Answer:
[tex]\frac{d^2y}{dx^2} = \frac{-4}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FactoringCalculus
Implicit Differentiation
The derivative of a constant is equal to 0
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Product Rule: [tex]\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
-y - 2x³ = y²
Rate of change of tangent line at point (-1, -2)
Step 2: Differentiate Pt. 1
Find 1st Derivative
Implicit Differentiation [Basic Power Rule]: [tex]-y'-6x^2=2yy'[/tex][Algebra] Isolate y' terms: [tex]-6x^2=2yy'+y'[/tex][Algebra] Factor y': [tex]-6x^2=y'(2y+1)[/tex][Algebra] Isolate y': [tex]\frac{-6x^2}{(2y+1)}=y'[/tex][Algebra] Rewrite: [tex]y' = \frac{-6x^2}{(2y+1)}[/tex]Step 3: Differentiate Pt. 2
Find 2nd Derivative
Differentiate [Quotient Rule/Basic Power Rule]: [tex]y'' = \frac{-12x(2y+1)+6x^2(2y')}{(2y+1)^2}[/tex][Derivative] Simplify: [tex]y'' = \frac{-24xy-12x+12x^2y'}{(2y+1)^2}[/tex][Derivative] Back-Substitute y': [tex]y'' = \frac{-24xy-12x+12x^2(\frac{-6x^2}{2y+1} )}{(2y+1)^2}[/tex][Derivative] Simplify: [tex]y'' = \frac{-24xy-12x-\frac{72x^4}{2y+1} }{(2y+1)^2}[/tex]Step 4: Find Slope at Given Point
[Algebra] Substitute in x and y: [tex]y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(-1)^4}{2(-2)+1} }{(2(-2)+1)^2}[/tex][Pre-Algebra] Exponents: [tex]y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(1)}{2(-2)+1} }{(2(-2)+1)^2}[/tex][Pre-Algebra] Multiply: [tex]y''(-1,-2) = \frac{-48+12-\frac{72}{-4+1} }{(-4+1)^2}[/tex][Pre-Algebra] Add: [tex]y''(-1,-2) = \frac{-36-\frac{72}{-3} }{(-3)^2}[/tex][Pre-Algebra] Exponents: [tex]y''(-1,-2) = \frac{-36-\frac{72}{-3} }{9}[/tex][Pre-Algebra] Divide: [tex]y''(-1,-2) = \frac{-36+24 }{9}[/tex][Pre-Algebra] Add: [tex]y''(-1,-2) = \frac{-12}{9}[/tex][Pre-Algebra] Simplify: [tex]y''(-1,-2) = \frac{-4}{3}[/tex]does anyone understand this
For this problem, 0.25 in = 50 m. So
11 in = (11 in) • (50/0.25 m/in) = 2200 m
Alternatively, if 0.25 in = 50 m, that means 1 in = 200 m. So 11 in = 11 (200 m) = 2200 m.
expression with parentheses..example and non-example
Answer:
With parentheses:
(3 - 4)(4 + 5)/3
Without parentheses:
7 + 6 - 11 × 2
Hope this helps! :)
Annie spent $143.89 at Kohls and there is a 6.25% sales tax. What will she pay in sales tax and
what is the total purchase price?
Answer:
net amount 143 89 tax 6.25 % which is $8.99 gross amount is $152.88
COLOR THEME
O Q ZOOM
5. Mrs. All collected notebook paper from her students at the beginning of the
school year. The model is shaded to show the fraction of notebook paper
that Mrs. Ali used in each of the following three months.
First month
Second month
Third month
What fraction of the notebook paper Mrs. All collected was used during
these three months?
Answer:
6
Step-by-step explanation:
PLEASE HELP!!
finding square roots of negative numbers
show your work
1-) V-18
2-) 2V-16
Answer:
Work shown below!
Step-by-step explanation:
[tex]\sqrt{-18}=\sqrt{18i^{2} } =\sqrt{2*9i^{2} }=3i\sqrt{2}[/tex]
[tex]2\sqrt{-16} =2\sqrt{16i^{2} } =4i*2=8i[/tex]
What is the perimeter of this figure?
6x+6
6x+10
4x+6
4x+8
Answer: 4x+8
Step-by-step explanation:
Okay since the area for the block is X, two numbers multiplied together is X.
Since the big block has an area of X^2, then this shows the sides to be X.
This gives the sides of the block with area X to be 1 and X.
Now just add up every side like this : 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + x + x + x + x to get 4x+8
Assuming each area code is just as likely as any other, what's the probability that the area code of two back to back spam calls are 804
Complete Question:
Yanay gets a lot of spam calls. An area code is defined to be a three digit number from 200-999 inclusive. In reality, many of these area codes are not in use, but for this question we'll simplify things and assume they all are.
Assuming each area code is just as likely as any other, what's the probability that the area code of two back to back spam calls are 804?
Answer:
1/6400 or 0.0000015625
Step-by-step explanation:
Given
Area Codes = 200 to 999 (inclusive)
Required
Determine the probability that back to back calls have area code 804
[First, we need to calculate the totality of area codes]
Total Area Codes = 999 - 200 + 1
Total Area Codes = 800
The probability of each code is 1/800
So, the probability of having back to back code of 804 is:
Probability = 1/800 * 1/800
Probability = (1/800)²
Probability = 1/640000
Hence, the required probability is 1/640000 or 0.0000015625
Randy Houck deposited his paycheck for $385.15, a refund check from a mail
order purchase for $125.95, and $37.20 in cash.
Answer:
The correct option is c. $548.30.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question. Please, see the attached pdf file for the complete question.
Also Note: This template does not allow the explanation to be added and saved here as it keeps on indicating that it contains some swearwords. The explanation is now given in the attached pdf file. Please, see the attached pdf file for the answer and explanation.
3 fair coins are tossed.
a) What is the probability of getting all 3 heads? (My Answer is 1/8)
b) What is the probability of getting all 3 tails? (My Answer is 1/8)
c) What is the probability of getting all 1 head and 2 tails? (My Answer is 3/8)
d) What is the probability of getting all 2 heads and 1 tail? (My Answer is 3/8)
My Question:
e) What do the probabilities from parts (a) to (e) add up to?
Answer:
1/8 + 1/8 + 3/8 + 3/8 = 2/8 + 6/8 = 8/8 = 1
So the answer would be 1.
Does anyone know the answers to this?
Answer:
i think the correct answer of these qusion is `B´
Answer:it’s 5
Step-by-step explanation:
Factor completely
w^2 + 12w -f^2+ 36
Assume you have a balance of $1,900 on a credit card.
If the credit card has an annual interest rate of 13.6% and only the minimum monthly
payment of $35 is made, how many months will it take to pay off the credit card?
principal=$1900
rate =13.6 %
simple interest= $35
Time=?
SIMPLE INTEREST ={PRINCIPAL×RATE×TIME}/{100}
$35= [tex]{$1900 ×13.6× TIME}{100} /[/tex]
$35×100=25840× TIME
TIME=[tex]\bold\frac{ 3500}{25840}[/tex]
TIME=[tex] 700/5168 [/tex]
TIME=[tex]{\tt{\green{\underline{\underline{\huge{0.1354489164}}}}}}[/tex] years
sorry I can't solve wrong answer
Harold brought 5 apples for $3.90.What is the unit price?
Answer:
.78
Step-by-step explanation:
3.90/5 = .78
Solve the quadratic equation using any appropriate method.
- 2x2 + 7x - 7 = 0
68=u-11
i need help lol pls
Answer:
u=79
Step-by-step explanation:
68=u-11
add 11 to 68
u=79
Rewrite the following to show the distributive property
4x(5+3)
Step-by-step explanation:
4x+8
basically u solve the number that is in parentheses then you are left with the number with a variable so u can't solve so that's ur equation
Answer:
32x
Step-by-step explanation:
1. rewrite
4x(5)+4x(3)
4(3) means 4*3
2. multiply
4x(5)= 20x
4x(3)= 12x
20x+12x
3. combine like terms
20x+12x= 32x
32x
If this is right can you make me brainliest
3(x – 2) – (1 – x) > 2x – 7
Write the equation of the line parallel to the line y= 5x + 3 that passes through the point (3,3)
Answer:
y=5x-12
Step-by-step explanation:
y=5x+3, and just replace the x and y to get the b. The slope is the same.
1) 3=5(3)+b
2)3=15+b
3)-12=b
4) y=5x-12
The $99.99 digital camera Mia purchased was on sale for 15% off. What amount did Mia get off the price? please leave an explanation
Answer: Sale Price = $84.99 (answer). This means the cost of the item to you is $84.99. You will pay $84.99 for a item with original price of $99.99 when discounted 15%. In this example, if you buy an item at $99.99 with 15% discount, you will pay 99.99 - 14.9985 = 84.99 dollars.
Step-by-step explanation:
solve for x and y!! will give brainliest !
Answer:
x = 60 and y=25
Step-by-step explanation:
it is equilateral triangle and an equilateral triangle is a triangle in which all three sides have the same length. In the familiar geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
which table of values matches the equation y=2x-3
Answer:
What are the possible answer??/
Step-by-step explanation:
The set of points satisfying the equation y = 2x - 3 is a. {(0, -3), (1, -1), (1.5, 0), (2,1)}.
An equation is the combination of 2 or more expressions separated by the equality sign(=), signifying the equality of expressions.
To obtain the set of points satisfying the equation y = 2x - 3.
The given equation is y = 2x - 3.
Let's take x = 0,
y = 2 × 0 - 3 = -3,
the point is (0, -3).
Let's take y = 0,
0 = 2x - 3
2x = 3
x = [tex]\frac{3}{2}[/tex]
x = 1.5,
the point is (1.5, 0).
Let's take x = 1,
y = 2 × 1 - 3 = -1,
the point is (1, -1).
Let's take y = 1,
1 = 2x - 3
2x = 1 + 3
2x = 4
x = [tex]\frac{4}{2}[/tex]
x = 2,
the point is (2,1).
Hence, the set of points satisfying the equation is {(0, -3), (1, -1), (1.5, 0), (2,1)}.
Learn more about Equation here:
https://brainly.com/question/28953876
#SPJ6
The complete question is as follows:
Which table of values matches the equation y = 2x - 3,
a. {(0, -3), (1.5, 0), (1, -1), (2,1)}.
b. {(0, -2), (1.5, 0), (1, -1), (2,1)}.
c. {(0, -3), (1.5, 0), (1, -4), (2,1)}.
d. {(-1,1), (0, -3), (1.5, 0), (1, -1)}.
The equation x^2/24^2 - y^2/b^2 = 1 represents a hyperbola centered at the origin with a directrix of x = 576/26.
What is the value of b?
A. 10
B. 16
C. 20
D. 26
Answer:
a
Step-by-step explanation:
edge
The value of B is 16.
The correct option is B
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
The standard equation for a hyperbola centered at the origin is:
(x²)/(a²) - (y²)/(b²) = 1
where "a" and "b" are the lengths of the transverse and conjugate axes, respectively. To find the value of "b" for the given hyperbola equation, we need to first rewrite it in the standard form.
(x²)/(24²) - (y²)/(b²) = 1
Multiplying both sides by (24²)(b²), we get:
b²(x²) - (24²)(y²) = (24²)(b²)
Dividing both sides by (24²), we get:
b²(x²)/(24²) - y² = b²
Comparing this with the standard equation, we can see that a = 24 and b is the square root of the constant term, which is b² = 576. Therefore, b = 24.
However, the given directrix of x = 576/26 is not consistent with the equation of the hyperbola. The directrix for a hyperbola with center at the origin and transverse axis along the x-axis is given by x = a²/b. Using the value of a = 24, we can find the directrix as:
x = (24²)/b
Setting this equal to 576/26, we get:
(24²)/b = 576/26
Solving for b, we get:
b = 16
Therefore, the correct answer is (B) 16.
To learn more about the quadratic equation;
https://brainly.com/question/17177510
#SPJ2
Help pls :))))))))))))))
Answer:left is 7 right is 6
Step-by-step explanation:
left is 7 right is 6
Answer:
the right side is 6 and the left side is 7
Step-by-step explanation:
These triangles are similar. Since the bottom side goes from 15 to 5, that means you divide the other 2 sides by 3 also.
Which of the following equations are written in standard form?
А. 3x + 5y = -7
B. 2y + x = 12
C. 5x+10y = -21
D. 1.2x + 5y = 23.7
PLEASE HELP ME ASAP
If the terminal point determined by t is (-5,-4), then
\sin (t) =
;
\cos (t) =
;
\tan (t) =
.
Answer:
The trigonometric ratios associated with (-5, -4) are [tex]\sin t \approx -0.625[/tex], [tex]\cos t \approx -0.781[/tex] and [tex]\tan t = 0.8[/tex].
Step-by-step explanation:
Let [tex]\vec u = (x,y)[/tex]. From Trigonometry, we remember the following definitions for the trigonometric ratios, dimensionless:
[tex]\sin t = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\cos t = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\tan t = \frac{y}{x}[/tex] (3)
If we know that [tex]x = -5[/tex] and [tex]y = -4[/tex], then the trigonometric ratios are, respectively:
[tex]\sin t = \frac{-4}{\sqrt{(-5)^{2}+(-4)^{2}}}[/tex]
[tex]\sin t \approx -0.625[/tex]
[tex]\cos t = \frac{-5}{\sqrt{(-5)^{2}+(-4)^{2}}}[/tex]
[tex]\cos t \approx -0.781[/tex]
[tex]\tan t = \frac{-4}{-5}[/tex]
[tex]\tan t = 0.8[/tex]
The trigonometric ratios associated with (-5, -4) are [tex]\sin t \approx -0.625[/tex], [tex]\cos t \approx -0.781[/tex] and [tex]\tan t = 0.8[/tex].
A paraboloid container is being filled with fluid at the rate of 4.5 cubic feet per minute. At what rate is the level of fluid changing when the depth
is 2.5 feet? The ratio of the radius to the height of the container is 3:7.
"V = 1/2 pir^2h
Answer:
2.62 ft./min
Step-by-step explanation:
Just took the test.
The IQ scores of the middle 50% of a population can be written as
I
100
15
where x is a person's IQ. Solve the inequality to find the IQ scores for the middle 50% of the population.
x 270 and x s 130
Ox570 and x 2 130
Oxs 90 and x 2 110
x 290 and x s 110
Complete question :
The IQ scores of the middle 50% of a population can be written as (x - 100) / 15 ≤ 2/3
Answer: 90 ≤ x ≤ 110
Oxs 90 and x 2 110
Step-by-step explanation:
Given the inequality:
The middle 50% of the population :
(x - 100) / 15 ≤ 2/3
The upper bound :
(x - 100) / 15 ≤ 2/3
multiply both sides by 15
(x - 100) / 15 * 15 ≤ 2/3 * 15
(x - 100) ≤ 2/3 * 15
x - 100 ≤ 10
x ≤ 10 + 100
x ≤ 110
The lower bound :
- (x - 100) / 15 ≤ 2/3
(-x + 100) / 15 ≤ 2/3
multiply both sides by 15
(-x + 100) / 15 * 15 ≤ 2/3 * 15
(-x + 100) ≤ 2/3 * 15
-x + 100 ≤ 10
-x ≤ 10 - 100
-x ≤ - 90
x ≤ 90
90 ≤ x ≤ 110
Help please
The answer choices are
A) x=3/x
B)x=9/x
C)0=3/x+x
D)0=9/x+x
Answer:
A
Step-by-step explanation:
Which graph shows the points (−11
2
, 1
2
) and (1.5, −0.5) plotted correctly?
On a coordinate plane, a point is 0.5 units to the right and 1.5 units up. Another point is 0.5 units to the left and 1.5 units down.
On a coordinate plane, a point is 1.5 units to the left and 0.5 units up. Another point is 1.5 units to the right and 0.5 units down.
On a coordinate plane, a point is 0.5 units to the left and 1.5 units up. Another point is 0.5 units to the right and 1.5 units down.
On a coordinate plane, a point is 1.5 units to the left and 0.5 units down. Another point is 1.5 units to the right and 0.5 units up.
Answer:
b
Step-by-step explanation: got it right on edge
Answer:
B
Step-by-step explanation:
got it right on edge
An item cost $420 before tax, and the sales tax is $33.60. Find the sales tax
Answer:
8%
Step-by-step explanation:
used a calculator