when we write d(x^2)/dx for example, we are writing dy in terms of dx, is the inverse true? when we have dx with respect to dy for dx/dy do we also write dx in terms of dy?

Answer:

a=58

Step-by-step explanation:

32+a=90

32-32+a=90-32

a=58

Answer:

\(y _{ \rm parallel} = - 5x +27\)

Step-by-step explanation:

The equation of line p is in point-slope form , that's

\(y-y_1=m(x-x_1)\)

Where:

Since line I is parallel to the line p , line I has the same slope as p. From the given equation of p , we can consider the slope of line p -5. Hence the slope of line I is also -5.

Now To determine the equation of I.

We have

So, the equation of line l is

\( y - 47 = - 5(x - ( - 4)) \\ \implies y - 47 = - 5 x- 20 \\ \implies \boxed{y _{ \rm parallel} = - 5x + 27}\)

And we're done!

Answer:

C. \(z = -20\sqrt{3}-i\,20\)

Step-by-step explanation:

The rectangular form of a complex number is represented by the following formula:

\(z = a+i\,b\) (1)

Where each coefficient can be determined as function of the polar components:

\(a = r\cdot \cos \theta\) (2)

\(b = r\cdot \sin \theta\) (3)

Where:

\(r\) - Magnitude of the complex number, dimensionless.

\(\theta\) - Direction of the complex number, measured in radians.

If we know that \(r = 40\) and \(\theta = \frac{7\pi}{6}\), then the rectangular form of the number is:

\(a = 40\cdot \cos \frac{7\pi}{6}\)

\(a = -20\sqrt{3}\)

\(b = 40\cdot \sin \frac{7\pi}{6}\)

\(b = -20\)

The rectangular form of \(z=40\cdot\left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6}\right)\) is \(z = -20\sqrt{3}-i\,20\). The correct answer is C.

Answer: c

Step-by-step explanation:

edge

Answer:2=42 3=82 4=122

Step-by-step explanation:

If there is already 2, all you have to do is take away 2 from 162 and then divide by the empty spaces (in this case 4) 160/4 = 40.

After 12 years, 1996 rabbits remained in the park when a state park had 330 rabbits living there.

Given that,

A state park had 330 rabbits living there. With continuous compounding, the population increased at a rate of 15% per year for 12 years.

We have to find after 12 years, how many rabbits remained in the park.

We know that,

The population of rabbit is p=330

The rabbit increasing rate is r=15%

Time is t=12 years

Use the continuously compounded formula to determine the number of rabbits after 12 years.

A= P\(e^{rt}\)

A=330\((2.17828)^{(0.15)(12)}\)

A= 1996.38

A=1996     (approximately)

Therefore, After 12 years, 1996 rabbits remained in the park when a state park had 330 rabbits living there.

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Answer:

$67400

Step-by-step explanation:

Given that :

Net income = 53246

Deduction (tax purposes) % = 21%

Gross income = net income + deduction

Let gross income = x

x = 53246 + 21% of x

x = 53246 + 0.21x

x - 0.21x = 53246

0.79x = 53246

x = 53246 / 0.79

x = 67400

Answer:

1/6

Step-by-step explanation:

Tell me if you need one

Answer:

0.875

Step-by-step explanation:

7/8 = 0.875

Answer:

0.875

Step-by-step explanation:

Try to make the denominator to power of 10

8 *125 = 1000

So, multiply both numerator and denominator by 125

\(\frac{7}{8}=\frac{7*125}{8*125}=\frac{875}{1000}=0.875\)

Answer:

3) 6/5

Step-by-step explanation:

3) 21/25÷7/10

21/25×10/7

3/5×2/1=6/5

Answer:

1. 1.8380952381

2.1.35555555556

3. 1.2

Hope this helps :-)

Answer:x=9z + 16

                  z= x/9 + 16/9

Step-by-step explanation: dont know if i solve for x or z so i did both  subtract 16 from both sides for x      

Isolate the variable by dividing each side by factors that don't contain the variable. for z let me know if u need help

Answer:

Hallooooooo

Step-by-step explanation:

A set of simultaneous equations is often known as a system of equations or an equation system. The solution of the system of equations is (1.791,11.374) and (-2.791, -2.374).

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.

Inconsistent System

For a system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

The solution of the two of the given function will be when the graph of the two the function will intersect with each other.

Using the graph the solutions are (1.791,11.374) and (-2.791, -2.374).

Hence, the solution of the system of equations is (1.791,11.374) and (-2.791, -2.374).

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Answer:

$y=\frac{-2}{9}x+\frac{61}$

Step-by-step explanation:

For two lines to be parallel to each other, it means they have to have the same slope. So, the question is really asking for the line through $(8, 5)$ that has the same slope as the line shown.

We can start by finding the slope of the line shown. Recall that given two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$, the slope of the line between them is $\frac{y_{2}-y_{1}}{x_{2}-x{1}}$, or more commonly remembered as rise over run. Plugging in the points $(-3, 1)$ and $(6, -1)$ into the equation for the slope, we see that the slope of the line shown is $\frac{-1-1}{6-(-3)}=\frac{-2}{9}$.

We recall that the point-slope form of a line is such that given a point $(x_{1}, y_{1})$ and the slope $m$, the equation for a line with that slope through the given point is $y-y_{1}=m(x-x_{1})$(Note: divide by $x-x_{1}$. What does that remind you of?). Plugging in our point and slope, we have that the equation for the line we want is $y-5=\frac{-2}{9}(x-8)$. Expanding the right-hand side gives $y-5=\frac{-2}{9}x+\frac{16}{9}$.

Adding $5$ to both sides gives the desired $\boxed{y=\frac{-2}{9}x+\frac{61}}$

Answer:

im guessing you meant -1/2 for the slope of the first line so it is going to be d. 2

Step-by-step explanation:

The slope of a perpendicular line is the negative reciprocal of the other line

C(x + 4)^3(x - 2). The value of M is 18.  

To find the value of M in the integral ∫ M (12x + 30) / (x^2 + 2x - 8) dx, we need to evaluate the integral and determine the value of M.

First, let's simplify the integrand:

∫ (12x + 30) / (x^2 + 2x - 8) dx

To simplify the denominator, we factorize it:

x^2 + 2x - 8 = (x + 4)(x - 2)

Now, we can rewrite the integral as:

∫ (12x + 30) / [(x + 4)(x - 2)] dx

To evaluate this integral, we can use partial fraction decomposition. Assuming that the integral can be expressed as:

∫ [(A / (x + 4)) + (B / (x - 2))] dx

By equating the numerators, we have:

12x + 30 = A(x - 2) + B(x + 4)

Expanding and collecting like terms, we get:

12x + 30 = (A + B) x + (-2A + 4B)

By comparing coefficients, we obtain the following system of equations:

A + B = 12 (equation 1)

-2A + 4B = 30 (equation 2)

Solving this system of equations, we find A = -6 and B = 18.

Now, we can rewrite the integral as:

∫ [(-6 / (x + 4)) + (18 / (x - 2))] dx

Integrating each term separately, we get:

-6 ∫ (1 / (x + 4)) dx + 18 ∫ (1 / (x - 2)) dx

Applying the natural logarithm integration rule, we have:

-6 ln| x + 4 | + 18 ln| x - 2 | + C

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Answer:

Store A would be the least expensive.

Step-by-step explanation:

Store A

70*0.10=7

70-7=63

63*0.10=6.30

63-6.30=57.70

$57.70

Store B

80-15=65

65*0.10=6.50

65-6.50=58.50

$58.50

Store C

90*0.10=9

90-9=81

81-20=61

$61

Answer:

Theres no graph form

Step-by-step explanation:

Answer:

it is a

Step-by-step explanation:

The coordinates of the triangle ΔC'D'E' will be (2, 1), (5, -3), and (2, -1). Then the correct option is C.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The triangle ΔCDE is shown below.

The triangle ΔC'D'E' after a rotation 270° counterclockwise about the origin.

The triangle ΔCDE and ΔC'D'E' are shown on the graph.

The coordinates of the triangle ΔC'D'E' will be (2, 1), (5, -3), and (2, -1). Then the correct option is C.

The transformation of the triangle is given below.

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The rule of arithmetic progression is -15, -9, - 3, 3, 9, 15.

So, to find the rule:

Therefore, the rule is -15, -9, - 3, 3, 9, 15.

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The parametric equation of a tangent line is x(t) = 1+t, y(t) = t, z(t) = 1.

What is the parametric equation?

A parametric equation is a sort of equation that uses an independent variable known as a parameter (commonly indicated by t) and in which dependent variables are expressed as continuous functions of the parameter and are not reliant on another variable.

Here, we have

Given: x = \(e^{t}\) ,y = t\(e^{t}\) ,z = t\(e^{t^2}\) ; (1,0,0)

We have to find the parametric equations for the tangent line to the curve.

r(t) = <  \(e^{t}\) , t\(e^{t}\) , t\(e^{t^2}\)>

For, t = 0

r(0) = <1, 0, 0>

Now, we differentiate r(t) with respect to t and we get

r'(t) = < \(e^{t}\), \(e^{t} +te^{t}\), \(e^{t^2}+2t^2 e^{t^2}\)>

At (1,0,0) , t = 0

r'(t) = < 1, 1, 1>

The equation of tangent line is given by:

<x(t),y(t),z(t)> =<1,0,0> + <1,1,1>t

= <1,0,0> + <t,t,t>

= <1+t,t,t>

Hence, the parametric equation of a tangent line is x(t) = 1+t, y(t) = t, z(t) = 1.

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If a differentiable function f: ℝ³ ⟶ ℝ has an absolute maximum value K ≠ 0 and an absolute minimum m, then the function f must have a critical point where the derivative of the function is zero (or undefined).

Given that, suppose f : ℝ³ ⟶ ℝ is a differentiable function which has an absolute maximum value K ≠ 0 and an absolute minimum m.

Since f is continuous on a compact set, it follows that f has a global maximum and a global minimum. We are given that f has an absolute maximum value K ≠ 0 and an absolute minimum m. Then there exists a point a ∈ ℝ³ such that f(a) = K and a point b ∈ ℝ³ such that f(b) = m.Then f(x) ≤ K and f(x) ≥ m for all x ∈ ℝ³.

Since f(x) ≤ K, it follows that there exists a sequence {x_n} ⊆ ℝ³ such that f(x_n) → K as n → ∞. Similarly, since f(x) ≥ m, it follows that there exists a sequence {y_n} ⊆ ℝ³ such that f(y_n) → m as n → ∞.Since ℝ³ is a compact set, there exists a subsequence {x_nk} and a subsequence {y_nk} that converge to points a' and b' respectively. Since f is continuous, it follows that f(a') = K and f(b') = m.

Since a' is a limit point of {x_nk}, it follows that a' is a critical point of f, i.e., ∇f(a') = 0 (or undefined). Similarly, b' is a critical point of f. Therefore, f has at least two critical points where the derivative of the function is zero (or undefined). Hence, the statement is true.

Therefore, the above explanation is verified that if a differentiable function f: ℝ³ ⟶ ℝ has an absolute maximum value K ≠ 0 and an absolute minimum m, then the function f must have a critical point where the derivative of the function is zero (or undefined).

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Answer:

 \(\frac{1}{x^2}\) + \(\frac{y^2}{x^4}\)

Step-by-step explanation:

\(\frac{x^2 + y^2}{x^4}\) = \(\frac{x^2}{x^4}\) + \(\frac{y^2}{x^4}\) = \(\frac{1}{x^2}\) + \(\frac{y^2}{x^4}\)

The solution of the expression (x²+y²)/x⁴ is [(1/x² + y²/x⁴)].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is  (x²+y²)/x⁴. The expression will be solved as,

E =  (x²+y²)/x⁴

Separate the terms into two fractions,

E =  (x²+y²)/x⁴

E = (x²/x⁴) + ( y² / x⁴)

Divide the divisible terms and solve,

E = (1/x² + y²/x⁴)

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Standard form: \(3t^8\)

Degree: 8

Leading coefficient: 3

Classification: This is a monomial, as it has only one term.

What is leading coefficient?

In a polynomial expression, the leading coefficient is the coefficient of the term with the highest degree, i.e., the term with the greatest exponent.

To write a polynomial in standard form means to arrange its terms in descending order of degree and write the coefficients in front of each term.

The given polynomial, \(3t^8\), is already in standard form since it has only one term, which is in descending order of degree.

The leading coefficient is the coefficient of the term with the highest degree, which is 3 in this case.

Since the polynomial has only one term, it is classified as a monomial.

Therefore, we can say that the polynomial is a monomial of degree 8 with a leading coefficient of 3.

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The probability of more than one tornado during a day is approximately 0.1219 or 12.19%.

To compute the probability of more than one tornado during a day, we need to use a Poisson distribution. The Poisson distribution is used to model the number of events that occur in a fixed interval of time, given the average rate of occurrence. In this case, the average rate of occurrence is 18 tornadoes per 30 days, or 0.6 tornadoes per day.

Let X be the random variable representing the number of tornadoes in a day. Then, X follows a Poisson distribution with parameter λ = 0.6. The probability of more than one tornado in a day can be computed as follows:

P(X > 1) = 1 - P(X ≤ 1)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [e^(-λ) * (λ^0 / 0!) + e^(-λ) * (λ^1 / 1!)]

= 1 - [e^(-0.6) * (0.6^0 / 0!) + e^(-0.6) * (0.6^1 / 1!)]

= 1 - [0.5488 + 0.3293]

= 0.1219

Therefore, the probability of more than one tornado during a day is approximately 0.1219 or 12.19%.

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Using sampling concepts, it is found that this is an example of independent samples.

In this problem, there are two sets of items, the data-set composed by the time taken by females, and the time taken by males.

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Answer:

35.3

explanation:

breakdown:

total:

\(\\ \rm{:}\dashrightarrow 7.06(5)\)

\(\\ \rm{:}\dashrightarrow (7+0.06)(5)\)

\(\\ \rm{:}\dashrightarrow 7(5)+0.06(5)\)

\(\\ \rm{:}\dashrightarrow 35+0.3\)

\(\\ \rm{:}\dashrightarrow 35.3\)