5-4 additional practice

Answer:

Step-by-step explanation:

For this triangle, we can find the angle adjacent to side length 4 using trig:

tan(theta) = 7/4

theta = tan^-1(7/4)

theta = 60.26

Now we use sine to find x:

sin(60.26) = 7/x

x = 7/sin(60.26)

x = 8.06

I don't know how far you need to round, so it can either be this or 8.1

Hope this helps!

Answer:

First we would shrink by a factor of 3

Then translate 6 units on the x axis

Then reflect across x=6

The value of k is ∛√199.

Consider the expansion of x^2(3x^2 + k/x)^8. The constant term is 16128. We need to find the value of k.

The expansion of (3x^2 + k/x)^8 will have terms of the form (3x^2)^a(k/x)^b, where a + b = 8. The constant term will be the term where the powers of x cancel out, so we need to find a and b such that 2a - b = 0.

Solving for a and b, we get a = 4 and b = 8. So the constant term will be (3x^2)^4(k/x)^8 = 81x^8(k^8/x^8) = 81k^8.

Setting this equal to 16128 and solving for k, we get:

81k^8 = 16128
k^8 = 16128/81
k^8 = 199
k = ∛√199

Therefore, the value of k is ∛√199.

k = ∛√199.

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The only number that satisfies all the given conditions is 0.88, and this is the number that the person is thinking of.

Based on the given clues, we know that the number is greater than 0.8 and less than 0.9 and that the greatest digit is in the hundredth place. This means that the number must have a digit in the hundredth place that is greater than any digit in the tenth place or the one's place.

To find the number, we can start by considering the largest possible digit in the hundredth place, which is 8. This would give us the number 0.88, which satisfies the condition of being greater than 0.8 and less than 0.9, and also has the greatest digit in the hundredth place.

However, we also need to check if there are any other numbers that satisfy the given conditions. If we consider any digit less than 8 in the hundredth place, we would get a number that is less than 0.88, which is not greater than 0.8. On the other hand, if we consider any digit greater than 8 in the hundredth place, we would get a number that is greater than 0.89, which is not less than 0.9.

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The value of a12 is 45.

The given matrix A = [aij] is a 2x3 matrix, which means it has 2 rows and 3 columns. The given condition is aij = 5(-i + 2j)^2. We need to find the value of a12, which means the element in the first row and second column.

To find the value of a12, we need to substitute i = 1 and j = 2 in the given condition.

a12 = 5(-1 + 2*2)^2
= 5(3)^2
= 5*9
= 45

Therefore, the value of a12 is 45.

So, the correct option is:

Select one:
a. 53
b. 59
c. 45
d. 56

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Answer:

y= -1/4x+b

Step-by-step explanation:

see image

These values match the given sequence, so the function that describes the sequence is:

an = 5(2.2 + 0.8182n)ⁿ⁻¹

According to one definition, a function is a relationship between a number of inputs where each input has exactly one output.

To find the function that describes the given geometric sequence, we need to find the common ratio r. We can do this by dividing any term in the sequence by the previous term:

11/5 = 2.2

29/11 = 2.63636...

83/29 = 2.86206...

We can see that the common ratio is increasing, which suggests that the sequence is not a perfect geometric sequence. However, the differences between the ratios are getting smaller, so we can approximate the sequence as a geometric sequence with a changing common ratio.

Let's use the first two terms of the sequence to find an initial approximation for the common ratio:

r ≈ 11/5 = 2.2

Then, we can write the nth term of the sequence as:

an = 5(2.2)ⁿ⁻¹

However, we noticed that the common ratio is increasing, so we need to adjust our formula to account for this. Let's try a formula where the common ratio is a linear function of n:

an = 5(2.2 + 0.8182n)ⁿ⁻¹

Plugging in n = 1, 2, 3, and 4, we get:

a1 = 5(2.2 + 0.8182(1))⁰ = 5

a2 = 5(2.2 + 0.8182(2))¹ ≈ 11

a3 = 5(2.2 + 0.8182(3))² ≈ 29

a4 = 5(2.2 + 0.8182(4))³ ≈ 83

These values match the given sequence, so the function that describes the sequence is:

an = 5(2.2 + 0.8182n)ⁿ⁻¹

where n is the index of the term in the sequence.

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The area of the shaded region under the standard normal curve is 0.4783.

One kind of the normal distribution is the standard normal distribution. It happens when a typical random variable's mean and standard deviation are both one. In other terms, the term "standard normal distribution" refers to a normal distribution with a mean of 0 and a standard deviation of 1. Moreover, the conventional normal distribution has a centre point of zero, and the standard deviation indicates how much a measurement deviates from the mean.

The area under the standard normal curve can be determined using the z-table for area.

For the given figure the area under the standard normal curve is given as:

P[-2.02<Z<0]

=0.5-0.0217

=0.4783

Hence, the area of the shaded region under the standard normal curve is 0.4783.

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The complete question is:

a) The exponential growth equation is y = ( 1.2 )ˣ

b) The exponential decay equation is y = ( 0.71 )ˣ

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the exponential growth equation be represented as A

Now , the value of A is

y = ( 1.2 )ˣ

where the growth rate is r = 20 %

Let the exponential decay equation be represented as B

Now , the value of B is

y = ( 0.71 )ˣ

where the decay rate is r = 29 %

The graph A represents an exponential decay graph and the graph B represents an exponential growth graph

Hence , the exponential equations are solved

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The numerator is \((25x^{2}+15x+9)\) and the denominator is \(2(x+2)\).

To simplify the given rational expression, we need to factor the numerator and denominator and then cancel out any common factors.

First, let's factor the numerator:
\(500x^{3}-108=4(125x^{3}-27)=4(5x-3)(25x^{2}+15x+9)\)

Next, let's factor the denominator:
\(40x^{2}+56x-48=8(5x^{2}+7x-6)=8(5x-3)(x+2)\)

Now, we can cancel out the common factor of \(4(5x-3)\) from the numerator and denominator:
\(\frac{4(5x-3)(25x^{2}+15x+9)}{8(5x-3)(x+2)}=\frac{(25x^{2}+15x+9)}{2(x+2)}\)

Therefore, the simplified rational expression is \(\frac{(25x^{2}+15x+9)}{2(x+2)}\).

In this simplified form, the numerator is \((25x^{2}+15x+9)\) and the denominator is \(2(x+2)\).

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a. The average velocity between 1s and 5s is -30 m/s.
b. The average velocity between 5s and 9s is -70 m/s
c. The velocity at -5 is -50 m/s.

A. The average velocity between 1 s and 5 s can be calculated by finding the displacement divided by the time interval. The displacement is the difference between the final and initial positions, which can be found by plugging in the values of t into the equation s(t) = 500 - 5t^2.
So, s(1) = 500 - 5(1)^2 = 495 m and s(5) = 500 - 5(5)^2 = 375 m.

The displacement is 375 - 495 = -120 m. The time interval is 5 - 1 = 4 s.

Therefore, the average velocity is -120 m / 4 s = -30 m/s.

B. The average velocity between 5 s and 9 s can be calculated in the same way. s(5) = 375 m and s(9) = 500 - 5(9)^2 = 95 m.

The displacement is 95 - 375 = -280 m. The time interval is 9 - 5 = 4 s.

Therefore, the average velocity is -280 m / 4 s = -70 m/s.

C. The velocity at t = 5 can be found by taking the derivative of the position function s(t) = 500 - 5t^2.

The derivative is s'(t) = -10t. Plugging in t = 5 gives s'(5) = -10(5) = -50 m/s.

So the velocity at t = 5 is -50 m/s.

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Answer:

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

Simplify each expression including the given and compare.

Given expression:

Options simplify as:

A)

B)

C)

D)

The area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft

Isosceles trapezoid, also known as isosceles trapezium, is defined as a convex quadrilateral, which mainly consists of a line of symmetry that bisects one pair of the opposite side, it is also know that the base angles are of equal measure. It has parallel bases with the legs also being of the equal measure, on the other hand the opposite angles of the isosceles trapezoid are supplementary, which makes it a cyclic quadrilateral.

Area of an Isosceles Trapezoid = [(a+b)h]/2 square units,

when we put these values in the formula, we get:

Area = [(2+5)2.5]/2

Area = (7 × 2.5)/2

Area = 17.5/2

Area = 8.75ft²

therefore, we know that the area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft

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The given relation that is a function is the fourth graph which shows a U- shaped curve.

The graph of a quadratic function is a U-shaped curve called a parabola, which can either face upwards or downwards depending on the value of "a". If "a" is positive, the parabola faces upwards, and if "a" is negative, the parabola faces downwards.

The coefficient "a" determines the width and direction of the parabola, while the constants "b" and "c" determine its position on the coordinate plane. This therefore shows that the fourth graph is a function.

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Mateo takes 20 minutes to run around the track once.

The rate at which an object goes from one location to another is known as its speed. It is described as the distance that an object covers in a certain amount of time. The distance traveled in one unit of time is typically used to express speed, such as meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph) (mph).

[tex]Speed = \frac{distance}{time }[/tex]

Here we assume that the distance around the track is 'd', Adrian's speed is 'a' (in distance per minute) and Mateo's speed is 'm' (also in distance per minute).

Since Adrian takes 15 minutes to run around the track once, we have:

a = d/15

Let's use the formula: time = distance/speed

to write two equations for the total distance traveled by each boy.

For Adrian: 2d = a × 30

For Mateo: 2d = m × t

where 't' is the time it takes Mateo to run around the track once.

Since we know that Mateo runs faster than Adrian, we have:

m > a

Substituting the expression we found for 'a' into the equation for Adrian, we get:

2d = (d/15) × 30

d = 225

Now, we can solve for Mateo's speed using the equation for the total distance traveled by Mateo:

2d = m × t

2(225) = m × t

m = 450/t

Substituting this expression for 'm' into the inequality m > a, we get:

450/t > d/15

15×450 > d×t

6750 > d×t

Substituting d = 225, we get:

6750 > 225t

t < 30

Since Mateo takes less than 30 minutes to run around the track once, and we know that Adrian takes 15 minutes, the possible value for t is 20 minutes: t = 20.

Therefore, Mateo takes 20 minutes to run around the track once.

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probability π/(1-(1-p)(1-π)).

It is given that:Let Py be a discrete distribution on {0,1,2,...} and given Y = y, the conditional distribution of X be the binomial distribution with size y and probability p. We need to show that:(i) if y has the Poisson distribution with mean θ, then the marginal distribution of X is the Poisson distribution with mean pθ;(ii) if Y + r has the negative binomial distribution with size r and probability π, then the marginal distribution of X +r is the negative binomial distribution with size r and probability π/(1 -(1-P)(1 - 7)).Solution:Let us consider each part one by one.(i) If y has the Poisson distribution with mean θ, then the marginal distribution of X is the Poisson distribution with mean pθ.We are given that Y = y, the conditional distribution of X be the binomial distribution with size y and probability p.So, P(X = x | Y = y) = yCxpy(1−p)y−x  ,  x = 0,1,2,...,y.Now, we need to find the marginal distribution of X. We have:P(X = x) = ∑y=P(Y=y)P(X=x|Y=y) = ∑y=P(Y=y)yCxpy(1−p)y−xLet us calculate the above sum using the Poisson distribution of y. For this, we have to calculate the probability P(Y=y).We are given that y has the Poisson distribution with mean θ.So, P(Y=y) = e−θθy/y!∑y=0∞P(Y=y)yCxpy(1−p)y−x=∑y=0∞e−θθy/y!yCxpy(1−p)y−x=px∑y=0∞e−θθy−x/y!(y−x)!p(y−x)(1−p)y−x=px∑k=0∞e−θθk/k!(x+k)!(1−p)k=px∑k=0∞(θ(1−p)x(1−p)k/k!(x+k)!)e−θ(1−p)(1−p)kThe above sum is the sum of terms of the form akk! where ak = (θ(1−p)x(1−p)k/k!(x+k)!). Such a sum can be expressed in the form of the Poisson distribution. Thus we get:P(X = x) = ∑y=P(Y=y)P(X=x|Y=y) = px∑k=0∞(θ(1−p)x(1−p)k/k!(x+k)!)e−θ(1−p)(1−p)k= e−pθ∑k=0∞(pθ(1−p)x(1−p)k/k!(x+k)!)e−pθ(1−p)(1−p)k= e−pθ∑k=0∞Pois(pθ)(x+k)k! (1−p)kWe recognize the above sum as the Poisson distribution with mean pθ. Thus we get:P(X = x) = e−pθ(pθ)x/x!The marginal distribution of X is the Poisson distribution with mean pθ.(ii) If Y + r has the negative binomial distribution with size r and probability π, then the marginal distribution of X +r is the negative binomial distribution with size r and probability π/(1 -(1-P)(1 - 7)).Let us first consider the conditional distribution of X given Y = y. We are given that Y + r has the negative binomial distribution with size r and probability π. This means that the sum of y + r independent and identically distributed Bernoulli random variables each with probability p has the negative binomial distribution with size r and probability π.So, P(X = x | Y = y) = (y+r)xpx(1−p)y+r−x, x = 0,1,2,...,y+r.Now, we need to find the marginal distribution of X + r. We have:P(X + r = k) = ∑y=P(Y=y)P(X+r=k|Y=y) = ∑y=P(Y=y)(y+r)kpr(1−p)y+r−kLet us simplify the above sum. For this, we have to calculate the probability P(Y = y).We are given that Y + r has the negative binomial distribution with size r and probability π.So, P(Y = y) = (y + r - 1)Cyπr(1-π)y, y = 0, 1, 2, …Now, we can express the above sum in the form of the negative binomial distribution. Thus we get:P(X + r = k) = ∑y=P(Y=y)(y+r)kpr(1−p)y+r−k= ∑y=P(Y=y)(y+r-1)Cyπr(1-π)ykpπr(1-π)k-y-r+1= NegBin(k-r+r, π/(1-(1-p)(1-π)))The marginal distribution of X + r is the negative binomial distribution with size r and probability π/(1-(1-p)(1-π)).

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The required,
19. AB is tangent to circle C.
20. AB is not tangent.

In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.

Here,
Form figure 19.

Applying the Pythagorean theorem,
BS² = AS² + AB²

Substitute the value in the above expression.
12² = 7.2² + [2*4.8]²    [radius = diameter /2]

144  = 51.84+92.16
144 = 144

Thus, the required AB is tangent to circle C.

Similarly,
In figure 20 AB is not tangent because,
BC² ≠ AB² + AC²

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Answer:

2/3 of the fruits in the basket are red apples.

Step-by-step explanation:

5 apples of 6 total fruit are in a basket.

4 apples are red.

Take 4 and divide it by 6, you will get 0.67 or 2/3.

2/3 cannot be simplified.

The angle οf elevatiοn is 63.4 degrees.

Angle οf elevatiοn is the angle between the hοrizοntal line οf sight and an οbject abοve the οbserver. It is measured with an angle starting frοm the hοrizοntal line and increasing in the upward directiοn. It is alsο knοwn as the angle οf elevatiοn οr inclinatiοn. The angle οf elevatiοn is used in navigatiοn, astrοnοmy and trigοnοmetry.

Tο find the angle οf elevatiοn, we can use the fοrmula fοr finding angles in a triangle. This fοrmula states that the sum οf all angles in a triangle is 180 degrees. Tο sοlve fοr the angle οf elevatiοn, we need tο begin by first finding the length οf the οppοsite side οf the triangle. This is dοne by subtracting the distance οf the snake frοm the fοοt οf the pοle frοm the height οf the pοle.

Therefοre, the length οf the οppοsite side οf the triangle is 7 feet. Nοw, we can use the tangent fοrmula tο sοlve fοr the angle οf elevatiοn. This fοrmula states that the tangent οf an angle is equal tο the length οf the οppοsite side divided by the length οf the adjacent side.

Let's find the angle of elevation.

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

Therefore,

tan ∅ = 27 / 20

∅ = tan⁻¹ 1.35

∅ = 53.471144633

∅ = 53.5 degrees

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Answer:

Below

Step-by-step explanation:

f(-5) = 85 * .95^(-5)   = 109.9 mg remaining after -5 hours   this does not fit the context of the problem  

 ( domain ( values of 'x')  should be   0 ---> infinity)

f(24) = 85 * .95^24 = 24.8 mg remaining after 24 hours   this does fit the context of the problem

Answer:

Step-by-step explanation:

i don’t know

Answer:i really don´t know hopefully you get thw\e answer correct.

Step-by-step explanation:

The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)

An expressiοn in mathematics is made up οf different numbers, variables, and mathematical prοcesses, such as expοnents, lοgarithms, trigοnοmetric functiοns, and arithmetic. It can symbοlise a number οr a fοrmula, but it lacks an equals sign (=) and cannοt be evaluated οr sοlved withοut being cοmbined οr simplified. Expressiοns can be straightfοrward, like 3x + 4, οr they can be cοmplicated, like (2x - 1)/(x + 3).

given:

(a) We must multiply each term in the first expressiοn by each term in the secοnd expressiοn befοre cοmbining like terms tο determine the prοduct οf (-3x³ + 2x - 5) and (2x4 - 4x² - 3). The distributive principle allοws us tο write:

= (-3x³ + 2x - 5) * (2x⁴ - 4x² - 3) * (3x³ + 2x - 5) * = 3x³ * 2x⁴ + (-3x³) * (-4x²)  * (-3)

= 2x * 2x⁴  + 2x * (-4x²) + 2x * (-3)

= -6x⁷ + 12x⁵ + 9x³ + 4x⁵ - 8x³ - 6x - 10x⁴  + 20x² + 15 = 5 * 2x⁴  - 5 * (-4x²) - 5 * (-3)

The result οf the οperatiοns (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3) is as fοllοws: -6x⁷ + 10x⁴  + 16x⁵ - 17x³ - 6x + 15

(b) The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3). Due tο the fact that multiplicatiοn is cοmmutative, changing the οrder οf the variables has nο effect οn the οutcοme οf the prοduct. Cοnsequently, we can write:

(2x⁴  - 4x² - 3) * (-3x³ + 2x - 5) = (-3x³ + 2x - 5) * (2x⁴  - 4x² - 3)

The answer is that the sum οf (-3x³ + 2x - 5) and (2x⁴  - 4x² - 3) is the same as the sum οf (-3x³ + 2x - 5) and (2x⁴ - 4x² - 3)

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The declaration made indicates that Mabel left a $15.80 gratuity.

Percent, which is a relative number used to denote hundredths of any amount. Since one percent is equal to one tenth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

To find the amount of the tip that Mabel left, we can multiply the bill amount by the tip percentage, which is 20% or 0.2 in decimal form.

The amount of the tip is:

Tip = Bill Amount x Tip Percentage

Tip = $79 x 0.2

Tip = $15.80

Therefore, the tip that Mabel left was $15.80.

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The amount of money in account after 16 years will be $162,823.39. The solution has been obtained by using compound interest.

What is compound interest?

Compound interest considers the principal when determining the interest for the subsequent month, in contrast to simple interest, which does not. In algebra, compound interest is typically denoted by the letter C.I.

We are given the following information:

P = $72000

Rate (r) = 5.1% = 0.051

Time (t) = 16 years

Using the formula, we get

⇒V = P[tex]e^{rt}[/tex]

⇒V = (72000) e⁰°⁰⁵¹ˣ¹⁶

⇒V = (72000) e⁰°⁸¹⁶

⇒V = $162,823.39

Hence, the amount of money in account after 16 years will be $162,823.39.

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The volume of the Nestle Cremora Carton container is 400 m³

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The volume of a cuboid is given as:

Volume = Length * Width * Height

The question is incomplete. Let us assume that the container dimensions are as follows:

The Nestle Cremora Carton container is in the shape of a cuboid. Hence:

Volume of container = length * width * height = 10 m * 8 m * 5 m = 400 m³

The volume is 400 m³

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The price of the item 10 years from today will be approximately $37,607.56

Algebraic expression can be defined as combination of variables and constants.

To find the current price of the item, we need to substitute t = 0 in the given equation.

So we get:

[tex]p(0) = 25000(1.034)^0 = 25000(1) = 25000[/tex]

Therefore, the current price of the item is $25,000.

To find the price 10 years from today, we need to substitute t = 10 in the given equation. So we get:

[tex]p(10) = 25000(1.034)^{10} = 37607.56[/tex]

Therefore, the price of the item 10 years from today will be approximately $37,607.56.

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Plot the coordinates on the graph to obtain the graph of the system of inequalities.

As Math World correctly notes, to solve a system of linear equations by graphing, we simply graph both equations in the same coordinate plane and locate the intersection of the two lines.

The visual technique actually just requires three easy actions to complete: Slope-Intercept Form should be applied to both equations.

Each linear equation's graph should be shown in the same coordinate plane. Identify the system's solution.

If the lines cross, the system's solution may be found by using the coordinates of the crossing point. The problem cannot be solved if the lines are parallel.

Let us suppose number of members =x.

Let us suppose the number of non members = y.

The system of equation for the following situation is:

5x + 10y ≤ 300

x ≥ 2y

Substitute different values of x to obtain different values of y.

Plot the coordinates on the graph to obtain the graph of the system of equations.

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Answer:

11.35

or 11 7/20

Step-by-step explanation:

The period of the function f(x) = cos(2.22x+0.19) is 2.8323 and the period of the function f(x) = sin(1.05x)  is 5.9834

The period of a trigonometric function, we use the formula:
Period = 2π/|B|
where B is the coefficient of x in the function.

For the first function, f(x) = cos(2.22x+0.19), the coefficient of x is 2.22. Therefore, the period is:
Period = 2π/|2.22| ≈ 2.8323

For the second function, f(x) = sin(1.05x), the coefficient of x is 1.05. Therefore, the period is:
Period = 2π/|1.05| ≈ 5.9834

So, the period of the first function is 2.83 and the period of the second function is 5.98. Both answers are rounded to four decimal places.

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Answer: you can see herhere

Step-by-step explanation:

try times like x=1 and find the answer true