g(x) = 1/3 * (2/9)^x. Does the function model growth or decay?

To find an expression for V(t), we can integrate V'(t) with respect to t. Doing so, we have:

V(t) = ∫V'(t) dt = ∫5700(t − 10) dt = 5700 ∫(t − 10) dt = 5700 [t^2/2 - 10t] + C

Since V(t) is the resale value of the computers, the constant of integration C should be the initial value of V(t), which is the cost of the computers. Therefore, we have:

V(t) = 5700 [t^2/2 - 10t] + 300000

Now, to find the value of the computers after 5 years, we can substitute t = 5 into the expression for V(t):

V(5) = 5700 [5^2/2 - 10*5] + 300000 = 5700 [25/2 - 50] + 300000 = 5700 [-12.5] + 300000 = -67500 + 300000 = 232500

Thus, the computers would sell for approximately $232,500 after 5 years.

Explanation: The function V'(t) gives the rate at which the resale value of the computers changes with time. In other words, it gives the slope of the function V(t) at any point in time. To find the function V(t) itself, we need to integrate V'(t) with respect to t. The constant of integration C is added to the result of the integration to ensure that the initial value of V(t) is equal to the cost of the computers. Once we have the expression for V(t), we can find the value of the computers at any point in time by substituting the appropriate value for t into the expression. In this case, we found that the value of the computers after 5 years is approximately $232,500.

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Let x= the co-efficient of x^2. So the co-efficient of given function is x=1.

Define co-efficient.

The term "coefficient" refers to a number or symbol that multiplies another number or symbol (used as a mathematical variable).

Write an example of co-efficient.

An amount multiplied by a variable is known as a coefficient. As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.

Let x= the co-efficient of x^2 So the co-efficient of given function is x=1.

The term multiplied with x^3 is the co-efficient of this expression. As there is not term with x^2 so it is 1.

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Answer:

x = 2 or x = -2

Step-by-step explanation:

5x² - 15 = 5​

⇌

5x² = 15 + 5

⇌

5x² = 20

⇌

x² = 20/5 = 4

⇌

x² = 2²

⇌

x² - 2² = 0

⇌

(x - 2)(x + 2) = 0

⇌   we use the zero product property

x - 2 = 0 or x + 2 = 0

⇌

x = 2 or x = -2

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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We are asked to show that the quotient ring U₂(ℝ)/I, where U₂(ℝ) is the ring of upper triangular 2 × 2 matrices and I is an appropriate ideal, is isomorphic to ℝ using the First Isomorphism Theorem.

To apply the First Isomorphism Theorem, we need to find a surjective ring homomorphism from U₂(ℝ) to ℝ and determine its kernel. The kernel will be the ideal I.

Consider the map φ: U₂(ℝ) → ℝ defined by φ([[a, b], [0, c]]) = a. This map takes an upper triangular 2 × 2 matrix to its upper left entry.

To show that φ is a surjective ring homomorphism, we need to demonstrate that it preserves addition, multiplication, and scalar multiplication, as well as cover the entire target space ℝ.

Next, we need to determine the kernel of φ, which consists of all matrices in U₂(ℝ) that map to 0 in ℝ. It can be shown that the kernel is the set of matrices of the form [[0, b], [0, 0]].

By the First Isomorphism Theorem, U₂(ℝ)/I is isomorphic to ℝ, where I is the ideal corresponding to the kernel of φ.

This demonstrates that the quotient ring U₂(ℝ)/I is isomorphic to ℝ, as desired.

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Answer:

= 7 + 2y.

Step-by-step explanation:

Collect like terms.

(9 − 2 ) + (7y − 5y )

Simplify.

= 7 + 2y.

Hope this helps.

Have a good night ma'am/sir.

Be safe!

Answer:

100.48 cm³

Step-by-step explanation:

Volume of a cone, V = 1/3 * pi * r² * h

Radius, r = 4 cm ; h = 6cm

V = 1/3 * 3.14 * 4² * 6

V = 1/3 * 3.14 * 16 * 6

V = 3.14 * 16 * 2

V = 3.14 * 32

V = 100.48 cm³

Hence, the volume of the cone is 100.48 cm³

The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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The correct step that involved in proving if x is a real number, then [x] [x] = 1 if x is not an Integer and [x] [x] = 0 if x is an Integer are:

a. If x is not an integer, then [x] is the integer just larger than x

b. If x is not an integer, then [x] is the integer just smaller than x

c. It is clear that if x is not an integer, then [x] and [] differ by 0.

d. It is clear that if x is not an integer, then [x] and [x] differ by 1.

e. If x is an integer, then [x] and [x] are equal, so [x-x=x-x=0. f. If x is an integer, then [x] and [x] are different, so [x] [x] = 0.

Since if x is not an integer, then [x] is the integer just smaller than x and [x] + 1 is the integer just larger than x.

Thus, we can write x as x = [x] + {x} where {x} is the fractional part of x.

[x] is an integer, {x} = x - [x].T

Now, we have [x] [x] = [x]([x]+{x}) = [x]^2 + [x]{x}.

Thus we can see that [x]^2 is an integer, and [x]{x} is a fraction, so it is between 0 and 1.

Hence, [x] [x] = 1 if x is not an Integer. If x is an Integer, then [x] and [x] are equal, so [x] [x] = 0.

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Answer:

55.9%

Step-by-step explanation:

To find the percentage of girls in the class, we can use the following formula:

Percentage = (Number of girls / Total number of students) * 100

Number of girls = 19

Total number of students = 34

Percentage = (19 / 34) * 100

                   = 55.88235 % ≈ 55.9 % ( rounded off to one decimal place)

Answer:

d.) x2+16x+64=36

Step-by-step explanation:

To find - Alicia is solving a quadratic equation. She wants to find the value of x by taking the square root of both sides of the equation. Which equation allows her to do this?

a.) x2+81x+18=54

b.) x2−8x+24=17

c.) x2+9x−24=25

d.) x2+16x+64=36

Proof -

The correct answer is - d.) x2+16x+64=36

x2+16x+64=36

⇒x² + 8x + 8x + 64 = 36

⇒x(x + 8) + 8(x + 8) = 36

⇒(x+8)(x+8) = 36

⇒(x+8)² = 36

Take square root both sides, we get

√(x+8)² = √36

⇒x + 8 = ± 6

⇒x + 8 = 6, x + 8 = -6

⇒x = 6 - 8 , x = -6 - 8

⇒x = -2, -14

So,

Equation (4) allows her to do the following thing she ants.

We have that the Density of metal X  is mathematically given as

∅ = 5048.33 Kg/\(m^{3}\)

Density is a word we use to describe how much space an object or substance takes up (its volume) in relation to the amount of matter in that object or substance (its mass). Another way to put it is that density is the amount of mass per unit of volume. If an object is heavy and compact, it has a high density.

Density of metal,

Generally the equation for the side of fcc  is mathematically given as

fcc = 2 × \(\sqrt{2}\) × radius of metal

fcc = 2 × 1.414 × 135

fcc = 381.78 ×  \(10^{-12}\) m.

where, volume of 1 unit cell of fcc

fccV = ( 381.78 ×  \(10^{-12}\) ) ^3

fccV = 55,646,713.615752 ×  \(10^{-36}\) \(m^{3}\)

And

weight of 1 atom

Wa = molecular weight / avagadro number

Wa = 42.3/(6.023 × \(10^{23}\))

Wa = 7.023 × \(10^{-23}\) gm/atom

Therefore, density is

∅ = (28.0923 ×  \(10^{-26}\)) / (55,646,713.615752 ×  \(10^{-36}\) )

∅ = 5048.33 Kg/\(m^{3}\)

Therefore, we have that the Density of metal X  is mathematically given as  ∅ = 5048.33 Kg/\(m^{3}\)

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Answer:

The laws of exponents are:

a)  (x^n)*(x^m) = x^(n + m)

b)  (x^n)/(x^m) = x^(n - m)

c)  (x^n)^m = x^(n*m)

Now, let's see the given equations:

1) (x-²)-³ = x⁶   (true)

Here we se the third law, the "c"

(x^(-2))^(-3) = x^(-2*-3) = x^6

Then this equation is correct.

2)  (a^m)^n = a^m^n   (false)

This law does not exist, this is false.

An example of why this is false is:

Let's use the values:

a = 2, m = 1, and n = 2

then, in the left side we have:

(2^1)^2 = (2)^2 = 4

And in the right side we have:

2^(1^2) = 2^(1) = 2

We can see that we have different things in the left side than in the right side, then that relation is false.

3)  a⁰ = 0  (false)

Let's rewrite this as:

a^0 = a^(n - n)

Now we can use the second law to rewrite this as:

a^(n - n)  = (a^n)/(a^n)

And we have a number divided by the exact same number, we know that this is equal to 1, then:

(a^n)/(a^n) = 1

this means that:

a^0 = 1.

Then this is also false.

The only correct option is the first one.

Here we want to answer some different things for the given equation, we will see that x is the independent variable, y is the dependent variable, and that the equation is a linear relationship.

A general linear relationship can be written as:

y = a*x + b

Where y is the dependent variable, x is the dependent variable, a is the slope and b is the y-intercept.

The given equation is of the form:

y = __*x + __

So this is a linear relationship where the slope and the y-intercept are missing.

Nos answering the questions:

What does x represent in your equation?

The independent variable.

What does y represent in your equation?

The dependent variable.

Is this a proportional relationship?

No, it is linear (it would be proportional only if b = 0, but we dont know that.),

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The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

We have,

To write the function represented by the graph in intercept form, we need to find the x and y intercepts and write the function as a product of linear factors.

From the graph and the given points, we can see that the function has

4 x-intercepts at -5, -2, 1, and 4.

We can also see that the function has 3 turning points at (-3.8, 95), (-1.4, 35), and (2.5, 40).

To find the y-intercept, we can use the point (-5.8, -160), which the curve emerges from.

This means that the function can be written in the form:

f(x) = a(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

where a is a constant to be determined.

To find the value of a, we can use any of the given points that lie on the curve. Let's use the point (-3.8, 95):

95 = a(-3.8 + 5.8)(-3.8 + 5)(-3.8 + 2)(-3.8 - 1)(-3.8 - 4)

Simplifying and solving for a, we get:

a = -95/((5.8)(3)(0.8)(4.8)(7.8)) ≈ -0.00038

Therefore,

The function represented by the graph in intercept form is:

f(x) = -0.00038(x + 5.8)(x + 5)(x + 2)(x - 1)(x - 4)

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The proof of the identity cos²x(1 + tan²x) = 1 is complete using the mentioned rules.

Hi! I'd be happy to help you complete the proof of the identity cos²x(1 + tan²x) = 1 using the given terms.

1. Statement: cos²x(1 + tan²x) = cosx (sec²x)
  Rule: Identity (using the identity tan²x = sec²x - 1)

2. Statement: cosx (sec²x) = cosx (1 + cos²x)
  Rule: Identity (using the identity sec²x = 1/cos²x)

3. Statement: cosx (1 + cos²x) = cos²x + cos⁴x
  Rule: Distributive Property (cosx * 1 + cosx * cos²x)

4. Statement: cos²x + cos⁴x = 1
  Rule: Pythagorean Identity (since cos²x + sin²x = 1, we substitute sin²x with 1 - cos²x and simplify)

So, the proof of the identity cos²x(1 + tan²x) = 1 is complete using the mentioned rules.

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Answer:

7 cannot be achieved

-1 + 6 = 5

-3 + 4 = 1

-5 + 2 = -3

as you can see, no combinations can form seven

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Answer:

695 km and hour

Step-by-step explanation:

Answer:

B. 4w + 10 = 46

Step-by-step explanation:

If we let l be the length of the rectangle and w its width

Fact 1: A rectangle's length is 5 centimeters greater than its width
This translates to l = w + 5 (1)

Fact 2: he perimeter of the rectangle is 46 centimeters
Perimeter is given by 2(l + w)
So fact 2 translates to:
2(l + w) = 45
2l + 2w = 46  (2)

Substitute l = w + 5 from (1) for l in (2):

2(w + 5) + 2w = 46
2w + 10 + 2w = 46

4w + 10 = 46

This is Option B

Answer:

C. 2w + 5 = 46

Reason why is because a rectangle has 4 sides, but you only want to multiply length times the width, to get the perimeter, which is why 2w in the equation is correct.

It also says 5 centimeters greater, the is why it would be + 5 instead of 10.

Step-by-step explanation:

Hope it helps! =D

Answer:

ST = 12 units

Step-by-step explanation:

Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is

\(\frac{ST}{SR}\) = \(\frac{TE}{RA}\) ( substitute values )

\(\frac{ST}{21-ST}\) = \(\frac{8}{6}\) ( cross- multiply )

6 ST = 8(21 - ST)

6 ST = 168 - 8 ST ( add 8 ST to both sides )

14 ST = 168 ( divide both sides by 14 )

ST = 12 units

-3.5, -3, -2 1/2, -2, 2.5

Answer:

-3.5, -3, -2½, -2, 2.5

Step-by-step explanation:

hope you have a great day!

Answer:

\(k=\frac{3}{10}\) or \(0.3\)

Step-by-step explanation:

\(\frac{3}{2k}=5\)

\(\frac{3}{2k}*2k=5*2k\) (Multiply both sides of the equation by \(2k\) to get rid of the denominator)

\(3=10k\) (Simplify)

\(10k=3\) (Symmetric Property of Equality)

\(\frac{10k}{10} =\frac{3}{10}\) (Divide both sides of the equation by \(10\) to get rid of \(k\)'s coefficient)

\(k=\frac{3}{10}\) or \(0.3\) (Simplify)

Hope this helps!

Answer:

50% If there's only black and white pieces. If there's more, please mention them.

Note: The must be \(0.04v^2\) instead of \(0.04v\).

Given:

The stopping distance, d ( in feet) for a van moving at a velocity (speed) v miles per hour is modeled by the equation:

\(d=0.04v^2+1.1v\)

To find:

The stopping distance for a velocity of 10 miles per hour.

Solution:

We have,

\(d=0.04v^2+1.1v\)

where, d is stopping distance and v is velocity.

Substitute v=10  in the given equation to find the stopping distance for a velocity of 10 miles per hour.

\(d=0.04(10)^2+1.1(10)\)

\(d=0.04(100)+11\)

\(d=4+11\)

\(d=15\)

So, the stopping distance for a velocity of 10 miles per hour is 15 ft.

Therefore, the correct option is c.

Step 1: redraw the figure given

Step 2: State the relationship between the lines

It can be observed that

(i) line XY is perpendicular to line PS

(ii) line XY is perpendicular to line QT

(iii) line PS is parallel to line QT

Hence, XY⊥PS, XY ⊥ QT, PS ║ QT, The Second option.

The given differential equation, y'' - 2y' + y = x^2e^(-x), is a second-order linear homogeneous differential equation with variable coefficients.

In the differential equation, the term y'' represents the second derivative of y with respect to x, y' represents the first derivative of y with respect to x, y represents the function y(x), and x^2e^(-x) is a non-homogeneous term on the right-hand side of the equation.

To classify the differential equation, we can examine the coefficients of the derivatives. Since the coefficient of y'' is 1 (non-zero), and the coefficients of y' and y are -2 and 1 (non-zero), respectively, the equation is a non-constant coefficient homogeneous differential equation.

In summary, the given differential equation, y'' - 2y' + y = x^2e^(-x), is a second-order linear non-constant coefficient homogeneous differential equation with a non-homogeneous term on the right-hand side.


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Answer:

The y-intercept answer will be 2/9

Answer:

b

Step-by-step explanation:

Answer:

Your answer is correct.

Step-by-step explanation:

82.3 - 46.5 = 35.8