Thi month, Kami old 70 figurine in 2 ize. The large figurine old for $12 each, and the mall figurine old for $8 each. The amount of money he received from the ale of the large figurine wa equal to the amount of money he received from the ale of the mall figurine. How many large figurine did Kami ell thi month?

To solve the given first-order linear differential equation du/dt = Pu with initial condition u(0)=[53​], we can apply the matrix exponential method. The solution to this equation is given by u(t) = e^(Pt)u(0), where e^(Pt) is the matrix exponential.

Given the projection matrix P = [21​21​​21​21​​], we can compute e^(Pt) and then multiply it by the initial condition u(0) = [53​].

Since part of u(0) increases exponentially while the nullspace part stays fixed, this indicates that one eigenvalue of P is positive, causing exponential growth, while the other eigenvalue is zero, keeping the nullspace part constant.

To solve the equation du/dt=Pu, where P is a projection, we can use the fact that P is idempotent (P^2=P) and hence diagonalizable. Let's denote the eigenvalues of P by λ_1 and λ_2, and the corresponding eigenvectors by v_1 and v_2, respectively. Since P is a projection, we have λ_1=1 and λ_2=0, and v_1 is the direction of the part of u that increases exponentially, while v_2 is the direction of the nullspace part of u that stays fixed.

Using the eigendecomposition of P, we can write u(t)=c_1e^λ_1tv_1+c_2e^λ_2tv_2=c_1e^t v_1+c_2v_2, where c_1 and c_2 are constants determined by the initial conditions. Specifically, we have u(0)=c_1v_1+c_2v_2=[5/3 1/3]^T, which implies c_1=(5/3)v_1^T[5/3 1/3]=(5/3), and c_2=[5/3 1/3]^Tv_2=(1/3).

Therefore, the solution of the differential equation is u(t)=(5/3)e^t v_1+(1/3)v_2, which means that the part of u in the direction of v_1 increases exponentially with a rate of e^t, while the part of u in the direction of v_2 stays fixed. This is consistent with the given initial condition that part of u increases exponentially while the nullspace part stays fixed.

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Answer:

-1/3

Step-by-step explanation:

Multiply by root 3 on the top and bottom. Root 3 times root 3 is 3. 2-3 is -1.

If the series ∑an and ∑bn are both convergent series with positive terms, then the series ∑anbn is also convergent.

This can be proven using the Comparison Test for series convergence. Since an and bn are both positive terms, we can compare the series ∑anbn with the series ∑an∑bn.

If ∑an and ∑bn are both convergent, then their respective partial sums are bounded. Let's denote the partial sums of ∑an as Sn and the partial sums of ∑bn as Tn.

Then, we have:

0 ≤ Sn ≤ M1 for all n (Sn is bounded)

0 ≤ Tn ≤ M2 for all n (Tn is bounded)

Now, let's consider the partial sums of the series ∑an∑bn:

Pn = a1(T1) + a2(T2) + ... + an(Tn)

Since each term of the series ∑anbn is positive, we can see that each term of Pn is the product of a positive term from ∑an and a positive term from ∑bn.

Using the properties of the partial sums, we have:

0 ≤ Pn ≤ (M1)(Tn) ≤ (M1)(M2)

Hence, if ∑an and ∑bn are both convergent series with positive terms, then ∑anbn is also convergent.

Therefore, the given statement is True.

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Therefore, the parametric equations for the tangent line at (0, 1, 0) are: x = t, y = 1 - 3t, z = 4t

To find the parametric equations for the tangent line to the curve, we need to first find the derivative of the given parametric equations. Taking the derivative of x, y, and z with respect to t, we get: dx/dt = 1, dy/dt = -3e^(-3t), and dz/dt = 4 - 4t^3.
Now, plugging in the specified point (0, 1, 0), we get dx/dt = 1, dy/dt = -3, and dz/dt = 4.
To find the parametric equations for the tangent line to a curve with given parametric equations at a specified point, we first find the derivatives of x, y, and z with respect to t. Then, we plug in the specified point and use the derivatives to write the parametric equations for the tangent line.

Therefore, the parametric equations for the tangent line at (0, 1, 0) are: x = t, y = 1 - 3t, z = 4t

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Answer:

Here is your answer my dear Mr.Watson.

Step-by-step explanation:

3) Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

x

=

1

,

−

5

4)x

=

i

√

10

4

,

−

i

√

10

4

9514 1404 393

Answer:

  g^-1(x) = 1/(x+2)

Step-by-step explanation:

To find the inverse of the function ...

  y = g(x)

swap the variables and solve for y.

  x = g(y)

  x = 1/y -2 . . . . . . . use the given g(x)

  x +2 = 1/y . . . . . . . add 2

  y(x +2) = 1 . . . . . . multiply by y

  y = 1/(x +2) . . . . . divide by the coefficient of x

The inverse function is ...

  \(\boxed{g^{-1}(x)=\dfrac{1}{x+2}}\)

_____

Additional comment

Please observe that when the fraction is typeset, as in the boxed answer, the fraction bar serves as a grouping symbol. It shows you that the denominator is the sum x+2.

When the same expression is written in plain text, only the first item after the division symbol (/ or ÷) is considered to be in the denominator. That is, 1/x+2 = (1/x)+2. The presence or absence of a (space) has no bearing on the correct interpretation of the expression. Only parentheses will serve as a grouping symbol in plain text expressions.

  g^-1(x) = 1/(x+2)

Answer:

The answer is "A" $256.63

Step-by-step explanation:

336 = (.045/12)(pv)/(1-(1+.045/12)^-72)

PV =  $21,166.65  

(.045*$21,166.65)/12 = $79.37

$336 - $79.37 = $256.63

Answer:

Step-by-step explanation:

Asymptote is the x axis for both functions. the y intercept is translated up to 125

A relation is a function if it has only One y-value for each x-value.

The asymptote and intercept of the given function compare to the asymptote and intercept of the function f(x) = 5ˣ

To find x- or y-intercepts, set the other variable equal to zero and solve in turn.

To find y-intercept: set x = 0 and solve for y. The point will be (0, y). To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

The asymptote is the x axis for both functions. the y intercept is translated up to 125.

Hence, asymptote is the x axis for both functions. the y intercept is translated up to 125.

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Answer: 0.67 Just subtract

Step-by-step explanation:

I'm confused about what you are asking But ill assume you want to subtract?

1.13 minus 0.46 is 0.67

Answer:

0.67

Step-by-step explanation:

just get the answer taking out

Answer:

dsf

Step-by-step explanation:

fewfgwe4g h5trh 5

Answer:

7x-26

Step-by-step explanation:

Answer:

f(x - 4) = 7x - 26

Step-by-step explanation:

Since the original equation was f(x) = 7x + 2, then to solve the following equation, you need to use the substitution method in relation to the added number (-4). So, if f(x - 4), you would now substitute the (x - 4), in place of the previous (x). Therefore the new problem would be f(x - 4) = 7(x - 4) + 2; after distributing, you would get 7x - 28 + 2. Then further simplifying, this would be 7x - 26, after doing -28 + 2. Finally, the answer would be f(x - 4) = 7x -26.

Step 1

Given;

Required; Find the equation of a line that goes through the point ( 1,- 6 ) and is perpendicular to the line: y = (1 / 8)x - 9

Step 2

For perpendicular lines, the relationship between the slopes is;

The y-intercept is found thus;

Answer; The required equation will be;

Answer:

Angle L= 53 degrees. Side ML = 4.521 and Side NL= 7.513

Step-by-step explanation:

Answer

The inverse of this function is given as

f⁻¹(x) = √(x - 10)

Domain in interval form = [10, ∞)

OR

Domain in inequality form = 10 ≤ x < ∞

Explanation

First of, the inverse of a function is a function that reverses the actions of the function. That is, for the inverse function, if we are given f(x), we would be able to obtain x.

The step to finding a function's inverse is to write y instead of f(x). We then rewrite by replacing the y by x and then make y the subject of formula, the y which is a subject of formula now, represents the inverse function, f⁻¹(x).

f(x) = x² + 10

We will write y instead of f(x)

y = x² + 10

We then replace y by x

x = y² + 10

We will then make y the subject of formula

x = y² + 10

y² + 10 = x

y² = x - 10

Take the square root of both sides

√(y²) = √(x - 10)

y = √(x - 10)

f⁻¹(x) = √(x - 10)

For the domain of this inverse of this function, we know that there is no real solution for the square root of a negative number, we know that the domain of this function has to be values of x that make the expression under the square root equal to or greater than 0.

x - 10 ≥ 0

Add 10 to both sides

x - 10 + 10 ≥ 0 + 10

x ≥ 10

Domain = [10, ∞) OR 10 ≤ x < ∞

Hope this Helps!!!

Answer:

Y = 3

Hope This Helps!

The IQ score that is higher than 90% of the population is 112.8.

We know that the IQ scores follow a normal distribution with a mean of 100 and a standard deviation of 10.

Let X be the random variable representing the IQ scores. We want to find the value x such that 90% of the observations lie above x.

Using the standard normal distribution table or calculator, we can find the z-score corresponding to the 90th percentile as 1.28.

The z-score formula is z = (x - μ) / σ, where μ is the mean, σ is the standard deviation and x is the value we want to find.

Plugging in the values, we get 1.28 = (x - 100) / 10. Solving for x, we get x = 100 + 12.8 = 112.8.

Therefore, the IQ score that is higher than 90% of the population is 112.8.

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Inference is referred to as all the data collected in a particular study.

Etymologically, the word "infer" means to "carry ahead." Inferences are stages in reasoning that connect premises to logical conclusions. The dichotomy between deduction and induction in inference theory, which dates at least to Aristotle in Europe, is a classic one (300s BCE). Deduction is inference that results in logical conclusions from premises that are known to be true or that are presumed to be true, while the logic of correct inference is investigated. A universal conclusion is inferred by induction from specific evidence. Contradistinguishing abduction from induction, Charles Sanders Peirce is credited with identifying a third sort of inference. Researchers in the domains of logic, argumentation studies, and cognitive psychology traditionally study human inference (i.e., how people draw conclusions); artificial intelligence researchers create automated inference systems to mimic human inference.

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Answer:

/5.2 + 81.9 = 47.2

Step-by-step explanation:

Subtract 81.9  from both sides of the equation

Simplify

Subtract the numbers

Multiply all terms by the same value to eliminate denominators

Cancel multiplied terms that are in the denominator

Multiply the numbers

Solution: k = -180.44

Responda:

R $ 15.600

Explicação passo a passo:

Deixe a dívida inicial = x = 100%

% pago = 20% = 0,2x

% esquerda =. 100% - 20% =. 80% = 0,8x

35% da dívida restante = 0,35 * 0,8x = 0,28x

Conseqüentemente,

0,28x = 4368

x = 4368 / 0,28

x = R $ 15.600

Logo, o valor inicial da dívida = R $ 15.600

Answer:

With a 20% discount, you will pay 80% of the original price. We can find the discounted price of the album as follows:

Step-by-step explanation:

Discounted price = 80% of $9.00 = 0.80 x $9.00 = $7.20

Therefore, you will pay $7.20 for the album during the sale at iTunes.

Answer:

So im pretty sure it would cost $7.20 don tget mad at me if i a wrong im just trying it to the best of my ability.

Step-by-step explanation:

Answer:

9a + 4b

Step-by-step explanation:

Start by multiplying the two values inside the parentheses (5a + 2b) by 2 to get 10a + 4b - a. Then, subtract the single a from the end to get 9a + 4b.

The variables a and b cannot be combined, so both variables must still be present in the final answer. Order of operations is also very important, because if you subtracted the a before multiplying, then you would get 8a, which isn't correct.

Answer:

The correct option is;

69 cm

Step-by-step explanation:

The z-score, or standard score is a measure of how far a data is from the mean

The z-score, is given by the relation;

\(z = \dfrac{x- \mu}{\sigma}\)

Z = Standard score

x = Value observed

μ = The mean height of the plants = 52.5 cm

σ = Standard deviation = 7.2 cm

Given that the z-score = 2.25, we have;

\(2.25 = \dfrac{x- 52.5}{7.2}\)

Therefore, x = 7.2 × 2.25 + 52.5 = 68.7 cm ≈ 69 cm

Therefore, the minimum required height for this type of plant to be displayed in the main lobby is 69 cm.

The equation that represents this situation is p = 4 + 5d

Algebraic expressions are known as mathematical expressions made up of:

From the information given, we have that:

The equation this represents is:

p = 4 + 5d

Thus, the equation that represents this situation is p = 4 + 5d

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Answer:

2

Step-by-step explanation:

It is the smallest among the given numbers.

Answer:

2 is the smallest number.

Step-by-step explanation:

2 is the smallest number because, if you will see all these numbers, they are in decimal and after decimal more values are given which is not equal to zero it is greater than zero. If you will convert the number 2 into decimal it will become 2.0, now here also after decimal more value is given but, it is equal to zero not greater than zero, if there were more zero then also its value will 2 only, but if we will put a number greater than zero then it can be greater than 2 but here it is not. So 2 is the smallest number.

Point M has the same distance from point A and point B (option d).

Given,

Line segment CD is the  perpendicular bisector of line segment  AB

AB ⊥ CD

Assume the conjecture that the set of  points equidistant from A

and B is the  perpendicular bisector of AB is true

Here,  line segment CD intersect line segment AB at M

Then, M is the mid-point of line segment AB

So, the length of  line AM = the length of line MB

That is, Point M has the same distance from both point A and point B.

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