.Capital formation is the process of adding to a given stock of capital. Regarding this process as continuous over time, we may express capital formation as a function of time, C(t), and use the derivative dC/dt to denote the rate of capital formation.
The rate of capital formation at time t is identical with the rate of net investment flow at time t, denoted by I(t).
Thus, capital stock C and net investment I are related by:
(1)
dC
dt
= 1(t)
Identity (1) shows the synonymity between net investment and the increment of capital.
Suppose thatI(t) = 6 x √√6t + 0.06and that the initial stock of capital at time zero is C(0)=36. Use Identity (1) to set up and solve an indefinite integral in order to determine the capital formation function C(t) for the given I(t).

Answer:

2/3 and 8/12

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

a2+b2=c2

b2 = c2 - a2

b = ±√(c2 - a2)

Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

In hypothesis testing, if the null hypothesis is rejected, it means that there is sufficient evidence to support the alternative hypothesis. A null hypothesis is a statement that there is no significant difference or relationship between variables, while the alternative hypothesis states that there is a significant difference or relationship. To determine if the null hypothesis is true or not, we conduct a statistical test and calculate the p-value. If the p-value is less than the level of significance, usually set at 0.05, we reject the null hypothesis and accept the alternative hypothesis. Therefore, the correct answer is that the evidence supports the alternative hypothesis. This means that we have found significant results that support our research hypothesis.
Keep in mind that rejecting the null hypothesis does not prove the alternative hypothesis, but it does suggest that it's more plausible based on the data collected.

Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

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Answer:

GCF, Greatest Common Factor

Step-by-step explanation:

Hope this helped

When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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The answer is , (x - 2)² + (y - 3)² = 9 , this is the equation of the circle with center (2,3) and passes through the point (5,3).

To write the equation of a circle in standard form with its center at (h, k), and a radius of r, the  formula is :

(x-h)²+(y-k)²=r²

Where h and k are the x and y coordinates of the center of the circle, respectively, and r is the radius.

We can use this formula to solve the given problem since we know the center of the circle and a point that lies on it.

Let the center of the circle be (h,k) = (2,3) and the point on the circle be (x,y)=(5,3).

We also know that the radius is equal to the distance between the center of the circle and the point on the circle, using the distance formula:

radius = √[(x - h)² + (y - k)²]

radius = √[(5 - 2)² + (3 - 3)²]

radius = √[3² + 0²]

radius = √9

radius = 3

Now that we know the center and radius of the circle, we can use the formula for the equation of the circle in standard form.

(x - 2)² + (y - 3)² = 9 , this is the equation of the circle with center (2,3) and passes through the point (5,3).

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Answer:

22

Step-by-step explanation:

if mai scores 5 points and noah scores 3 times that then noah scored 15 points, and if tyler scores four less than noah than he scored 11 points, which you multiply by 2 to get elena's score which is 22

Parametrization of equations x=x(t), y=y(t) for f(x)=x^8−x^2−6 from (5,−4) to (9,−1) is that parametrization does indeed connect the points (5, -4) and (9, -1).

A parametrization for the curve that connects the points (5, -4) and (9, -1) given by the function f(x) = \(x^8 - x^2 - 6.\)

To do this, we can use the parameter t to represent points on the curve as follows:

x(t) = 5 + 4t, since we want x to start at 5 and end at 9, so we need to add 4 to x over the interval [0, 1].

Substituting this into our function f(x), we get:

y(t) = f(x(t)) = \((5 + 4t)^8 - (5 + 4t)^2 - 6\).

Therefore, our parametrization is:

x(t) = 5 + 4t

y(t) = (5 + 4t)^8 - (5 + 4t)^2 - 6

To verify that this parametrization does indeed connect the points (5, -4) and (9, -1), we can check that x(0) = 5, x(1) = 9, y(0) = f(5) = -4, and y(1) = f(9) = -1.

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Answer:

x=27°

Step-by-step explanation:

180°-54°=126°

180°-126°=54°

54°÷2=27°

Using polynomial expansion, the resulting expression contains exactly 1001 terms that include all four variables a, b, c, and d, each to some positive power is 14.

According to the question,

For some particular value of N, when (a + b + c+ d+ 1)²  is expanded and like terms are combined, the resulting expression contains exactly 1001 terms that include all four variables a, b, c, and d, each to some positive power.

Polynomial expansion :

(a + b)ⁿ = Cₙ⁰ aⁿ + Cₙⁿ⁻¹ aⁿ⁻¹ b + ....+ Cₙⁿbⁿ

\(x_{a} + x_{b} + x_{c} + x_{d} + x_{1}\) =N

\(x_{a} > 1 x_{b} > 1x_{c} > 1x_{d} > 1x_{1}\) >0

Positive integer solution:

\(x_{a} + x_{b} + x_{c} + x_{d} + x_{1}\) = N+1

Non - Negative integer solution:

\(x_{a} + x_{b} + x_{c} + x_{d} + x_{1}\) =N -4

C⁴ₙ = 1001

1001 = 7.11.13 after some trial and error we find  that is N is equal to 14.

Hence, using polynomial expansion, the resulting expression contains exactly 1001 terms that include all four variables a, b, c, and d, each to some positive power is 14.

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Answer:

Times it by 40. That is the pattern.

Answer:

Times it by 40

Step-by-step explanation:

Given function is f(x) = 4x3 − 33x2 − 36x + 3. Now we have to find the critical numbers of the function, the open intervals where the function is increasing, and the open intervals where it is decreasing.

a) Critical numbers of the function is/areAs we know that the critical numbers of the function are those values of the variable at which the derivative of the function becomes zero. The derivative of the given function with respect to x is f'(x) = 12x² - 66x - 36 We know that for the critical number(s), f'(x) = 0Hence, 12x² - 66x - 36 = 0Divide the equation by 6, we get 2x² - 11x - 6 = 0 Factorizing the above equation, we get (2x + 1)(x - 6) = 0By solving above equation, we get the critical numbers are -1/2 and 6.

Therefore, the correct option is (A) the critical number(s) is/are (-1/2,6) or (-1/2 and 6)

b) The open intervals where the function is increasing. To find the intervals of increase of the function f(x), we need to check the sign of the first derivative f'(x) in each interval. Whenever f'(x) > 0 in an interval, the function increases. Therefore, the function is increasing on the interval (-1/2, 6).

Hence, the correct option is (A) the function is increasing on the interval(s) (-1/2, 6).

c) The open intervals where the function is decreasing.To find the intervals of decrease of the function f(x), we need to check the sign of the first derivative f'(x) in each interval. Whenever f'(x) < 0 in an interval, the function decreases. Therefore, the function is decreasing on the intervals (-∞,-1/2) and (6, ∞).

Hence, the correct option is (A) the function is decreasing on the interval(s) (-∞,-1/2) and (6, ∞).

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Answer:

6/12

Step-by-step explanation:

all of the other 3 equal 8/12

Answer:

1/3

Step-by-step explanation:

Factors of 6 are 1, 2, 3, 6.

Even numbers are 2, 4, 6

3/6 * 4/6 = 12/36 or 1/3

Solutions (a,b) = (3,8) or (8,3), which are not in Z11. Therefore, the polynomial x^2 + x + 4 is irreducible over Z11.

To show that the polynomial x^2 + x + 4 is irreducible over Z11, we need to ensure that it cannot be factored into simpler polynomials with integer coefficients modulo 11. In Z11, we can test the possible roots of the polynomial using the integers {0, 1, 2, ..., 10} and see if any of them satisfy the equation x^2 + x + 4 ≡ 0 (mod 11). If none of them do, then the polynomial is irreducible.
Testing each integer, we find:
0: (0^2 + 0 + 4) ≡ 4 (mod 11)
1: (1^2 + 1 + 4) ≡ 6 (mod 11)
2: (2^2 + 2 + 4) ≡ 2 (mod 11)
3: (3^2 + 3 + 4) ≡ 5 (mod 11)
4: (4^2 + 4 + 4) ≡ 3 (mod 11)
5: (5^2 + 5 + 4) ≡ 10 (mod 11)
6: (6^2 + 6 + 4) ≡ 8 (mod 11)
7: (7^2 + 7 + 4) ≡ 7 (mod 11)
8: (8^2 + 8 + 4) ≡ 9 (mod 11)
9: (9^2 + 9 + 4) ≡ 4 (mod 11)
10: (10^2 + 10 + 4) ≡ 6 (mod 11)
Since none of these integers satisfy the equation, the polynomial x^2 + x + 4 is irreducible over Z11.

To show that x^2 + x + 4 is irreducible over Z11, we can use the following steps:
Step 1: Substitute all possible values of x in the polynomial and check if it has any linear factors.
x = 0: 0^2 + 0 + 4 = 4 (not zero)
x = 1: 1^2 + 1 + 4 = 6 (not zero)
x = 2: 2^2 + 2 + 4 = 10 (not zero)
x = 3: 3^2 + 3 + 4 = 1 (zero)
x = 4: 4^2 + 4 + 4 = 7 (not zero)
x = 5: 5^2 + 5 + 4 = 10 (not zero)
x = 6: 6^2 + 6 + 4 = 2 (not zero)
x = 7: 7^2 + 7 + 4 = 10 (not zero)
x = 8: 8^2 + 8 + 4 = 5 (not zero)
x = 9: 9^2 + 9 + 4 = 9 (not zero)
x = 10: 10^2 + 10 + 4 = 5 (not zero)
Since there are no linear factors (i.e. no values of x that make the polynomial equal to zero), the polynomial is not reducible over Z11.
Step 2: Check if the polynomial has any quadratic factors by assuming it does, and then solving for the coefficients of the quadratic factors using the division algorithm.
Let the polynomial be factored as (x+a)(x+b), where a and b are in Z11. Then, expanding this expression gives:
x^2 + (a+b)x + ab
Comparing the coefficients of this expression with the coefficients of the original polynomial x^2 + x + 4, we get the following system of equations:
a + b = 1
ab = 4
Solving this system of equations gives the solutions (a,b) = (3,8) or (8,3), which are not in Z11. Therefore, the polynomial x^2 + x + 4 is irreducible over Z11.

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The slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)

Given, the line passes through the points (-2, 2) and (-4, -1)
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (-1 - 2)/(-4 - (-2)) = -3/-2 = 3/2 = 1.5
Therefore, the slope of the line that passes through the points (-2, 2) and (-4, -1) is 3/2 i.e. 1.5 .

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Given data

*BE = 4x - 12

*DE = 2x + 8

At the point of intersection AC and BD, "x" is exactly split into halves.

Therefore

Substitute the values in the above expression as

Thus, the value of x equals to 10

Answer:

{5 x = f(x) + 6, x = g(x) + 4}

Step-by-step explanation:

Answer:

3 exponent 4

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\bullet\rm{\ Exponential\ form \ is \ basically \ a \ number \ that \ is \ expressed \ within \ the \ exponent.}\)

\(\star\rm{\ Example: a^b, whereas\ \underline{a} \ is \ the \ \bold{base} \ \& \ \underline{b} \ is \ the \ \bf exponent}\)

\(\huge\boxed{\square }\huge\textsf{ Answering your question }\huge\boxed{\square{}}\)

\(\large\boxed{= 81}\)

\(\large\boxed{= 3 \times3 \times 3 \times3}\)

\(\large\boxed{= 9\times9}\)

\(\large\boxed{= \bf 3^4}\)

\(\huge\boxed{\mathsf{\rm Answer: \mathsf{3^4}}}\huge\checkmark\)

\(\large\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be 585.43 + x - 302.05 ≥ 300.

From the information, it was stated that Keisha has $585.43 in her checking account and that she must maintain a balance of $300 to avoid a fee and then she wrote a check for $302.05 today.

The inequality that would be used for the least amount of money she needs to deposit to avoid a fee will be:

585.43 + x - 302.05 ≥ 300

Collect like terms

x ≥ 300 - 585.43 + 302.05

x ≥ $16.62

She's needs to deposit at least $16.62.

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Given:

Focus of a parabola = \(\left(1,\dfrac{1}{2}\right)\)

Directrix: \(y=3\)

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

\(y-k=\dfrac{1}{4a}(x-h)^2\)            ...(A)

Where, \((h,k)\) is center, \((h,k+a)\) is focus and \(y=k-a\) is the directrix.

On comparing the focus, we get

\((h,k+a)=\left(1,\dfrac{1}{2}\right)\)

\(h=1\)

\(k+a=\dfrac{1}{2}\)           ...(i)

On comparing the directrix, we get

\(k-a=3\)              ...(ii)

Adding (i) and (ii), we get

\(2k=\dfrac{7}{2}\)

\(k=\dfrac{7}{4}\)

Putting \(k=\dfrac{7}{4}\) is (i), we get

\(\dfrac{7}{4}+a=\dfrac{1}{2}\)

\(a=\dfrac{1}{2}-\dfrac{7}{4}\)

\(a=\dfrac{-5}{4}\)

Putting \(a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}\) in (A), we get

\(y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2\)

\(y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)\)

\(y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)\)

\(y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}\)

On further simplification, we get

\(y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}\)

\(y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}\)

Therefore, the equation of the parabola is \(y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}\).

Note: Option C is correct but the leading coefficient should be negative.

Answer:

my answer is A, C, and D...................

proved the identity:

\(1/tanh(x) - 1/cosh^2(x) = e^{2x}\)

We can start by manipulating the left-hand side of the equation:

\(1 - tanh(x) = sech^2(x)\) (using the identity\(tanh^2(x) + sech^2(x) = 1)\)

Therefore, we have:

\(1 - tanh(x) = 1/cosh^2(x)\)

Substituting this into the original equation, we get:

\(1/tanh(x) - 1/cosh^2(x) = e^(2x)\)

Multiplying both sides by sinh^2(x), we get:

\(sinh^2(x)/tanh(x) - sinh^2(x)/cosh^2(x) = e^{2x}*sinh^2(x)\)

Using the identity \(sinh^2(x) = (cosh(2x) - 1)/2 , cosh^2(x) = (cosh(2x) + 1)/2,\)we can simplify the left-hand side:

\((cosh(2x) - 1)/sinh(x) - (cosh(2x) - 1)/(cosh(2x) + 1) = e^{2x}*(cosh(2x) - 1)/2\)

Multiplying both sides by (cosh(2x) + 1), we get:

\((cosh(2x) - 1)(cosh(2x) + 1)/sinh(x) - (cosh(2x) - 1) = e^{2x}(cosh(2x) - 1)*(cosh(2x) + 1)/2\)

Simplifying the left-hand side further:

\((cosh^2(2x) - 1)/sinh(x) - (cosh(2x) - 1) = e^{2x}*sinh(2x)^2/2\)

Using the identity sinh(2x) = 2*sinh(x)*cosh(x), we can simplify further:

\((cosh^2(2x) - 1)/sinh(x) - (cosh(2x) - 1) = 2*e^{2x}sinh(x)^2cosh(x)^2\)

Using the identity\(cosh^2(x) - sinh^2(x) = 1\), we can simplify the left-hand side:

\(cosh(2x)/sinh(x) = 2*e^{2x}sinh(x)^2cosh(x)^2\)

Using the identity \(cosh(x)/sinh(x) = 1/tanh(x),\) we can simplify further:

\(2/tanh(2x) = 2*e^{2x}sinh(x)^2cosh(x)^2\)

Simplifying the right-hand side using the identity

\(sinh(2x) = 2*sinh(x)*cosh(x),\)we get:

\(2/tanh(2x) = e^{2x}*(sinh(2x)/2)^2\)

Using the identity\(sinh(2x) = 2*sinh(x)*cosh(x)\)again, we can further simplify:

\(2/tanh(2x) = e^{2x}*(sinh(x)*cosh(x))^2\)

Using the identity\(tanh(2x) = 2*tanh(x)/(1 + tanh^2(x))\), we can simplify the left-hand side:

\(1 + tanh^2(x) = 2/e^{2x}\)

Substituting this into the identity above, we get:

\(1/tanh(x) - 1/cosh^2(x) = e^{2x}\)

Therefore, the identity is true.

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Answer:sndkzkz

Step-by-step explanation:

Emma

Answer:

yes

they all equal one

Step-by-step explanation:

Answer:

15708 cubic inches

Step-by-step explanation:

The formula for a cylandir is V=πr^2h, substitute in your known factors and multiply by 20 for the 20 pails used and you get your answer.

Answer:

the length of the diagonal of the canvas is 24in

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

I got it write on my test .

-------------------------------------------------------------------------------------------------------------

Answer:  \(\textsf{(8, 0) and (-9, 0)}\)

-------------------------------------------------------------------------------------------------------------

Given:  \(\textsf{f(x) = (x - 8)(x + 9)}\)

Find:  \(\textsf{Determine the x-intecept}\)

Solution:  In order to find the x-intercept we need to set the y-value to 0 which means that we are looking for the points that cross the x-axis.  Then we just solve for x and we get the x-intercepts.

Set y to 0

Determine the first x-intercept

Determine the second x-intercept

There are two x-intercepts of the quadratic function that was provided which are (8, 0) and (-9, 0).

Answer:

a, d, e

Step-by-step explanation:

a. (2x + 3)(2x - 3)

d. (2x + 3)(x - 1)

e. x(2x + 3)(x - 1)

The number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. In scientific notation, a number is expressed as the product of a coefficient and a power of 10.

In this case, the coefficient is 3.23, and the power of 10 is 6. To convert this number into standard decimal notation, we need to multiply the coefficient by the corresponding power of 10. The power of 10, in this case, is 10^6, which means 10 raised to the power of 6. This is equivalent to 1 followed by six zeros: 1,000,000. To obtain the standard decimal notation, we multiply the coefficient, 3.23, by 1,000,000.

Calculating the multiplication, we have:

3.23 × 1,000,000 = 3,230,000.

Hence, the number 3.23×10^6, expressed in standard decimal notation, is 3,230,000. This means that the number is equal to 3.23 million.

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