Let f and g be two functions whose second derivatives are defined. Then (f · g) '' = f · g '' + f '' · g. true or false?
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The statement (f · g)'' = f · g'' + f'' · g is false. The second derivative of a product of two functions is given by a different formula.
The statement (f · g)'' = f · g'' + f'' · g is false.
The second derivative of a product of two functions, f(x) and g(x), is given by (f · g)'' = f''g + 2f'g' + fg''.
To see why the given statement is false, consider the example where f(x) = x and g(x) = x^2. The left-hand side is 0, but the right-hand side is not zero, so the statement does not hold true.
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Related Questions
please explain how you got the answer
Answers
Answer:
part a.
2/3 = x/6
3x = 12
x = 4
that is the answer
A lady wants to make an open-top box for packing baked goods by cutting equal squares from each corner of an 11in. by 16 in. piece of cardboard as shown in the diagram. she figures that versatility the area of the bottom must be 80in^2. What size of square Should be cut from each corner? (round three decimal places)
Answers
Final answer:
The size of the square to be cut from each corner of the cardboard to create a box with a desired area of 80in^2 is approximately 1.553 inches.
Explanation:
The size of the square should be cut from each corner of an 11in. by 16 in. piece of cardboard to create a box with a desired area of 80in2 is approximately 1.553 inches.
To calculate this, we start by finding the area of the original cardboard piece, which is 11*16=176in2. Then, we subtract the area of the four squares cut out, 4x2, from the original area to get the area of the box's base, which is 176 - 4x2=80. Solving for x gives us the size of the square to be cut out.
Using the following arithmetic sequence, find the 29th term: –36, –32, –28, –24.
A. 100
B. 64
C. 76
D. 73
Answers
a29=-36+(28×4)=76
a+(n-1)d
a = the first term -36
n = the term you are looking for 29
d = common difference 4 (-32 - (-36) = 4
-36 + (29 - 1) 4
-36 + (28 *4)
-36 + (112)
-36 + 112 = 76
C. 76
Danielle runs an afterschool program for children. the local baseball team donated 220 game tickets to the program. if danielle divides the tickets evenly among the 4 units in the program, how many tickets will each unit get?
Answers
Answer: 55 tickets
Step-by-step explanation:
Given : The local baseball team donated 220 game tickets to the program.
Also, Danielle divides the tickets evenly among the 4 units in the program.
Then, the number of tickets will each unit get =[tex]220\div 4[/tex]
i.e. the number of tickets will each unit get =55
Hence, Each units will get 55 tickets.
y = 3x
x = 25
y = __
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You have the value for x, 25.
Plug in the value for x: [tex]y=3x\rightarrow y=3(25)[/tex]
[tex]y=75[/tex]
y= 3(25)
y=75
Solve 5x2 = −30x − 65
Answers
5x^2+30x+65=0
5 (x^2+6x+13)=0
x^2+6x+13=0
a=1 b=6 c=13
disctirminant=b^-4ac
disctirminant=6^2-4.1.13
disctirminant=36-52
disctirminant= -16
x1= -6+square root of -16/2.1
x1= -6+4i/2=2i-3
x2= -6- square root of -16/2.1
x2= -6-4i/2= -3-2i
To solve 5[tex]x^2[/tex] = -30x - 65, we can use the quadratic formula. However, the equation has no real solutions.
Explanation:To solve 5[tex]x^2[/tex] = -30x - 65, we can start by rearranging the equation to form a quadratic equation in standard form. The equation becomes 5[tex]x^2[/tex]+ 30x + 65 = 0. We can then solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
In this case, the quadratic equation does not factor easily, so we can use the quadratic formula. The quadratic formula is x = (-b ± sqrt([tex]b^2[/tex] - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. Plugging in the values, we get x = (-30 ± sqrt([tex](-30)^2[/tex] - 4(5)(65))) / (2(5)). After simplifying, we get x = (-30 ± sqrt(900 - 1300)) / 10.
Since the expression inside the square root is negative, there are no real solutions to the equation. Therefore, the equation 5[tex]x^2[/tex] = -30x - 65 has no solution.
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What is the solution set for the open sentence with the given replacement set?
x^2 + 12 = 8x, {2,4,5,8}
A. 2
B. 4
C. 5
D. 8
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the following sequence is an arithmetic sequence.you are now shown very many terms of this sequence,but you are shown enough to fill in the missing number.what number goes in the blank? 14, _,56 ...?
Answers
because it is arithmetic not geometric 14,x,56 An = An-1 + d x = 14 +d --> d = x-14 56 = x +d --> d = 56-x By substitution x-14 = 56-x 2x = 70 x = 35 the sequence is 14,35,56
Write in scientific notation:
527,000
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4 x 3/5 as a mixed number
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Hannah brought 3 / 4 yards of felt for a project. she use 1/8 yard.what fraction of a yard of fill did she have left over?
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[tex] \frac{3}{4} -\frac{1}{8} = \frac{6}{8} - \frac{1}{8}= \frac{5}{8} [/tex]
The strength of a cable is proportional to the square of its diameter. If a 2-cm cable will support 800kg, how much will a 3-cm cable support?
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strength1/(d1)^2 = strength2/(d2)^2
800kg/(2cm)^2 = strength2/(3cm)^2
strength2 = 800 kg * (3 cm)^2/(2 cm)^2
strength2 = 800 kg * 3^2/2^2
strength2 = 800 kg * 9/4
strength2 = 1800 kg
The strength of a cable is directly proportional to the square of its diameter. This relationship allows us to compute the strength of a cable of given diameter. Using given data, a cable with 3cm diameter can support 1800kg.
Explanation:The strength of a cable is said to be proportional to the square of its diameter. This is a mathematical concept of direct proportionality. In this specific case, the proportionality can be written as S=k(D^2), where S is the strength (or weight it can support), D is the diameter and k is a constant.
For a 2-cm cable, we can plug the values into the equation to find the constant: 800= k(2^2), therefore k=800/4=200.
Now, knowing that k=200, we can calculate the strength of a 3-cm cable by plugging in the values: S=200*(3^2) =1800. Therefore, a cable with a 3-cm diameter can support 1800kg.
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TRUE or FALSE. If chord AB Is 3 inches from the center and chord CD is 5 inches from the center of the same circle, then chord CD is the longer chord.
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The answer to this is: TRUE
The leg of a right triangle is 2 units and the hypotenuse is 3 units. What is the length, in units, of the other leg of the triangle?
A.Square root of 5 units
B.Square root of 13 units
C.5 units
D.13 units
B???
Answers
3^2=2^2+length ^2
9-4=length ^2
length = square root of 5
a
Square root of 5 units
Step-by-step explanation:
i just had this problem
Find the 40th term of the following arithmetic sequence: 16, 6, –4, –14.
A. –545
B. –374
C. –222
D. –105
Answers
not 100% sure but hopefully its right...
The 40th term of the given arithmetic sequence is -374. Hence the correct option is B.
The 40th term of the arithmetic sequence is found using the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.
Given the sequence: 16, 6, -4, -14, the common difference d = 6 - 16 = -10. Plugging into the formula: a40 = 16 + (40-1)(-10) = -374.
What is the distance between these two points on a number line?
–93 and 114
A.–207
B.–21
C.21
D.207
Answers
The distance cannot be a negative number, so options C or D can be correct. However, choice C cannot be correct since the first point is negative.
The distance is:
114 - (-93) = 114 + 93 = 207
Katrina's bank statement shows a closing balance of $172.62. There are no outstanding checks or deposits. Her checkbook shows a balance of $190.62. What might account for the different balances?
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Answer:
trasposing of numbers
Step-by-step explanation:
What is 10 plus 10. what is 456 plus 543.?
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Answer:
10 + 10 = 20 ; 456 + 543 = 999
Step-by-step explanation:
which number is greater [-6.809]___[-6.812]
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The given amount converted to units?
120 s; minutes
a. 3.25min b. 1.75min c. 2min d. 1.3min
Please respond with a explanation thank you.
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60s is 1 minute, so 2*60s = 2 minutes
Find the factored form of 4x3 – 8x2 – 12x
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which percent represents the fraction 4/5
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Write each improper fraction as a mixed number. 15/4
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hope this helps you
A school crossing sign has the dimensions shown. The sign can be thought of as a composite figure of a rectangle and a triangle, or two identical trapezoids. The area of the sign is ____ in2. (Enter only the number.) ...?
Answers
Below is the answer:
Area of rectangle = 30*15 = 450
Area of triangle = 30*15/2 = 225
Add the Area of rectangle and the Area of triangle you will get 675
What are the square roots of 256?
A.
128 and –128
B.
15 and –15
C.
13 and –13
D.
16 and –16
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Which statement defines the term capacity?
Answers
The correct answer is:
Credit grantors' measurement of a person's ability to repay loans.
Explanation:
When lending money, financial institutions look at a variety of factors. One of the most important is the ability of the person taking out the loan to repay it. Financial institutions refer to this as "capacity."
What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12?
(–∞, –3]
[–3, ∞)
(–∞, 15]
[15, ∞)
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solve for x :
−3(6−2x)≥4x+12
−18+6x≥4x+12
2x≥30
x≥15
So the answer is D ) 15 to +infinity
I hope my answer has come to your help. God bless and have a nice day ahead!
Answer:
answer d 15 to ifinity
Step-by-step explanation:
Arthur baked 1 7/12 dozen muffins. Nina baked 1 1/12 dozen muffins. How many dozen muffins did they bake?
Answers
Answer:
Total number of dozen muffins they both bake is [tex]2\frac{8}{12}[/tex]
Step-by-step explanation:
Given : Arthur baked [tex]1\frac{7}{12}[/tex] dozen muffins. Nina baked [tex]1\frac{1}{12}[/tex] dozen muffins.
We have to find the total number of dozen muffins did they both bake.
To find the total number of dozen muffins did they both bake is equal to number of dozen of muffins Arthur bake and number of dozen of muffins Nina bake
That is
Mathematically written as ,
Total number of dozen muffins = number of dozen of muffins Arthur bake + number of dozen of muffins Nina bake
Given : Arthur baked [tex]1\frac{7}{12}[/tex] dozen muffins
and Nina baked [tex]1\frac{1}{12}[/tex] dozen muffins.
Total number of dozen muffins = [tex]1\frac{7}{12}+1\frac{1}{12}[/tex]
Simplify, we get,
Total number of dozen muffins = [tex]1\frac{19}{12}+\frac{13}{12}[/tex]
Adding, we get,
Total number of dozen muffins = [tex]1\frac{19+13}{12}=\frac{32}{12}[/tex]
Thus, Total number of dozen muffins they both bake is [tex]2\frac{8}{12}[/tex]
Aaron borrows $150 from his friend austin. he promises to pay back the money in 4 monthly installments. each month he wants to pay half the amount he paid the previous month. assuming austin does not charge any interest, how much should aaron pay the first month to repay the money as scheduled?
Answers
The Equation :
x+1/2x+1/4x+1/8x = 150
Multiply every term by 8 to get whole numbers
8x+4x+2x+x = 1200
15x = 1200
x = 80
Aaron should pay $80 in the first month to satisfy the conditions of repaying $150 in 4 monthly installments, with each subsequent payment being half of the previous one.
Explanation:Aaron needs to pay back a total of $150 in 4 monthly installments, with each payment being half the amount of the previous month. Let's denote the first payment amount as X. Then, the second payment would be X/2, the third would be X/4, and the fourth would be X/8. These four payments need to sum up to $150, which is the total amount Aaron borrowed.
To find the value of X, we can set up the following equation based on the aforementioned information:
X + X/2 + X/4 + X/8 = 150
To solve this equation, we should find a common denominator, which is 8 in this case, and rewrite the equation as:
8X/8 + 4X/8 + 2X/8 + X/8 = 150
Adding the numerators together gives us:
(8X + 4X + 2X + X) / 8 = 150
15X / 8 = 150
Multiplying both sides by 8 and then dividing by 15 gives us:
X = (150 × 8) / 15
X = 1200 / 15
X = 80
Thus, Aaron should pay $80 in the first month to repay the money on schedule as he promised.
A student attempts to solve for c in the equation below.
Which statement best applies to the work shown below?
A.
The student followed all rules correctly and solved for c.
B.
In step 2 of the student’s work they made a mathematical error.
C.
The student’s answer is negative but it should be positive.
D.
The student combined like terms incorrectly in step 1.
Answers
Answer:
A. The student followed all rules correctly and solved for c
Step-by-step explanation:
Given the equation [tex]3c + 6 - 4c = 12 c + 7[/tex], the student followed all rules correctly because:
step 1: He combined like terms correctly for c in the left side from the equation[tex]3c - 4c = - c[/tex]
step 2: he subtracted 6 from both sides[tex]-c +6 + (-6) = 12c +7+(-6)[/tex]
step 3: To isolate “c”, he substracted 12c from both sides[tex]-c +(-12c) = 12c +(-12c) +1[/tex]
Step 4: finally he divided both sides by [tex]-13[/tex][tex]-\frac{13c}{13}= -\frac{1}{13}[/tex]
And he got it:
[tex]c = -\frac{1}{13}[/tex]
Now we´ll check this work with the original equation:
[tex]3c + 6 - 4c = 12 c + 7[/tex]
[tex]3(-\frac{1}{13}) + 6 - 4(-\frac{1}{13}) = 12(-\frac{1}{13}) + 7[/tex]
[tex]-\frac{3}{13} + 6 +\frac{4}{13} = -\frac{12}{13} +7[/tex]
[tex]6 + \frac{1}{13} = \frac{79}{13}[/tex]
[tex]\frac{79}{13} = \frac{79}{13}[/tex]
Very good √