Eric is working on the problem:
Hank's Auto Wash recently acquired an automatic car-washing machine that is
expected to generate $45,000 in revenue per year, t years from now, for the next 6
years. If the income is reinvested in a business earning interest at the rate of 8% per
year, compounded continuously, find the Accumulated Total Value of this income
stream at the end of 6 years.
Which of the following is NOT a good method for solving the problem?

The equation that represents the situation is a = b- 4.

Since the plant grows at a constant rate, we can assume that the height of the plant is increasing linearly with time.

Let's use the data from Week 1 and Week 2 to find the rate of growth for each plant:

For Plant A: Growth rate = (24 cm - 22 cm) / (2 weeks - 1 week) = 2 cm/week

For Plant B: Growth rate = (28 cm - 26 cm) / (2 weeks - 1 week) = 2 cm/week

Since the growth rate is constant, we can use the equation of a line to model the height of each plant over time:

For Plant A: a = 2t + b, where t is the time in weeks and b is the initial height of the plant.

For Plant B: b = 2t + c, where c is the initial height of Plant B.

We can find the values of b and c by substituting the data from Week 1 into these equations:

For Plant A: 22 = 2(1) + b, so b = 20.

For Plant B: 26 = 2(1) + c, so c = 24.

Now we can substitute these values into the equations for Plant A and Plant B:

Plant A: a = 2t + 20

Plant B: b = 2t + 24

To find an equation that gives Plant A's height in terms of Plant B's height, we can solve the equation for t in terms of b:

b = 2t + 24

2t = b - 24

t = (b - 24) / 2

Then we can substitute this expression for t into the equation for Plant A:

a = 2t + 20

a = 2[(b - 24) / 2] + 20

a = b - 24 + 20

a = b - 4

So the equation we were looking for is:

a = b - 4

Therefore, to find Plant A's height in centimeters given Plant B's height in centimeters, we simply subtract 4 from Plant B's height.

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The solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.

Exponential functions are always increasing or decreasing, depending on the sign of the base "a".

The graph of an exponential function has a characteristic shape that depends on the base "a". When "a" is greater than 1, the graph is an increasing curve that becomes steeper as x increases; when "a" is between 0 and 1, the graph is a decreasing curve that approaches the x-axis as x increases.

Starting with the equation:

[tex]-3xe^{(5w)} = -88[/tex]

We can first isolate the exponential term by dividing both sides by -3x:

[tex]e^{(5w)} = \dfrac{88 }{ (3x)}[/tex]

Then, taking the natural logarithm of both sides, we get:

[tex]5w = ln(\dfrac{88} { 3x})[/tex]

Finally, dividing both sides by 5, we obtain the solution for w:

[tex]w = (\dfrac{1}{5}) ln(\dfrac{88} { 3x})[/tex]

Therefore, the solution for w is given by the natural logarithm of 88 divided by 3x, all raised to the power of 1/5.

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After considering the given data we conclude that angle t as a function of the height x is θ = tan⁻¹ (x/300), and angle t in degrees when x is equal to 150, 300, and 600 meters is 63.4°, the graph represent a curve when drawn.

The angle of elevation of the camera can be evaluated by

θ=tan⁻¹(x/2000)

Here, x = height of the rocket.

Hence, the angle t as a function of the height x is given by:

θ = tan⁻¹ (x/300)

To evaluate the angle t in degrees when x is equal to 150, 300, and 600 meters, we stage these values into the equation above:

θ = tan⁻¹ (150/300) = 26.6° (approximate to 1 decimal place)

θ = tan⁻¹ (300/300) = 45° (approximate to 1 decimal place)

θ = tan⁻¹ (600/300) = 63.4° (approximate to 1 decimal place)

To graph t as a function of x, we can plot the values of θ for different values of x. The graph will be a curve that starts at 0° when x=0 and increases as x increases.

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The Binomial coefficients, we get:

(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3

Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.

To expand (2x+5y)^3, we can use the Binomial Theorem, which states that:

(a + b)^n = nC0a^n + nC1a^(n-1)b + nC2a^(n-2)b^2 + ... + nCn-1ab^(n-1) + nCn b^n

where nCk represents the binomial coefficient, which is the number of ways to choose k items from a set of n items.

In this case, we have:

a = 2x

b = 5y

n = 3

So, we can apply the Binomial Theorem as follows:

(2x+5y)^3 = 3C0 (2x)^3 + 3C1 (2x)^2(5y) + 3C2 (2x)(5y)^2 + 3C3 (5y)^3

Simplifying each term using the binomial coefficients, we get:

(2x+5y)^3 = 8x^3 + 60x^2y + 150xy^2 + 125y^3

Therefore, (2x+5y)^3 expands to 8x^3 + 60x^2y + 150xy^2 + 125y^3.

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Answer:

Step-by-step explanation:

so how to help you but you do a good job

The L.C.M of c, 3c , 3 is 3c.

The L.C.M of c, 3c, and 3, we first need to factor each term:
c cannot be factored any further.
3c can be factored as 3 x c.
3 cannot be factored any further.
Next, we look for the highest common factors among the factors of these terms.

The only common factor is 3, which is included in both 3c and 3.
Therefore, the L.C.M of c, 3c, and 3 is 3c.
The L.C.M (Least Common Multiple) of c, 3c, and 3 can be found by analyzing the factors of each term.
For c, the only factor is c itself.
For 3c, the factors are 3 and c.
For 3, the only factor is 3.
Now, find the LCM by taking the highest power of each unique factor:
LCM(c, 3c, 3) = 3 * c = 3c

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Answer:

A food manufacturer may use zero-rated goods in the manufacturing of a food product, but when the consumer buys the final product, it includes a VAT.

Step-by-step explanation:

When C = 20, F is equal to 68, and when F = 100, C is approximately 37.78.

Given the equations:

C = (5/nine) * (F - 32)

F = (9/5) * C + 32

If we replace specific values for F or C, we will locate the corresponding price for the opposite variable. Here are some examples:

Let's expect C = 20. Substituting this fee into the second equation:

F = (9/five) * 20 + 32

F = 36 + 32

F = 68

Therefore, when C = 20, F is equal to sixty-eight.

Let's expect F = a hundred. Substituting this cost into the primary equation:

C = (five/9) * (100 - 32)

C = (5/9) * 68

C = 340/9

C ≈ 37.78

So, whilst F = one hundred, C is approximately 37.78.

These examples exhibit how you may locate the values of F and C by using substituting one variable into the equations and fixing for the alternative variable. Remember, you could choose any unique values for F or C and perform the calculations consequently.

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The correct question is:

"C=5/9 (f -32)

F= 9/5C + 32

Solve for F and C"

The equation of the polynomial is f ( x ) = -13.5 ( x + 2 )²( x - 3 )

Given data ,

The equation of degree 3 polynomial function with real coefficients

And ,  zeros x = - 2 with multiplicity 2 and x = 3 with multiplicity 1

where function passes through the point (1, 54)

If a polynomial function has a zero x = a with multiplicity k, then the factor (x - a)^k appears in its factored form.

Therefore, a degree 3 polynomial function with zeros x = -2 with multiplicity 2 and x = 3 with multiplicity 1 can be written in factored form as:

f(x) = a(x + 2)²(x - 3)

where a is a constant factor. To find the value of a, we use the fact that the function passes through the point (1, 54):

f(1) = a(1 + 2)²(1 - 3) = 54

a(-1)²(-2) = 54

-4a = 54

Divide by -4 on both sides , we get

a = -13.5

Hence , the equation of the degree 3 polynomial function with the given zeros and passing through the point (1, 54) is f ( x ) = -13.5 ( x + 2 )²( x - 3 )

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Hello!

area

= (b x h)/2

= (18in x 7in)/2

= 126in²/2

= 63in²

Answer:

63 in²

Step-by-step explanation:

1/2 bh=area of the triangle

Answer:

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

We know the tangent is perpendicular to radius.

Find the slope of the radius using its endpoints:

Perpendicular lines have negative reciprocal slopes, therefore the slope of the tangent is:

The matching choice is 2.

This given function does not have an end behavior since it is not a polynomial.

The end behavior of a function describes the behavior or trend of the function as the input values (x) approach positive or negative infinity. It helps us understand what happens to the function's values as x becomes very large or very small.

We have three possible cases of end behavior of a function which are;

The end behavior of a function is often determined by using the leading term of the function, which is the term with the highest power of x.

In the given problem;

[tex]f(x) = \frac{8x^6 - 16x^3 + 8}{4x^2 - 4x - 24}[/tex]

The end behavior of this function does not exist because this function is not a polynomial

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1. The product of MG is as follows;

[tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36 \\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]

2. The values are k₁ = -9, k₂ = -9, t₁ = 0 and t₂ = -1 given that G = M⁻¹

Matrix M and matrix G are given as

M = [1, 4, 5; t₁, 3, -1; 1, t₂, 1] and

G = [2, k₁, -19; 1, -4, k₂; -1, 5, 11]

MG becomes

1×2 + 4×1 + 5×-1         1k₁+4×-4+ 5×5       1×-19+4k₂+5×11

t₁×2+3×1+-1×-1             t₁k₁+3×-4+-1×5       t₁×-19+3k₂+-1×11

1×2+t₂×1+1×-1               1k₁+t₂×-4+-1×5        1×-19+t₂k₂+1×11

=

1             k₁+9         4k₂+36

2t₁          k₁t₁-17        3k₂-19t₁-11

t₂+1        k₁-4t₂+5      k₂t₂-8

To solve G = M⁻¹ we know it is an identity matrix

I = | 1 0 0 |

    | 0 1 0 |

    | 0 0 1 |

We can equate the elements of MG and I to find the values of t₁, t₂, k₁, and k₂:

1 = 1,         k₁+9 = 0,       4k₂+36 = 0

2t₁ = 0     k₁t₁-17 = 1        3k₂-19t₁-11 = 0

t₂+1 = 0     k₁-4t₂+5 = 0   k₂t₂-8 = 1

k₁+9 = 0           4k₂+36 = 0            2t₁ = 0          t₂+1 = 0

k₁ = -9                 k₂ = -9                   t₁ = 0           t₂ = -1

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The amount of money that you would have by day 30 would be $ 2, 147 ,483 ,646.

To find the total amount of money you would have by day 30, we can use the formula for the sum of a geometric progression:

Sum = a x ( 1 - r ⁿ ) / ( 1 - r )

The sum would be the amount after 30 days which is:

Sum = 2 x  (1 - 2 ³⁰ ) / ( 1 - 2 )

Sum = 2 x ( 1 - 1, 073, 741,824 ) / ( - 1 )

Sum = 2 x (- 1 ,073 ,741,823) / ( -1 )

Sum = $ 2, 147 ,483 ,646

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Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\textsf{Prove that}\;\;\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A) = \sin^3A}[/tex]

Rewrite 240° as (180° + 60°):

[tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(180^{\circ}+60^{\circ}+ A)[/tex]

As sin(180° + x) = -sin(x), we can rewrite sin³(180° + 60° + A) as:

[tex]\sin^3(180^{\circ}+60^{\circ}+ A)=-\sin^3(60^{\circ}+ A)[/tex]

Substitute this into the expression:

[tex]\sin^3A + \sin^3(60^{\circ} + A) -\sin^3(60^{\circ}+ A)[/tex]

As the last two terms cancel each other, we have:

[tex]\sin^3A[/tex]

Hence proving that:

[tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A) = \sin^3A[/tex]

As one calculation:

    [tex]\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(240^{\circ}+ A)[/tex]

[tex]=\sin^3A + \sin^3(60^{\circ} + A) + \sin^3(180^{\circ}+60^{\circ}+ A)[/tex]

[tex]=\sin^3A + \sin^3(60^{\circ} + A) -\sin^3(60^{\circ}+ A)[/tex]

[tex]=\sin^3A[/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\textsf{Prove that}\;\;\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A) = -\dfrac{3}{4}\sin 3A}[/tex]

Use the sine and cos double angle identities to rewrite sin(3x) in terms of sin(x):

[tex]\begin{aligned}\sin(3x)&=\sin(2x+x)\\&=\sin2 (x)\cos (x)+\sin (x)\cos2 (x)\\&=(2\sin (x)\cos (x))\cos (x)+\sin (x)(1-2\sin^2 (x))\\&=2\sin (x)\cos^2 (x)+\sin (x)-2\sin^3 (x)\\&=2\sin (x)(1-\sin^2 (x))+\sin (x)-2\sin^3 (x)\\&=2\sin (x)-2\sin^3 (x)+\sin (x)-2\sin^3 (x)\\&=3\sin (x)-4\sin^3 (x)\end{aligned}[/tex]

Rearrange to isolate sin³x:

[tex]\begin{aligned}\sin(3x)&=3\sin (x)-4\sin^3 (x)\\\\4\sin^3 (x)&=3\sin (x)-\sin (3x)\\\\\sin^3 (x)&=\dfrac{3\sin (x)-\sin (3x)}{4}\end{aligned}[/tex]

Use this expression to rewrite the terms in sin³A on the left side of the equation:

   [tex]\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A)[/tex]

[tex]=\dfrac{3\sin A-\sin3A}{4}+ \dfrac{3\sin (120^{\circ} + A)-\sin (3(120^{\circ} + A))}{4}+\dfrac{3\sin (240^{\circ}+ A)-\sin (3(240^{\circ}+ A))}{4}[/tex]

[tex]=\dfrac{3\sin A-\sin3A+3\sin (120^{\circ} + A)-\sin (360^{\circ} + 3A)+3\sin (240^{\circ}+ A)-\sin (720^{\circ}+ 3A)}{4}[/tex]

As sin(x ± 360°n) = sin(x), we can simplify:

[tex]\sin(360^{\circ}+3A) = \sin (3A)[/tex]

[tex]\sin(720^{\circ}+3A) = \sin (3A)[/tex]

Therefore:

[tex]=\dfrac{3\sin A-\sin3A+3\sin (120^{\circ} + A)-\sin (3A)+3\sin (240^{\circ}+ A)-\sin (3A)}{4}[/tex]

[tex]=\dfrac{3\sin A-3\sin3A+3\sin (120^{\circ} + A)+3\sin (240^{\circ}+ A)}{4}[/tex]

Factor out the 3 in the numerator:

[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (120^{\circ} + A)+\sin (240^{\circ}+ A)\right)}{4}[/tex]

Rewrite 240° = 180° + 60°:

[tex]\sin(240^{\circ} + A) = \sin(180^{\circ} + 60^{\circ} + A)[/tex]

As sin(180° + x) = -sin(x), we can rewrite sin(180° + 60° + A) as:

[tex]- \sin(60^{\circ} + A)[/tex]

Therefore:

[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (120^{\circ} + A)-\sin (60^{\circ}+ A)\right)}{4}[/tex]

As sin(120° + x) = sin(60° - x) then:

[tex]=\dfrac{3\left(\sin A-\sin3A+\sin (60^{\circ} -A)-\sin (60^{\circ}+ A)\right)}{4}[/tex]

As sin(60° - x) - sin(60° + x) = -sin(x), then:

[tex]=\dfrac{3\left(\sin A-\sin3A-\sin A\right)}{4}[/tex]

Simplify:

[tex]=\dfrac{-3\sin3A}{4}[/tex]

[tex]=-\dfrac{3}{4}\sin3A[/tex]

Hence proving that:

[tex]\sin^3A + \sin^3(120^{\circ} + A) + \sin^3(240^{\circ}+ A) = -\dfrac{3}{4}\sin 3A[/tex]

a. The rate of change of the relation is 2.

b. The value of n is 14.5.

In Mathematics and Geometry, the rate of change (slope) of any straight line can be determined by using this mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the rate of change (slope) of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (10 + 1)/(3.5 + 2)

Rate of change (slope) = 11/5.5

Rate of change (slope) = 2

Part b.

Next, we would determine the value of n as follows;

2 = (43 - 32)/(20 - n)

2(20 - n) = 11

40 - 2n = 11

2n = 29

n = 14.5

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+* Answer *+

$5,590

*+Step-by-step explanation:*+

$5,000 x 5.9% = $295
$95 x 2 (months), = 590

5,000 + 590 = 5,590

So therefore you have $5,590 dollars.

hope this helps! : )

Factor of x ^2+7x−18 is (x−2)(x+9).

We have,

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

We are given a polynomial expression in terms of variable x as:

x² - 7x + 18

so, we have,

x ^2+7x−18

=x ^2−2x+9x−18

=x(x−2)+9(x−2)

=(x−2)(x+9)

∴ x ^2+7x−18=(x−2)(x+9)

Hence, Factor of x ^2+7x−18 is (x−2)(x+9)

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complete question:

Factor completely x² - 7x + 18.

Prime

(x-9)(x-2)

(x-9)(x+2)

(x + 9)(x+2)

The calculated volumes of the figures are 11264 cubic units, 14482.28 cubic units, 3744 cubic units, 475.2 cubic units, 18824.14 cubic units and 91.99 cubic units

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * 2.8³

Evaluate

Volume = 91.99

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The value of the missing side length x in the right triangle is 15 inches.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

The image in the diagram is a right triangle:

Hypotenuse = 17 inches

Leg 1 = 8 inches

Leg 2 = x

To solve for x, we use the pythagorean theorem.

( hypotenuse )² = ( leg 1 )² + ( leg 2 )²

( leg 2 )² = ( hypotenuse )² - ( leg 1 )²

( leg 2 )² = ( 17 )² - ( 8 )²

( leg 2 )² = 289 - 64

( leg 2 )² = 225

Take the square roots

Leg 2 = √225

Leg 2 = 15 inches.

Therefore, the value of x is 15 inches.

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The difference between the interquartile range of Matt's remaining vacation days an Linda's remaining vacation days is given as follows:

-3.5.

The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.

Matt's ordered data-set is given as follows:

5, 9, 11, 12.

Hence the quartiles are:

Hence the IQR is of:

IQR = 11.5 - 7 = 4.5.

Linda's ordered data-set is given as follows:

0, 6, 9, 13.

The quartiles aret

The IQR is of:

IQR = 11 - 3 = 8.

Hence the difference is of:

4.5 - 8 = -3.5.

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The distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles. Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).

1. Find the distance from the satellite to the points of tangency Solution: Firstly, we need to draw a rough diagram of the scenario to easily understand it. Consider a satellite revolving around an alien planet in a synchronous orbit 18,000 miles above its surface.

We can see that B and D are the points of tangency of the satellite signal with the planet, and C is the center of the planet. Hence, the figure will look like the following: Image Source: Synchronous Orbit - Wikimedia Commons Now, we need to find the distance from the satellite to the points of tangency.

Hence, the distance from the satellite to the points of tangency, B and D, is 61861.9 miles (approximately 61862 miles).2. Find the percentage of the planet's equator within range of the satellite's signal Solution: We can see that the planet's equator can be represented by a circle with a radius of 3500 miles. Hence, the circumference of the circle would be 2π × 3500 miles ≈ 21991.5 miles.

We know that the satellite's signal can be received directly up to a distance of 61862 miles from it. Hence, the length of the portion of the equator within range of the satellite's signal would be twice the distance from the satellite to the point of tangency, which is 2 × 61862 ≈ 123724 miles. Now, we need to find the percentage of the planet's equator within range of the satellite's signal.

Hence, we need to find the time taken for the satellite signal to reach points B and E. We can see that the distance from the satellite to point B is 61862 miles and the distance from the satellite to point E is 3500 miles. Hence, the time taken for the satellite signal to reach point B would be: Time taken to reach point B = Distance / Speed = 61862 / 186000 ≈ 0.332 seconds Now, we need to find the time taken for the satellite signal to reach point E.

Hence, the time difference between the satellite signal reaching points B and E is approximately 0.07 seconds.4. Find the speed of the satellite Solution: We know that the satellite takes 36 hours to complete one revolution around the planet along with the point directly below it on the planet's surface. Hence, we need to find the distance travelled by the satellite in 36 hours to find its speed.

We can see that the distance travelled by the satellite in one revolution is equal to the circumference of the circle with a radius of 3500 miles, which is 2π × 3500 miles ≈ 21991.5 miles. Hence, the distance travelled by the satellite in 36 hours would be: Distance travelled in 36 hours = (21991.5 / 24) × 36 = 549787.5 miles.

Now, we can find the speed of the satellite as follows: Speed of the satellite = Distance / Time = 549787.5 / (36 × 3600) ≈ 4.76 miles/sec. Hence, the speed of the satellite is approximately 4.76 miles/sec (approximately 17136 miles/hr).

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The implications of Constructivist approach in teaching mathematics is that it helps the students to develop a better way to comprehend the content of what they are being taught.

A constructive approach of teaching mathematics believes that students construct knowledge rather than just passively take in information.

A constructive approach of teaching also believes that students integrate new knowledge with existing knowledge to create a deeper understanding of the mathematics being taught to them.

Therefore, constructive approach of teaching can help the students to comprehend the content of what they are being taught.

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the maximum area that can be enclosed with a budget of $6000 is 1,500,000 square meters.

Let's assume we purchase x meters of metal bars and y meters of wooden bars. The cost equation can be expressed as:

3x + 2y = 6000   (total cost equation)

We want to maximize the area, which is given by the equation:

Area = x * y

To solve this problem, we can use the method of substitution or elimination. Let's use substitution.

From the total cost equation, we can express x in terms of y:

x = (6000 - 2y) / 3

Now we can substitute this value of x into the area equation:

Area = [(6000 - 2y) / 3] * y

Simplifying further:

Area = (6000y - 2y^2) / 3

The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = -2 and b = 6000, so:

y = -6000 / (2 * -2) = 1500

Substituting this value of y back into the cost equation, we can find the corresponding value of x:

x = (6000 - 2 * 1500) / 3 = 1000

Therefore, with a budget of $6000, we can purchase 1000 meters of metal bars and 1500 meters of wooden bars, resulting in the maximum area.

Area = x * y = 1000 * 1500 = 1,500,000 square meters

So, the maximum area that can be enclosed with a budget of $6000 is 1,500,000 square meters.

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The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.

The volume of a solid is the three dimensional space the solid occupies.

The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;

Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³

Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³

70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³

The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0

The number of times Johnny needs to use the wheelbarrow is about 41 times

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Answer:

Step-by-step explanation:

Given:

a₁ = 3

an+1 = (an)² + 1To find:

a₃Solution:

We can use the recursive formula given to find the value of a₃.a₂ = a₁ + 1² = 3 + 1 = 4

a₃ = a₂² + 1 = 4² + 1 = 17Therefore, the value of a₃ is 17.Answer: a₃ = 17

Answer:

24

Step-by-step explanation:

As x is now equal to 5, all you have to do is substitute it into were x is in the f(x) formula given.

x^2-1 turns into (5)^2-1=

25-1=

24

Answer:

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

The function y = x² - 5 is the translation of the parent function y = x² down by 5 units.

Since the parent function is y = x², it is a parabola that has its vertex at the origin and opens up as its coefficient is positive.

Looking at the answer choices, we see option A is the correct one.

Other options are incorrect:

The average response time for the ambulance company is 13 minutes, with 95% of response times falling between 10 and 16 minutes.

The response times for a specific ambulance company follow a normal distribution with a mean of 13 minutes. This means that the majority of response times will cluster around the average of 13 minutes.

Furthermore, we know that 95% of the response times fall within the range of 10 to 16 minutes. This suggests that the response times are relatively consistent, with only a small percentage of outliers falling outside this range.

In summary, the average response time for this ambulance company is 13 minutes, and 95% of their response times fall between 10 and 16 minutes.

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