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]
Given the diagram to the right,determine m
Answer:
The measure of Angle S is 75 (degrees).
Step-by-step explanation:
Key skills needed to solve this are: Sums of a triangle, one variable equation, operations
1) All the angles in a triangle add up to equal 180 degrees.
2) We can use this to say that Angle S + Angle R + Angle T is 180 degrees.
3) Subsitute in the expression for each angle: 7x+40+8x+25+5x+15 = 180
4) Combine like terms
7x + 8x + 5x is 20x & 40 + 25 + 15 is 80
This means that 20x + 80 = 180
5) Move 80 to the right side: 20x = 100
6) Divide by 20 andbget x equal to 5
7) To find Angle S, you need to plug in 5 into the expression.
7x + 40 = 7(5) + 40 = 35 + 40 = 75 degrees
The measure of Angle S is 75
Sammy solved 68 math problems in 17 minutes. At what rate did Sammy solve the math problems?
Answer:
4 math problems per minute
Step-by-step explanation:
68 ÷ 17 = 4
4 math problem per minute
Answer:
9.71428571429 or 9.7
Step-by- step explanation:
ok so for this we need to divide 68 into 17 , we get the large number above.
What is the answer to 3x^2+2x^2+5x^2 ?
Answer:
10x²
Step-by-step explanation:
all have the same exponential value so you can add them directly
The perimeter of the rectangle shown is 96 feet. Determine the length and width of the rectangle.
Answer:
45
Step-by-step explanation:
detrain of the value they was given
Answer:
Length = 37 feet
width = 11 feet
Step-by-step explanation:
First, let us find the value of x.
They've already given that the perimeter of this rectangle is 96 feet.
So,
4x - 7 + 4x - 7 + x + x = 96
10x - 14 = 96
10x = 96 + 14
10x = 110
Divide both sides by x.
x = 11 feet
And now we can find the value of the width and length.
Given that,
Length = ( 4x - 7 ) ⇒ ( 4 × 11 - 7 )
44 - 7
37 feet
Width = x ⇒ 11 feet
Let me know if you have any other questions :-)
10 to the power of -3
Answer:
its 0.001
Step-by-step explanation:
Hope this helps :)
Answer:
0.001
Step-by-step explanation:
10^-3 = 0.001
You don't multiply since it's a negative power.
Ace
The four-sided geometric figure pictured is called a parallelogram. One feature of parallelograms is that opposite sides have equal lengths.
A parallelogram is shown. It is folded from one point to another to form 2 triangles.
The dotted line splits the parallelogram into two triangles. What is true about the congruency of the two triangles?
More information is needed.
The triangles can be proven congruent using SSS.
The triangles can be proven congruent using HL.
The triangles are not congruent.
Answer: The triangles can be proven congruent using SSS.
HOPE THIS HELPS
CAN YOU PLEASE GIVE ME BRAINLIEST
Answer:
The triangles can be proven congruent using SSS.
Step-by-step explanation:
The four-sided geometric figure pictured is called a parallelogram. One feature of parallelograms is that opposite sides have equal lengths.
A parallelogram is shown. It is folded from one point to another to form 2 triangles.
The dotted line splits the parallelogram into two triangles. What is true about the congruency of the two triangles?
More information is needed.
The triangles can be proven congruent using SSS.
The triangles can be proven congruent using HL.
The triangles are not congruent.
Triangle V P M. Angle V is 52 degrees, angle P is 78 degrees, angle M is x degrees. What is the measure of AngleM?
Answer:
The answer is 50
Step-by-step explanation:
Got it right on edge
Answer:
50 the guy under me got it right on edge 2021
Step-by-step explanation:
Hopes this helps!!! ^^
Match each mixed number to it's improper fraction.
Answer:
9/2
5/3
13/4
3/2
Step-by-step explanation:
Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twice the distance from P to" B(6, 2, −3).
Answer:
Equation of Sphere = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 18x - 4/3y +10z + 142/3 = 0
Step-by-step explanation:
Data Given:
P = (x,y,z)
Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)
Solution:
Find the equation of the sphere:
It is given that:
PA = 2PB
Squaring both sides:
[tex](PA)^{2} = (2PB)^{2}[/tex]
[tex](PA)^{2} = 4 (PB)^{2}[/tex]
[tex](x - (-3))^{2}[/tex] + [tex](y - 6)^{2}[/tex] + [tex](z-3)^{2}[/tex] = 4 x [tex](x-6)^{2}[/tex] + [tex](y-2)^{2}[/tex] + [tex](z-(-3))^{2}[/tex]
Solving the above equation:
[tex](x + 3))^{2}[/tex] + [tex](y - 6)^{2}[/tex] + [tex](z-3)^{2}[/tex] = 4 x {[tex](x-6)^{2}[/tex] + [tex](y-2)^{2}[/tex] + [tex](z + 3))^{2}[/tex]}
[tex]x^{2}[/tex] + 9 + 6x + [tex]y^{2}[/tex] + 36 - 12y + [tex]z^{2}[/tex] + 9 - 6z = 4 { [tex]x^{2}[/tex] + 36 - 12x + [tex]y^{2}[/tex] + 4 - 4y + [tex]z^{2}[/tex] + 9 + 6z}
[tex]x^{2}[/tex] + 9 + 6x + [tex]y^{2}[/tex] + 36 - 12y + [tex]z^{2}[/tex] + 9 - 6z = 4[tex]x^{2}[/tex] + 144 - 48x +4[tex]y^{2}[/tex] + 16 - 16y + 4[tex]z^{2}[/tex] + 36 + 24z
Putting the right hand side = 0 and solving the equation:
[tex]x^{2}[/tex] - 4[tex]x^{2}[/tex] + [tex]y^{2}[/tex] - 4[tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 4[tex]z^{2}[/tex] + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0
-3[tex]x^{2}[/tex] - 3[tex]y^{2}[/tex] -3[tex]z^{2}[/tex] + 54x + 4y -30z -142 = 0
Taking (-) common
- ( 3[tex]x^{2}[/tex] + 3[tex]y^{2}[/tex] + 3[tex]z^{2}[/tex] - 54x - 4y +30z + 142) = 0
3[tex]x^{2}[/tex] + 3[tex]y^{2}[/tex] + 3[tex]z^{2}[/tex] - 54x - 4y +30z + 142 = 0
dividing the whole equation by 3
[tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 54/3x - 4/3y +30/3z + 142/3 = 0
[tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 54/3x - 4/3y +30/3z + 142/3 = 0
[tex]x^{2}[/tex] + [tex]y^{2}[/tex] + [tex]z^{2}[/tex] - 18x - 4/3y +10z + 142/3 = 0
The equation of the sphere for all surface point P such that [tex]AP = 2\cdot BP[/tex] is [tex]x^{2}+y^{2}+z^{2}-18\cdot x -\frac{4}{3}\cdot y + 10\cdot z +\frac{142}{3} = 0[/tex].
Procedure - Determination of the equation of a sphereGeometric locus and Pythagorean expansionMathematically speaking, we have the following geometric locus:
[tex]AP = 2\cdot BP[/tex] (1)
Then, we expand the expression presented above by Pythagorean theorem, used to determine the length of a line segment in the field of analytical geometry:
[tex]\sqrt{(x +3)^{2} + (y-6)^{2} + (z-3)^{2}} = 2\cdot \sqrt{(x-6)^{2}+(y-2)^{2}+(z+3)^{2}}[/tex]
[tex](x+3)^{2}+(y-6)^{2}+(z-3)^{2} = 4\cdot (x-6)^{2}+4\cdot (y-2)^{2}+4\cdot (z+3)^{2}[/tex]
ResolutionNow we expand and simplify the resulting expression:
[tex]x^{2}+6\cdot x + 9 + y^{2}-12\cdot y + 36 + z^{2}-6\cdot z + 9 = 4\cdot (x^{2}-12\cdot x +36) + 4\cdot (y^{2}-4\cdot y +4) + 4\cdot (z^{2}+6\cdot z + 9)[/tex]
[tex]x^{2} + y^{2} + z^{2} + 6\cdot x -12\cdot y - 6\cdot z +54 = 4\cdot x^{2} +4\cdot y^{2} + 4\cdot z^{2} -48\cdot x -16\cdot y +24\cdot z +196[/tex]
[tex]3\cdot x^{2} + 3\cdot y^{2} + 3\cdot z^{2} -54\cdot x -4\cdot y + 30\cdot z + 142 = 0[/tex]
[tex]x^{2}+y^{2}+z^{2}-18\cdot x -\frac{4}{3}\cdot y + 10\cdot z +\frac{142}{3} = 0[/tex] (2)
This expression corresponds to the general form of the equation of the sphere for all surface point P such that [tex]AP = 2\cdot BP[/tex]. [tex]\blacksquare[/tex]
To learn more on geometric loci, we kindly invite to check this verified question: https://brainly.com/question/521553
HELPP!!! DON'T ANSWER IF YOU ARE NOT SURE PLEASE !!
Select the reason why these triangles are similar. If they are not, select “not similar”
Well we need what reasons they could be similar. Is that all you are given or are there options?
HELP ME QUICK!!!!.!.!..
Which graph represents a proportional relationship?
Answer:
we need a picture
Step-by-step explanation:
Segment GH is a mid segment of triangle JKL.Select all of the equations that could be used to find the value of x.
Answer:
A. 2(5x + 2) = 3x + 32
F. ½(3x + 32) = 5x + 2
Step-by-step explanation:
GH = 5x + 2
KL = 3x + 32
Based on the midsegment theorem,
½(KL) = GH
That is:
½(3x + 32) = 5x + 2
Or
2(GH) = KL
That is:
2(5x + 2) = 3x + 32
Which expression is equivalent to
14x + 35 - 21y
Expression 1: 2x + 5 - 3y
Expression 2: 7(2x + 5 - 3y)
Expression 3: 7xy(2 + 5 - 3)
Expression 4: 7x(2+5+3y)
Answer:
Expression 1
Step-by-step explanation:
14x + 35 - 21y
[tex]14x + 35 - 21y \\ \frac{14x}{7} + \frac{35}{7} - \frac{21y}{7} \\ 2x + 5 - 3y[/tex]
Answer:
Its Expression 2: 7(2x + 5 - 3y)
Step-by-step explanation:
just got it right
-5(2x - 7) + 24 = 89
Answer:
x=-3
Step-by-step explanation:
First you must distribute -5 to 2x and -7
so you get
-10x+35+24=89
then you will subtract 35 from both sides and get
-10x+24=54 then you will subtract 24 from each side and get
-10x=30 then you will divide -10 and get
x=-3
Which number is irrational?
1) -4
2) 2/9
3) [tex]\sqrt{11}[/tex]
4) 8.25
HEEELPPP WILL DO ANYTHING FOR IT
Answer:
well hunny child whats the equation y'all use?
Step-by-step explanation:
Answer:
i wish i could help but what ik bout this is dat every triangle is 180* if dat help :(
but hey keep trying u can do dis :) <3
13. The programmer at a local public radio station is compiling data on listeners who stream podcasts. An executive for the national broadcaster has communicated that the overall population mean is 20,500 with a standard deviation of 2,180. The local programmer has a sample of 30 podcasts for her station. By the central limit theorem, which interval do about 99.7% of the sample means fall within?
A. 20,102 and 20,898
B. 20,282 and 20,718
C. 19,306 and 21,694
D. 19,704 and 21,296
Answer:
C. 19,306 and 21,694
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, for samples of 30:
Mean: 20,500
Standard deviation: [tex]s = \frac{2180}{\sqrt{30}} = 398[/tex]
99.7% of the sample means fall within 3 standard deviations of the mean, by the Empircal Rule with the Central Limit Theorem:
Lower bound: 20500 - 3*398 = 19,306
Upper bound: 20500 + 3*398 = 21,694
So the correct answer is option C.
A jet travels 4648 miles against the wind in 8 hours and 5368 miles with the wind in the same amount of time. What is the rathe of the jet in still air and what is the rate of the wind?
Answer:
The rate of the jet in still air is 738 mph and the rate of the wind is 90 mph
Step-by-step explanation:
Check: (738+90)*6 = 648*6 = 3888 mike's against the wind
(738-90)*6 = 828*6 = 4968 miles with the wind
Solve the proportion. Please show me step by step how to solve this. Thanks
4.6/6 = w/3
9514 1404 393
Answer:
w = 2.3
Step-by-step explanation:
It looks like you have ...
4.6/6 = w/3
To solve this, you need to clear the 3 from the denominator of the w term. Do that by multiplying both sides of the equation by 3.
3(4.6/6) = 3(w/3)
4.6(3/6) = w . . . . simplify (rearrange the product to make mental arithmetic easier: 3/6 = 1/2)
w = 2.3 . . . . . . . . do the arithmetic
Answer:
2.3
Step-by-step explanation:
4. Evaluate 5x2 + 16y for x = 2 and y = -3
Answer:
-28
Step-by-step explanation:
=5(2)²+16(-3)
=5(4)+(-48)
=20-48
=-28
Answer:
-28
Step-by-step explanation:
Expression: 5x²+16y
x=2 and y=-3
We'll substitute x as 2 and y as -3
5(2)²+16(-3)
Following Order of Operations, do the exponent part first
5(4)+16(-3)
Multiply
20-48
subtract
-28
Hope this helps
What is the price of an $100 handbag during a 25% clearance sale?
Answer:
75 dollars
Step-by-step explanation:
what is the answers to 3 1/4 *1 1/3 this is a 15 point offer!!!
Answer:
3 1/4*1 1/3 = 4 1/3
Step-by-step explanation:
I have a confusion is it 3 1/4 *1 1/3 does 3 and 1 have space or 31/4 *11/3 fully joined!?
Pls help best will get Brainliest
Missing addend: 1/2 + 1/4
Missing Sums: 5/8 and 3/4
Step-by-step explanation:
The pattern of the addend is that the first term increases by 1/8 and the second term is always 1/4. If only the first term increases by 1/8, that means the total sum will increase by 1/8 each time also.
A figure has been dilated from center 0 by a scale factor of = 7/6 . What scale factor would shrink the dilated figure back to the original size?
Answer:
6/7
Step-by-step explanation:
1 x 7/6 x 6/7 = 1
A scale factor of 6/7 would shrink the dilated figure back to its original size.
To return the dilated figure back to its original size, you would need to use a scale factor that is the reciprocal of the original dilation scale factor. The reciprocal of a fraction is obtained by flipping the numerator and denominator.
Given the original dilation scale factor of 7/6, the scale factor that would shrink the dilated figure back to the original size is:
Reciprocal of 7/6 = (6/7)
So, using a scale factor of 6/7 would shrink the dilated figure back to its original size.
To know more about scale factor
https://brainly.com/question/29967135
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I GIVEEEEE BRASINLILST
Answer:
Answer: Choice G.
Step-by-step explanation:
Dilations
Suppose a point P(x,y) is dilated across the origin, that is, the origin is the center of dilation, by a scale factor k.
The image of P is P' whose coordinates are P'(kx,ky).
If an image is formed by several points and each one is dilated by the same factor, then:
If |k| > 1, the image maps to a stretched or larger image.
If |k| < 1, the image maps to a shrunk or shorter image.
We have a hexagon graphed on a coordinate grid. The hexagon is dilated to create a larger hexagon. This means k must be greater than 1 and it should multiply each original coordinate (x,y).
Options F and H don't multiply by the coordinates but add to them, thus they are not valid answers.
Option J actually multiplies by the factor 0.2 but since it's less than 1, it does not correspond to an enlargement.
Only option G multiplies by a factor 4/3=1.3 greater than 1.
Answer: Choice G.
I need youre helpppp
Answer:
B , C, and D
Step-by-step explanation:
x + y and x+ z both make a straight line which is 180 degrees, and Z and Y are congruent angles.
7.
2. What is the product of 50 and 100?
2
50
O 150
O 5,000
.
Answer:
it's 5000
Step-by-step explanation:
50*100=5000
hope it helps:p
Solve the linear equation below for x. *
3x + 4 = 8x – 9
A. 2.6 B. 1 C. 1.09 D. 2
HELP PLSSSS ASAP ILL MARK AS BRAINLIEST AND 30 POINTS
Answer:
A- 4.50
B- unit price is 2 dollar per a hat. Price would be 24 dollars
C- unit price is .40
D- 69
Step-by-step explanation: