(6x+y)(6x-7) What is the answer?

The differentiation of the stated series expansion of  f term-by-term to obtain the corresponding series expansion for the stated derivative of f is  [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)Xⁿ⁻¹

f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ

⇒ f'(x) = d/dx [[tex]\sum_{n=0}^{\infty}[/tex](-1)ⁿ 3ⁿXⁿ]

= [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿ d/dx (xⁿ)

= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿ(nxⁿ⁻¹)

= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ3ⁿnxⁿ⁻¹

= [tex]\sum_{n=1}^{\infty}[/tex] ((-1)ⁿnxⁿ⁻¹)3ⁿ

= [tex]\sum_{n=1}^{\infty}[/tex] (-1)ⁿ(n3ⁿ)xⁿ-1

In mathematics, differentiation is used to calculate rates of change. In mechanics, for example, velocity is the rate of change of displacement (with regard to time).

The acceleration is the rate of change of velocity (with respect to time).

They are employed in many fields, including

They can be used to represent:

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Full Question:

Differentiate the given series expansion of f term-by-term to obtain the corresponding series expansion for the derivative of f.

If f(x) = 1/ (1 + 3x) = [tex]\sum_{n=0}^{\infty}[/tex] (-1)ⁿ3ⁿxⁿ

Lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,

The Converse of Same-Side Interior Angles Theorem states that, if the sum of two interior angles on same side of a transversal equals 180 degrees, then the lines they lie on are parallel to each other.

Since  M<7 + m<11 = 180, lines a and b are parallel based on the Converse of Same-Side Interior Angles Theorem,

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Answer:

96

Step-by-step explanation:

(2^22-2^20) (3^24-3^22) (4^26-4^24)

=[(2^2-1)2^20][(3^3-1)3^22][(4^2-1)4^24]

=3*2^20*8*3^22*15*4^24

=2^23*3^23*4^24*15

=2^23*3^23*2^48*3*5

=2^71*3^24*5.

∵(2^22-2^20) (3^24-3^22) (4^26-4^24)=2^x × 3^y × 5^z，

∴x=71, y=24, z=1,

∴x+y+z=71+24+1=96.

Her answer should look like y = x + 2, x ≤ 2

The complete question is added as an attachment

From the attached graph, we have the following points

(x, y) = (2, 4) and (0, 2)

See that the difference between the y and x values is 2 where y > x

So, we have

y - x = 2

Add x to both sides

y = x + 2

The highest value of x in the graph is 2.

So, we have

x ≤ 2

Hence, her answer should look like y = x + 2, x ≤ 2

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Answer:

[tex]a=22, b=11\sqrt{3}[/tex]

Step-by-step explanation:

Given a 30-60-90 triangle, the shortest side is always opposite of the smallest angle, in this case 11 is opposite the 30° angle. The largest side of a 30-60-90 triangle will always be twice the smallest, giving [tex]a[/tex] a measure of [tex]22[/tex]. To get the side across the 60° angle we multiply the smallest side by the square root of 3. Meaning [tex]b=11\sqrt{3}[/tex]

The question that could be answered by using a logarithm is explained below

The question is: Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.

The question is asking you to solve y = f(x)

You already did this using a constant for y. Do the same thing with y instead of the constant.

y = 4(1.0256^x)

y/4 = 1.0256^x . . . . . . . divide by 4

log(y/4) = x·log(1.0256) . . . . . take logs

log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x

Now, you have a model for x in terms of y, which is what the question is asking for.

x = log(y/4)/log(1.0256)

When y=12, this is .x = log(12/4)/log(1.0256) ≈ 43.46 weeks

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Answer:

  (c)  25/4

Step-by-step explanation:

A perfect square trinomial is obtained by "completing the square." The constant in a perfect square trinomial is the square of half the x-coefficient.

A "perfect square trinomial" is the square of a binomial.

  (x +a)² = x² +2ax +a²

Of note here is that the constant (a²) is the square of half of the x-term coefficient:

  ((2a)/2)² = a²

The given expression (x² +5x) has an x-term coefficient of 5. The square of half that is ...

  (5/2)² = 25/4

The constant that must be added to make x² +5x into a perfect square trinomial is 25/4.

  (x² +5x) +25/4 = x² +5x +25/4 = (x +5/2)²

Answer:

(2, 60°)

Step-by-step explanation:

A point in polar form (a,b) is represented by a radius and an angle (r, ϴ). To convert, use the formula r² = a² + b² to get r, and  [tex]tan^{-1}[/tex](b/a) = ϴ

[tex]r = \sqrt{1^{2} + \sqrt{3} ^{2} }[/tex]

[tex]r = \sqrt{1+3}[/tex]

[tex]r = \sqrt{4}[/tex]

= 2

[tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]/1) = ϴ

= 60°

The standard equation for the circle is (x - 1 ) ^2 + (y + 3)^2 = 2 ^2

A circle is a closed curve that is drawn from a fixed point called the center in which all points on the curve are the same distance from the center of the center. The equation of a circle with center (h, k) and radius r is given by:

(x-h)^2 + (y-k)^2 = r^2

This is the standard form of the equation. So if we know the coordinates of the center of the circle and also its radius, we can easily find its equation.

Consider any point P(x, y) on the circle. Let "a" be the radius of the circle which is equal to OP.

We know that the distance between the point (x, y) and the origin (0,0) can be found using the distance formula which is equal to -

√[x^2+y^2]= a

Therefore the equation of a circle with center as origin is,

x^2+y^2= a^2

Where "a" is the radius of the circle.

An alternative method

Let's derive another way. Assume that (x,y) is a point on the circle and the center of the circle is at the origin (0,0). Now, if we draw a perpendicular from the point (x,y) to the x-axis, we get a right triangle, where the radius of the circle is the hypotenuse. The base of the triangle is the distance along the x-axis and the height is the distance along the y-axis. Applying the Pythagorean theorem here, we therefore obtain:

x^2+y^2 = radius^2

We need to find the standard equation for the circle with center (1,-3) that passes through the point (2,2)

Standard equation for circle is

(x-h)^2 + (y-k)^2 = r^2................(1)

Here h = 1 , k = -3 and r = 2

put this value of h, k and r in equation (1), we get

(x - 1 ) ^2 + (y + 3)^2 = 2^2

Hence the standard equation of the circle is

(x - 1 ) ^2 + (y + 3)^2 = 2 ^2

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Answer:

Step-by-step explanation:

sin(28) = 2184 / x

x= 2184/ sin(28) = 2184 / 0.4694 = 4652.75

4652.75 / 12  =  387.7 ft

ANSWER: 387.7ft

In the given case, The length of the zipline needed is approximately 96.7 feet.

To find the length of the zipline needed, we can use trigonometry. Let's start by drawing a sketch to visualize the problem. | | zipline | | | | | | | | | | John | Building 28°

John's location, with the angle of elevation labeled as 28°. John is 182 feet away from the base of the building, and he is 71.5 inches tall.

To find the length of the zipline, we can use the tangent function.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is John's height, and the adjacent side is the distance between John and the building. Using the tangent function, we have: tan(28°) = opposite / adjacent

We want to find the length of the zipline, which is the hypotenuse of the right triangle formed by John, the building, and the zipline. Let's call this length "x".

Therefore, we can rewrite the equation as: tan(28°) = 71.5 inches / 182 feet To solve for x, we need to convert the units so that they match.

Let's convert inches to feet: 71.5 inches = 71.5 inches * (1 foot / 12 inches) ≈ 5.96 feet (rounded to the nearest hundredth)

Now, let's solve for x: tan(28°) = 5.96 feet / 182 feet

To isolate x, we can multiply both sides by 182 feet: x ≈ tan(28°) * 182 feet Using a calculator, we find that tan(28°) ≈ 0.5317.

Multiplying this by 182 feet, we get: x ≈ 0.5317 * 182 feet ≈ 96.7 feet (rounded to the nearest tenth) .

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Step-by-step explanation:

Well first let's find the derivative in using the power rule

h'(t) = (-4.9)t + 157

h'(t) = -9.8t + 157

we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.

h'(1452.602) = -9.8(1452.602) + 157

h' = 14,078.500

Answer:

x² + 5x - 14 = (x + 7)(x - 2)

x² - 3x - 54 = (x - 9)(x + 6)

x² + 8x + 12 = (x + 2)(x + 6)

x² - 11x + 30 = (x - 5)(x - 6)

x² - 25 = (x + 5)(x - 5)

x² + 8x - 9 = (x - 1)(x + 9)

Step-by-step explanation:

To factor x² + ax + b, look for two numbers whose sum is a and whose product is b.

The factorization of x² - a² is (x + a)(x - a).

x² + 5x - 14 = (x + 7)(x - 2)

x² - 3x - 54 = (x - 9)(x + 6)

x² + 8x + 12 = (x + 2)(x + 6)

x² - 11x + 30 = (x - 5)(x - 6)

x² - 25 = (x + 5)(x - 5)

x² + 8x - 9 = (x - 1)(x + 9)

The factored form of the given expressions are

y = (x -2)(x +7)

y = (x +6)(x -9)

y = (x +2)(x +6)

y = (x -5)(x -6)

y = (x +5)(x -5)

y = (x -1)(x +9)

y = (x +4)(x -4)

From the question we are to factor the given quadratic expressions

y = x² +7x -2x - 14

y = x(x +7) -2(x +7)

y = (x -2)(x +7)

y = x² -9x +6x - 54

y = x(x -9) +6(x -9)

y = (x +6)(x -9)

y = x² +6x +2x +12

y = x(x +6) +2(x +6)

y = (x +2)(x +6)

y = x² -6x -5x +30

y = x(x -6) -5(x -6)

y = (x -5)(x -6)

y = (x +5)(x -5)

y = x² +9x -x -9

y = x(x +9) -1(x +9)

y = (x -1)(x +9)

y = (x +4)(x -4)

Hence, the factored form of the given expressions are

y = (x -2)(x +7)

y = (x +6)(x -9)

y = (x +2)(x +6)

y = (x -5)(x -6)

y = (x +5)(x -5)

y = (x -1)(x +9)

y = (x +4)(x -4)

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Answer:

42

Step-by-step explanation:

-14 1/9 is about -14.

-2 9/10 is about -3.

Multiplying these, we get (-14)(-3)=42.

He need to charge 24$ per tree if he wants to make a profit of $600.

According to statement

Noah knows that his profit, P, in dollars, are P= −3x^2 + 150 − 1200.

Now, we find the value of x when the profit is $600

Where X represent the Amount he charges per tree.

The given equation is P= −3x^2 + 150 − 1200.

Substitute the value of p is $600 in the above written equation

Then

600 = −3x^2 + 150 − 1200.

After solving the equation by a substitution method the value of X becomes

600+1200-150 = -3(x)^2

x = (1650/3)^1/2

x= 24$

it means the charge per tree is 24$.

So, He need to charge 24$ per tree if he wants to make a profit of $600.

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The 680 tons of fuel needed to cover the next 1790 miles distance.

According to the statement

We have given that the ship covered a 1651 miles distance at 20 knots by a 580 tons of fuel oil.

And distance remaining to next port is 1790 miles and speed increases to 25 knots.

And we have to find that how much fuel used to reach that port.

So, Distance covered = 1651 mile

fuel used = 580 tons

distance covered with 1 tons fuel = 1651/580

distance covered with 1 tons fuel = 2.85 mile at a speed of 20 knots.

so, The fuel consumption for 1790 mile is = 1790/2.85

The fuel consumption for 1790 mile is = 628 tons of fuel needed.

So, The 680 tons of fuel needed to cover the next 1790 miles distance.

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The 98% confidence interval for the average amount spent by 10 to 11-year-olds on a trip to the mall is 23.36 ± 2.933.

The confidence interval for a given level of percentage is given by

C. I = μ ± Z(σ/√n)

Where,

μ - mean, σ - standard deviation, n - sample size, and z - critical value.

The critical value is calculated by

step 1: 100% - (the confidence level)

step 2: Converting the step 1 result into decimal value

step 3: dividing the step 2 result by 2

This is indicated by α/2. So, from the normal distribution table, the z-value at α/2 is said to be the required critical value and denoted by Z_(α/2) or Z.

It is given that,

A survey of several 10 to 11-year-olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46

Sample size n = 6

Step 1: Finding the mean for the given amounts of the survey:

Mean μ = (18.31 + 25.09 + 26.96 + 26.54 + 21.84 + 21.46)/6

             = 23.36

Step 2: Finding the standard deviation:

Standard deviation σ = √summation(x - mean)²/n

On calculating, we get σ = 3.09

Step 3: Finding the critical value:

It is given that the confidence level is 98%

So, (100% - 98%) = 2%

Converting into decimal gives 0.02

So, α/2 = 0.02/2 = 0.01

Thus, at 0.01, the critical value Z = 2.326

Step 4: Constructing the confidence interval:

C.I = 23.36 ± (2.326) × (3.09/√6)

    = 23.36 ± (2.326 × 1.261)

    = 23.36 ± 2.933

So, the lower bound = 23.36 - 2.933 = 20.427

the upper bound = 23.36 + 2.933 =26.293

Therefore, the 98% confidence interval lies from 20.427 to 26.293.

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The slope-intercept formula of the linear equation is:

[tex]y = \frac{3}{7}x + 7[/tex]

A linear function is modeled by:

y = mx + b

In which:

The y-intercept is of b = 7. The line also goes through point (0,-3), hence the slope is:

m = 3/7.

Thus the equation is:

[tex]y = \frac{3}{7}x + 7[/tex]

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m∠ AEM = 20°

From the given figure, we can see that m∠ AEM is alternate to m∠ ACE

Note that m∠ ACE = 20°

Alternate angles are equal.

If m∠ ACE is alternate to m∠ AEM

Then, m∠ AEM = 20°

Hence, m∠ AEM = 20°

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Answer:

6b-4b=a+3a

2b=4a

4a=2b

a=2b/4

a=b/2

The function represented is analyzed below.

The function represented by the graph is related to a piecewise function.

The key features of the function include:

The function has a constant value in interval (0, 15) which is 40.

It decreases at first and then increases from 45 to 65.

It increases linearly from 65 to 90.

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Answer:

x = 8

Step-by-step explanation:

[tex]2logx=log64\\logx^2=log64[/tex]

now that both sides has log, you can remove them and leave it as:

[tex]x^{2} =64\\[/tex]

take the square root of both sides:

[tex]x = [8, -8]\\x = 8[/tex]

logarithmic equations can't have negative solutions, plus -8 isn't an option

i hope this helped!

Here, given

sides of polygon= a(3,7)b(3,3)c(7,3)d(7,7)

Let, 3 = x1 & 7= y1   , 3= x2  & 7= y2   , 7= x3  & 3= y3   ,  7=  x4  & 7= y4

[tex]\frac{1}{2}[/tex] [det.(9-21)+det.(9-21)+det.(49-21)+det.(49-21)] {we took determinants of all the given sides}

[tex]\frac{1}{2}[/tex] (32)

16cm^2

Hence, the area of the polygon is 16cm2.

The formula for calculating the area of ​​a regular polygon is: area = (number of sides x 1 side length x apothem distance) / 2, where the value of the apothem is the formula apothem = [(1) Length side). / {2 × (tan (180 / number of sides))}].

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Factoring the roots, the values of A and B are given as follows:

The expression is:

[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]

We have that:

[tex]\frac{45}{40} = \frac{9}{8}[/tex]

Hence:

[tex]\sqrt{\frac{45\alpha z^3}{40y}} = \sqrt{\frac{9\alpha z^3}{8}} = \sqrt{\frac{9\alpha z^2 \times z}{4 \times 2}} = \frac{A\sqrt{\alpha z}}{B\sqrt{2y}}[/tex]

Hence, comparing the last two equalities:

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Answer:

100 minutes

Step-by-step explanation:

3 hours= 180 min

180/9 = 20

20 x 5 =100 min

The ratio of its width to its length is; 5 :9.

The ratio of its length to its perimeter is; 9: 28.

1). From the task content, the land measures 4.5 km long and 2.5 km wide. Hence, the ratios is; 2.5: 4.5.

Therefore, we have; 5: 9 by expression as whole number ratios.

2) Since the perimeter of the rectangle is; 2(2.5+4.5) = 14.

The ratio of length to perimeter expressed simply is therefore; 9: 28.

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The operation is 365*24*60*60*1000 = 31536*10^6.

As we know the year has 365 days.

Each day has 24 hours.

Each hour has 60 minutes.

Each minute has 60 seconds.

Each second has 1000 millisecond.

Therefore number of milliseconds in a year is

365*24*60*60*1000 = 31536*10^6.

Hence we get the The operation is 365*24*60*60*1000 = 31536*10^6.

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V = π r2h. Volume Calculations. Round ( Cylinder) Tanks. Example 1. Find the Volume in cubic feet of a tank having a radius of 10 feet and ...

Missing: 7500m ‎Give ‎SF.

In the case of a hollow cylinder, we measure two radii, one for the inner circle and one for the outer circle formed by the base of a hollow cylinder. Suppose, r1 and r2 are the two radii of the given hollow cylinder with 'has the height, then the volume of this cylinder can be written as; V = πh(r12 – r22).

To find the volume of a box, simply multiply the length, width, and height — and you're good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters.

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