Answer:
[tex]\displaystyle f''(1) = \frac{7}{\sqrt{43}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopeCalculus
Derivatives
Derivative Notation
Taking Derivatives with respect to x
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Chain Rule: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Function: y = f(x), twice differentiable.
[tex]\displaystyle f(1) = 3\\\frac{dy}{dx} = (4y^2 + 7x^2)^{\frac{1}{2}}[/tex]
Step 2: Differentiate
Remember we are taking the derivative with respect to x.
Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{\frac{1}{2} - 1} \cdot \frac{dy}{dx} (4y^2 + 7x^2)[/tex][2nd Derivative] Simplify: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{-\frac{1}{2}} \cdot \frac{dy}{dx} (4y^2 + 7x^2)[/tex][2nd Derivative - Chain Rule] Basic Power Rule: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{-\frac{1}{2}} \cdot (0 + 2 \cdot 7x^{2 - 1})[/tex][2nd Derivative] Simplify: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{1}{2}(4y^2 + 7x^2)^{-\frac{1}{2}} \cdot 2 \cdot 7x[/tex][2nd Derivative] Simplify: [tex]\displaystyle \frac{d^2y}{dx^2} = \frac{7x}{\sqrt{7x^2 + 4y^2}}[/tex]Step 3: Evaluate
We are given x = 1 and f(1) = 3. This will tell us the instantaneous slope.
Substitute [2nd Deriv]: [tex]\displaystyle f''(1) = \frac{7(1)}{\sqrt{7(1)^2 + 4(3)^2}}[/tex][√Radical] Exponents: [tex]\displaystyle f''(1) = \frac{7(1)}{\sqrt{7(1) + 4(9)}}[/tex][Fraction] Multiply: [tex]\displaystyle f''(1) = \frac{7}{\sqrt{7 + 36}}[/tex][√Radical] Add: [tex]\displaystyle f''(1) = \frac{7}{\sqrt{43}}[/tex]This tells us that the rate of change of the slope of the tangent line is [tex]\displaystyle \frac{7}{\sqrt{43}}[/tex].
We can also write an equation for the instantaneous slope:
[Equation] [tex]\displaystyle y - 3 = \frac{7}{\sqrt{43}}(x - 1)[/tex]
3x + y = -3
y = x + 5
Substitution pls show solving
Answer:
( -2, 3 )
Step-by-step explanation:
3x + y = -3
y = x + 5
Since "y" has been given to us, all we need to do is substitute.
3x + x + 5 = -3
Combine like terms
4x + 5 = -3
Subtract 5 onto both sides
4x + 5 - 5 = -3 - 5
4x = -8
Divide by 4 into both sides to isolate the variable
4x/4 = -8/4
x = -2
Now that we have x ( -2 ), we can substitute that to get what y is.
y = x + 5
y = -2 + 5
y = 3
( x, y ) ---> ( -2, 3 )
Hope this helped!
Have a supercalifragilisticexpialidocious day!
A notebook cost $4.50 plus sales tax. The sales tax is $.36. what is the sales tax rate?
Answer:
It's simple the answer is 8%
Step-by-step explanation:
$. 36/ $4.50 × 100 = 8%
Answer:
8%
Step-by-step explanation:
Sales price x sales tax rate = sales tax
4.50 x sales tax rate = .36
sales tax rate = .36/4.50
sales tax rate = .08 or 8%
Suppose 22 % of students chose to study German their sophomore year, and that meant that there were 66 such students. How many students chose not to take
German their sophomore year?
Answer:
If 66 is 22%, that means that the remaining 78% is 234 students. So 234 students chose not to take German their sophomore year. hope this helps :))))
The number of leaves that fall off a tree n days after day 1 is given by the function f (n) = 3(2)".
What does the value 3 mean in this function
Answer:
the amount of leaves that fall of the tree in one day
Step-by-step explanation:
n is the amount of days
f is the amount of leaves that fall in a day
any help for math lesson
Answer:
12.5
Step-by-step explanation:
We can turn this into a cross - multiplication problem.
n / 7.5 = 25 / 15
All we have to do is cross multiply to get 15n = 7.5*25
As a result, we get 15n = 187.5
Divide by 15 on both sides to get 12.5
Double check
We can double check this answer by dividing 15/7.5 and 15/7.5, because ratios are the same if they are just multiplied versions of themselves
So, we get 2 for both answers, meaning that 12.5 is correct
Need help only on odds please
Answer:
Step-by-step explanation:
1) (i) HG ≅ ST ; GI ≅ TR ; IH ≅ RS
ΔHGI ≅ ΔSTR by S S S congruent
(ii) ∠H ≅ ∠S ; HG ≅ ST ; ∠G ≅ ∠T
ΔHGI ≅ ΔSTR by A S A -> Angle Side Angle congruent.
3) LM ≅ XY ; MK ≅ YZ ; KL ≅ ZX
ΔLMK ≅ ΔXYZ Side Side Side congruent
∠K ≅ ∠Z ; KL ≅ ZX ; ∠L ≅ ∠X
ΔLMK ≅ ΔXYZ by Angle Side Angle congruent
A gardening club has 21 members, of which 13 are males and the rest are females. What is the ratio of females to all
Club members.
Answer:
There are 8 Females out of the 21
Find the distance from C to G.
4
86
7
64
3
32
Answer: 64/3
Step-by-step explanation:
verify the identity
[tex]cot(x-\frac{\pi }{2} )[/tex] = - tan x
please show all steps
Answer:
Step-by-step explanation:
[tex]\tan (x-\frac{\pi }{2} )=\frac{tan~x-tan~\frac{\pi }{2} }{1+tan~x~tan~\frac{\pi }{2} } \\or~\cot(x-\frac{\pi }{2} )=\frac{1+\tan~x~\tan\frac{\pi }{2} }{\tan~x-\tan~\frac{\pi }{2} } \\divide~the~R.H.S. ~by~\tan ~x~\tan~\frac{\pi }{2} \\=\frac{\cot~x~\cot~\frac{\pi }{2} +1 }{\cot~\frac{\pi }{2} -\cot~x} \\\cot\frac{\pi }{2} =0\\\cot(x-\frac{\pi }{2} )=\frac{\cot~x ~\times~0+1}{0-\cot~x} \\\cot~(x-\frac{\pi }{2} )=-\frac{1}{\cot~x} =-\tan~x[/tex]
Rajeev deposits $800 in a savings account earning interest at a rate of 4% compounded annually. How much is in his account after five years?
Answer:
960
Step-by-step explanation:
We know that 4 percent of 800 dollar is 32 dollar. So 32 time 5 (because it ask us how much after 5 year) is 160. Now we add it to 800 because it ask the total in his account so it 960.
After five years, Rajeev have $960 in his account.
What is mean by Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
Rajeev deposits $800 in a savings account earning interest at a rate of 4% compounded annually.
Here, Principal amount = $800
Rate = 4%
Time = 5 years
Hence,
Interest = PRT/100
= 800 x 4 x 5 / 100
= 160
Thus, Total amount after 5 years is,
⇒ 800 + 160
⇒ $960
Therefore, After five years, Rajeev have $960 in his account.
Learn more about the addition visit:
https://brainly.com/question/25421984
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WILL DO ABSOLUTELY ANYTHING FOR THIS ONE HELP ASAP TIMES
Given:
The graph of a function [tex]y=h(x)[/tex].
To find:
The interval where [tex]h(x)>0[/tex].
Solution:
From the given graph graph it is clear that, the function before x=0 and after x=3.6 lies above the x-axis. So, [tex]h(x)>0[/tex] for [tex]x<0[/tex] and [tex]x>3.6[/tex].
The function between x=0 and x=3.6 lies below the x-axis. So, [tex]h(x)<0[/tex] for [tex]0<x<3.6[/tex].
Now,
For [tex]-1<x<0[/tex], the graph of h(x) is above the x-axis. So, [tex]h(x)>0[/tex].
For [tex]0<x<1[/tex], the graph of h(x) is below the x-axis. So, [tex]h(x)<0[/tex].
For [tex]1<x<2[/tex], the graph of h(x) is below the x-axis. So, [tex]h(x)<0[/tex].
Only for the interval [tex]-1<x<0[/tex], we get [tex]h(x)>0[/tex].
Therefore, the correct option is A.
Evaluate function expressions 4 x f(6) - 6 x g(5) =
9514 1404 393
Answer:
24
Step-by-step explanation:
Find the parts of the expression from the graph, and evaluate the expression.
f(6) = -6
g(5) = -5
Then we have ...
f(6) -6·g(5) = (-6) -6(-5) = -6 +30 = 24
If f(x) = 3x – 7 and g(x) = x2 – 5x + 5, then f(x) = g(x) for
what values of x?
a. x = 3 and x = 4
b. X = 6 and x = 2
c. x = -6 and x = -2
d. x = -3 and x = -4
Answer:
b
Step-by-step explanation:
3x - 7 = x² - 5x + 5
x² - 5x + 5 - 3x + 7 = 0
x² - 8x + 12 = 0
(x-6)(x-2)=0
x = 6
x = 2
Pls help this is due by midnight
Answer:
Cost of four DVD= 36.7, but due to 25% discount it cost 27.57. Then add 7.75 taxes and he payed 29.71. Answer is 29.71
Step-by-step explanation:
Answer:
$27.71
Step-by-step explanation:
Price of 1 DVD: $9.19
Price of 4 DVDs: 4 * $9.19 = $36.76
Discount: 25%
Now we find 25% of $36.76.
25% of $36.76 =
= 0.25 * $36.76
= $9.19
The 25% discount amounts to $9.19. We now subtract $9.19 from $36.76 to find the discounted price.
$36.76 - $9.19 = $27.57
Now we need to apply the 7.75% tax to $27.57.
7.75% of $27.57 =
= 0.0775 * $27.57
= $2.14
The sales tax is $2.14.
Now we add the sales tax amount to the total discounted price.
$27.57 + $2.14 = $29.71
Answer: $27.71
The perimeter of a rectangle is 98 feet. The ratio of its length to its width is 5:2.
Find the area of the rectangle.
Answer:
the area is 50
Step-by-step explanation:
value of the 5:2
14 years ago the age of the mother was 4 times the age of her daughter. The presen
age of the mother is 2 times the age of her daughter will be 4 years hence. What
their present ages?
Answer:
Daughter is 25, mother is 58
Step-by-step explanation:
Let m = age of mother now
Let d = age of daughter now
m - 14 = 4(d - 14)
m = 2(d + 4)
m - 14 = 4d - 56
m = 2d + 8
subtracting them gets
14 = -2d + 64
2d = 50.
d = 25
m = 58
3÷657 using partial products
Answer:
219
Step-by-step explanation:
solve. 7/20n = 8/5. enter a fraction or a whole number
Answer:
7/32
Step-by-step explanation:
[tex]\frac{7}{20n}=\frac{8}{5}[/tex]
we can multiply the elements on the diagonal so
20n*8=7*5
160n=35
we divide the relation by 160
n=35/160=7/32
Qualitative" variables are measured on either ordinal or nominal scales
Answer:
I don't get it. Is that the full question?
Find the least common multiple of: 6, 3, 2
least common multiple of 6,3,2 is 6.
- 6 is the smallest number that is divisible by all three.
Answer:
.5
Step-by-step explanation:
The Question is above.
Step-by-step explanation:
given
g(r)= -1 -7r
g ( 6) = - 1 - 7 * 6
= - 1 - 42
= - 43
Erik works 55 hours a week making $12.50 hour? His employer pays time and a half for hours over 40. Find his gross pay.
Answer:
781.25
Step-by-step explanation:
Regular pay = 40*12.50 = 500.00
Overtime = 15*12.5*1.5 = 281.25
Gross pay = 500.00 + 281.25 = 781.25
PLS HELP WILL MARK BRAINLIST
Determine which is the better buy. (picture below)
Answer:
Cheese B
Step-by-step explanation:
Find the cost of 1 slice for Cheese A:
Set up a proportion: [tex]\frac{3.59}{10} = \frac{x}{1}[/tex] Cross multiply, then divide: 3.59 × 1 = 3.59, 3.59 ÷ 10 = 0.359So, the cost of 1 slice of Cheese A is $0.359Find the cost of 1 slice for Cheese B:
Set up a proportion: [tex]\frac{5.12}{16} = \frac{x}{1}[/tex] Cross multiply then divide: 5.12 × 1 = 5.12, 5.12 ÷ 16 = 0.32So, the cost of 1 slice of Cheese B is $0.32Make a conclusion:
Because $0.32 is less than $0.359, Cheese B is the better buy.
I hope this helps!
Can someone help me on this
Answer:
Step-by-step explanation:
I don’t get it too
A TV has an original price of $599. Enter the new price after the given percent of change.
20% increase
The percent decrease is ? %
Answer:
The new price = $718. 8
Step-by-step explanation:
Original Price = $599
Given that the increase is 20%.
i.e.
Thus,
The amount of 20% Percentage increase = 20/100 × 599
= 0.2 × 599
= $119.8
Therefore,
New price = Original price + 20% increase amount
= 599 + 119.8
= $718. 8
Therefore, the new price = $718. 8
The IRS was interested in the number of individual tax forms prepared by small accounting firms. The IRS randomly sampled 50 public accounting firms with 10 or fewer employees in the Dallas-Fort Worth area. The following frequency table reports the results of the study.
Number of Clients Frequency
25 up to 40 3
40 up to 55 11
55 up to 70 24
70 up to 85 8
85 up to 100 4
Estimate the mean and the standard deviation. Round squared deviations to the nearest whole number and the final answer to 2 decimal places.
Answer:
Estimates of the number of individual tax forms prepared by small accounting firms:
1. Mean = 10
2. Standard deviation = 7.56
Step-by-step explanation:
a) Data and Calculations:
Number of Clients Frequency Mean Diff Squared Deviation
25 up to 40 3 -7 49
40 up to 55 11 1 1
55 up to 70 24 14 196
70 up to 85 8 -2 4
85 up to 100 4 -6 36
Sum 50 286
Mean of frequencies = 10 (50/5) 57.2 (286/5)
Standard deviation = square root of 57.2 = 7.56
b) The IRS can obtain the mean value of the number of individual tax forms prepared by small accounting firms by dividing the sum of the frequencies by the numbers (50/5). Similarly, the IRS can calculate the standard deviation of the number of individual tax forms prepared by small accounting firms, which measures how spread out the data is about the mean value, by working out the mean of the frequency numbers. Then subtract the mean for each number and square each result. Add up the squared differences and divide by the number to get the mean. Finally, take the square root of the mean differences.
200-3.5 x 2.8 what is the product?
Answer:
190.2
Explanation:
3.5x2.8=9.8
200-9.8=190.2
Answer:
how do you find the product of 3.5 x 2.8
Step-by-step explanation:
explain how you got it.
Calculate the value of this expression by writing the decimal factors as fractions, then writing their product as a decimal. Show your reasoning. (0.01)⋅(0.02) this is 6th grade math
Answer:
0.0002
Step-by-step explanation:
Answer:
0.0002
Step-by-step explanation:
Diana buys 5 sodas every week. Which of the following expressions shows the total number of sodas she buys in y weeks? (4 points)
Group of answer choices
5y
Fraction y over 5
5 + y
5 + 5y
Answer:
Shalom Guys I will try my best to answer this! ok i think it would be #2 have a great day i hope i could help the squad says hi!
~Piper Rokelle
Step-by-step explanation:
Somebody please help me :(
Answer:
A, C, E
Step-by-step explanation:
Factory M makes 200 screwdrivers per hour.
Factory N makes 100 screwdrivers per hour.