }[/tex] , ∞ ) , g(x) is increasing .
⇒ at ( - [tex]\sqrt{\frac{5}{2} }[/tex] , - [tex]\frac{9}{4}[/tex] ) and at ( [tex]\sqrt{\frac{5}{2} }[/tex] , [tex]\frac{9}{4}[/tex] ) , g(x) reaches its minimum
Related Questions
giving crown
1) At the store, 2 pounds of beans cost $3.15, 5 pounds of rice cost $7.50, 4 pounds of cabbages cost $4.54, and 7 pounds of alfalfa cost $8.95. Which item has the lowest unit price?
(A) Beans(B) Rice(C) Cabbages(D) Alfalfa
2) Peanuts are sold at the general store in the following quantities: 2¢ for one peanut; 50 peanuts for 99¢, 100 peanuts for $1.99, and 50,000 peanuts for $1000. Which quantity has the lowest unit price?
(A) 1 peanut(B) 100 peanuts(C) 50 peanuts(D) 50,000 peanuts
3)The ratio of trees to shrubs in the garden was 7 to 13. If there were 273 shrubs in the garden, how many trees were there?
(A) 420(B) 147(C) 1911(D) 507
Answers
Answer:
3) = B
Explanation:There are 147 trees.
A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in 10 hours? What is the rate of speed of the jet?
Answers
980 miles
Step-by-step explanation:
5 hours =490miles
1 hour =490/5=98miles
10hours = 98×10=980miles
DEFG is a cyclic quadrilateral. If ∠E = 27°, find ∠G.
Answers
For a cyclic quadilateral, the combination of opposite angles = 180°. So <G is opposite to <E so G must be 153°
Guided Practice
Which model is most appropriate for the set of points?
(–3, 6), (–1, 0), (0, –1), (1, –1.5)
A.
exponential
B.
quadratic
C.
linear
Answers
Answer:
B. quadratic
Step-by-step explanation:
Answer: The model that is most appropriate for the set is: Quadratic
Answer:
exponential
Step-by-step explanation:
Just took the test
− 10x− 6y = 12
4x+ 7y =− 14
Answers
x=0, y=-2
tell me if u need the explanation
If 40% of a number is equal to two-third of another number, what is the ratio of the first number to the second number.?
Answers
Answer:
5:3
Step-by-step explanation:
40% = 2/5
If the numbers are x and y, then
2/5 x = 2/3 y
Divide both sides by 2/5
x = (2/3 * 5/2)y
x = 10/6 y
x = 5/3 y
So the required ratio is 5 : 3.
Checking this result:
10% of 5 = 2
2/3 of 3 = 2 also.
Evaluate the six trigonometric functions of the angle 0
Answers
# Sin θ = 9/15.
# Cos θ = 12/15.
# Cosec θ = 15/9.
# Sec θ = 5/4
Step-by-step explanation:
[tex]by \: using \: pythagorian \: triplets[/tex]
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {9}^{2} + {12}^{2} = {c}^{2} [/tex]
[tex]81 + 144 = {c}^{2} [/tex]
[tex]225 = {c}^{2} [/tex]
[tex]c = 15.[/tex]
[tex] \sin θ = \frac{9}{15} [/tex]
[tex] \cos θ = \frac{12}{15} = \frac{4}{5} [/tex]
[tex] \csc θ = \frac{15}{9} [/tex]
[tex] \secθ = \frac{5}{4} [/tex]
What is the value of the expression -5pqr when
p = 3, q= -5, and r = 2?
Answers
Answer:
150
Step-by-step explanation:
-5pqr
Let p = 3, q= -5, and r = 2
-5(3)(-5)(2)
-15(-5)(2)
75(2)
150
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{pink}{☆Answer}}}}}}:)}[/tex]
See this attachment
Which function has a domain of all real numbers?
Answers
Answer:
c part ....
please mark brainlest
A fair spinner has 9 equal sections: 3 red, 4 blue and 2 green.
It is spun twice.
What is the probability of getting the same colour twice?
Answers
Answer:
9
Step-by-step explanation:
because it has 9 equal section
A mixture of jellybeans is to contain twice as many red as yellow, three times as many green as yellow, and twice as many pink as red. Red jelly beans cost $1.50 per pound, yellow cost $3.00 per pound, green cost $4.00 per pound, and pink only costs $1.00 per pound. How many pounds of each color jellybean should be in a 10 pound canister that costs $2.20 per pound?
Answers
How do I solve this?
Answers
Answer:
y = 0.8x – 2
Step-by-step explanation:
Slope (m) =
ΔY/ ΔX = 4 /5 = 0.8
y=.8x+b
plug in point
b=-2
If b = -1, which one is the value of b^3?
Answers
Answer:
b=-1Put the value of b in b^3[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]
Hence b^3=-1
Solve for x
Need help asap
Answers
Answer:
[tex]x=55[/tex]
Step-by-step explanation:
Corresponding angles of two parallel lines are always equal. The angle on "top" of [tex]2x+6[/tex] corresponds with the angle marked as [tex]x+9[/tex]. Therefore, its measure must also be [tex]x+9[/tex].
Since these two angles form one side of a line which has 180 degrees, we have the following equation:
[tex]2x+6+x+9=180[/tex]
Combine like terms:
[tex]3x+15=180[/tex]
Subtract 15 from both sides:
[tex]3x=165[/tex]
Divide both sides by 3:
[tex]x=\frac{165}{3}=\boxed{55}[/tex]
Translate sentence into equation
nine more than a product of a number and 4 is 8
Answers
Answer:
If x is the required number, equation will be 9+4x=8
The power 9 squared is equivalent to 81. What is the value of 9 Superscript negative 2?
Answers
Answer:
1/81
Step-by-step explanation:
9^2 = 81
We know that a^ -b = 1/a^b
9^-2
1/9^2
1/81
Answer:
1/81
Step-by-step explanation:
Edge
A bakery sold a total of 500 cupcakes in a day, and 83% of them were vanilla flavored. How many of the cupcakes sold that day were vanilla flavored?
Answers
Answer:
percent * base = amount
.83 * 500 = amount
amount = 415
Step-by-step explanation:
Evaluate:
3 - - 10-9 divided by (-1)
Answers
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{3 - -10 - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{= 3 - (-10) - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{= 3 + 10 - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{3 + 10}\\\\\mathsf{= \bf 13}[/tex]
[tex]\mathsf{= \bold{13} - \dfrac{9}{-1}}[/tex]
[tex]\mathsf{\dfrac{9}{-1}}\\\\\mathsf{= 9\div-1}\\\\\mathsf{= \bf -9}[/tex]
[tex]\mathsf{= 13 - (\bf -9)}[/tex]
[tex]\mathsf{= 13 + 9}[/tex]
[tex]\mathsf{= \bf 22}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 22}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
In how many ways could the blanks below (marked with []) be filled if all the coefficients must be positive integers? []a + []b + []a = 10a + 7b
Answers
5 times.
1a + 7b + 9a = 10a + 7b
2a + 7b + 8a = 10a + 7b
3a + 7b + 7a = 10a + 7b
4a + 7b + 6a = 10a + 7b
5a + 7b + 5a = 10a + 7b
Bike speed of 21miles per hour. What is the speed per minute how many miles will the cyclist travel in 10 minutes
Answers
Answer:
First part: 0.35 miles per minute
Second part: 3.5 miles in 10 minutes
Step-by-step explanation:
Think about this as a fraction. Fractions can't be added nor subtracted unless they share the same denominator. So for this case, we have to turn hours into minutes. So 21 mph becomes 21 miles per 60 minutes. Then, we divide 60 from each side to find the speed per minute. 21/60 = 0.35, so the answer to the first part is 0.35 miles per minute.
Using what we got, we can answer the second part of the distance covered in 10 minutes. So, we just multiply 0.35 by 10 which is 3.5 miles covered in 10 minutes.
Solve for x in the inequality below. 4x-8<5x+4
Answers
Answer:
Step-by-step explanation:
4x-8<5x+4
4x<5x+12
-x<12
flip sign
x > -12
Answer:
-12 < x
Step-by-step explanation:
4x-8<5x+4
Subtract 4x from each side
4x-4x-8<5x-4x+4
-8 < x+4
Subtract 4 from each side
-8-4 < x+4-4
-12 < x
4.
The cost price of a television set was RM 2000. It was marked for sale at 20%
higher than its cost price. Later when the model was outdated, it was sold at a
discount of 20%. Find the profit or loss.
Answers
Answer:
Loss of RM 80
Step-by-step explanation:
See the image I have shared with you for explanation
BP, Buying price
SP, selling price
In the American version of the Game Roulette, a wheel has 18 black slots, 18 red slots and 2 green slots. All slots are the same size. A person can wager on either red or black. Green is reserved for the house. If a player wagers $5 on either red or black and that color comes up, they win $10 otherwise they lose their wager. What is the expected value of playing the game once
Answers
Answer:
-$0.26
Step-by-step explanation:
Calculation to determine the expected value of playing the game once
Expected value= [18/(18+18+2) x $5)]- [20/(18+18+2) x $5]
Expected value= ($18/38 x $5) - (20/38 x $5)
Expected value= ($2.37-$2.63)
Expected value= -$0.26
Therefore the expected value of playing the game once is -$0.26
What is the value of f(x) = 2 • 2 x for f(–2)?
Answers
Answer:
-8
Step-by-step explanation:
you know, all you have to do in such a case is simply taking the given -2 and put it, where there is "x" in the function expression and then calculate this. if necessary with a calculator.
2×2×x with x=-2 is
2×2×-2 = -8
Answer:
- 8
Step-by-step explanation:
f ( x ) = 2 . 2 x
f ( - 2 )
= 2 . 2 ( - 2 )
= 2 x 2 x ( - 2 )
= - 8
answer nowwwwwwwwwwwwwwwwwwwwwwwwwwww
Answers
Answer:
7/6
Step-by-step explanation:
(7x/12)/(x/2)
=7/6
Explanation: (7x/12)(x/2)
(25 POINTS)Please help me, and show all of your work step by step.
Now say you invest $6,500 and the highest interest rate you can find is 2.5% compounded annually, but you would have to leave this investment in the account for a minimum of 5 years. If you decide to wait 5 years to buy the car, how much more money will you have to save to buy a car at the price of $8,000? Use the compound interest formula A = P(1 + i)^n.
A = accumulated amount
P = principle
i = interest rate
n = number of years
Answers
Answer:
$ 645.85
Step-by-step explanation:
First you would plug 6,500 into P. The plug 2.5% as 0.025 into i. And plug the years (5) into n.
A = 6500 (1 + 0.025)^5 = 7354.15
That is the amount that would be in the account at the end of the 5 years.
Then you take the cost of the car (8,000) and subtract the money left in the account (7,354.15).
8000 - 7354.15 = 645.85
Your final answer would be rounded to the nearest cent, or the hundredths place.
Instructions: Fill in the last step of solving the quadratic equation by factoring. 3x2−2x−5=0 Step 1: Rewrite middle term. 3x2−5x+3x−5=0 Step 2: Group terms together and find GCF. (3x2−5x)+(3x−5)=0 x(3x−5)+1(3x−5)=0 (3x−5)(x+1)=0 Step 3: Apply the Zero Product Property. 3x−5=0 or x+1=0 Step 4: Solve. x= or x=
Answers
Answer:
x = (5/3)
x = -1
Step-by-step explanation:
[tex]3x^2 -2x - 5 =0\\\\(3x^2+3x) + (-5x - 5) = 0\\\\(3x-5)(x+1)=0\\\\\left \{ {{3x-5=0} \atop {x+1=0}} \right.\\\\===========\\\\3x - 5 = 0\\\\3x - 5 + 5 = 0 + 5\\\\3x = 5\\\\\frac{3x=5}{3}\\\\x = \frac{5}{3}\\\\===========\\\\x + 1 = 0\\\\x + 1 - 1 = 0 - 1\\\\x = -1 \\\\===========\\\\\boxed{\text{Therefore:}}\\\\\boxed{ x = \frac{5}{3} \text { or } x = -1}[/tex]
You would just need to solve the two equations from step three for 'x'.
Hope this helps you.
Divide:
14m^2 - 28m^8 +7m/ 7m
Answers
Answer:
3m -4m^7 +1
STep
Answer:
3m -4m^7 +1
Step-by-step explanation:
(14m^2 - 28m^8 +7m)/ 7m
Break the division into pieces
14m^2/7m -28m^8 /7m +7m/7m
3m -4m^7 +1
The coach of a lacrosse team bought ice cream cones to celebrate a victory. A single-scoop cone was $3 and a double-scoop cone was $5 The coach bought 15 cones and paid $57. A system of equations describing this situation could be written in the form below where s represents the number of single cones andd represents the number of double cones. What is the sum of A, B, C and E?
Answers
Answer:
s=9
d=6
Step-by-step explanation:
s+d=15
3.s+5.d=57
⇒s=9 và d=6
The sum of A, B, C, and E is 23. Let's set up a system of equations based on the given information: s: number of single-scoop cones
d: number of double-scoop cones
1. The coach bought 15 cones in total:
s + d = 15
2. The cost of a single-scoop cone was $3 and the cost of a double-scoop cone was $5, and the total payment was $57:
3s + 5d = 57
Now, let's find the values of s and d by solving the system of equations.
First, we can use the first equation to solve for s in terms of d:
s = 15 - d
Now, substitute this value of s into the second equation:
3(15 - d) + 5d = 57
Now, solve for d:
45 - 3d + 5d = 57
2d = 57 - 45
2d = 12
d = 6
Now that we have the value of d, we can find the value of s using the first equation:
s = 15 - d
s = 15 - 6
s = 9
So, the number of single-scoop cones (s) is 9, and the number of double-scoop cones (d) is 6.
Now, let's find the sum of A, B, C, and E:
A: The number of single-scoop cones (s) is 9.
B: The number of double-scoop cones (d) is 6.
C: The cost of a single-scoop cone is $3.
E: The cost of a double-scoop cone is $5.
A + B + C + E = 9 + 6 + 3 + 5 = 23
So, the sum of A, B, C, and E is 23.
To know more about sum:
https://brainly.com/question/31538098
#SPJ2
Emily says that the lengths of the sides of her prism are 6 inches 5 inches
and 3 inches. Is Emily correct? Use words and numbers to explain why or
why not.
