Which graph represents the function f(x)=3⋅5^x?

a. To approximate the given quantity using Taylor polynomials with n=3, we need to use the formula for the Taylor polynomial of degree n:

Pn(x) = f(a) + f'(a)(x-a) + (1/2!)f''(a)(x-a)^2 + (1/3!)f'''(a)(x-a)^3 + ... + (1/n!)f^(n)(a)(x-a)^n
where f(x) = sinh(x), a = 0. The derivatives of sinh(x) are:
f'(x) = cosh(x), f''(x) = sinh(x), f'''(x) = cosh(x), and so on.
Therefore, the Taylor polynomial of degree 3 for sinh(x) centered at a = 0 is:
P3(x) = x + (1/2!)(x)^3
To approximate sinh(0.24), we substitute x = 0.24 into the formula above:
P3(0.24) = 0.24 + (1/2!)(0.24)^3 = 0.240008
b. To compute the absolute error in the approximation assuming the exact value is given by a calculator, we need to subtract the actual value of sinh(0.24) from the approximation we obtained in part a:
Error = |P3(0.24) - sinh(0.24)| = |0.240008 - 0.241663| = 0.001655
Therefore, the absolute error in the approximation is 0.001655.
To approximate sinh(0.17), we use the same formula and substitute x = 0.17:
P3(0.17) = 0.17 + (1/2!)(0.17)^3 = 0.170005
To compute the absolute error in this case, we subtract the actual value of sinh(0.17) from the approximation we obtained:
Error = |P3(0.17) - sinh(0.17)| = |0.170005 - 0.17031| = 0.000305
Therefore, the absolute error in the approximation for sinh(0.17) is 0.000305.

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Yes, you can be certain that there are at least two guests who had the same number of handshakes. This is due to the Pigeonhole Principle.

As the party organizer, you shake hands with all 80 guests, which means you have 80 handshakes. The guests can have a minimum of 0 handshakes (if they don't shake hands with anyone except you) and a maximum of 79 handshakes (if they shake hands with everyone except themselves). There are 80 guests (excluding yourself), so there are 80 "pigeonholes" for the number of handshakes. The range of possible handshakes among the guests is from 0 to 79, which creates 80 possible outcomes or "pigeons."

According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons. In this case, there are 80 pigeonholes (guests) and 80 pigeons (possible handshakes). Therefore, at least two guests must have had the same number of handshakes.

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Step-by-step explanation:

31/2×5/23 (use reciprocal)

31×5=155

155÷46=3.369565217

155/46

3 and 17/46

Answer:

that's a good question

Step-by-step explanation:

Max purchased 4 lip gloss tubes and 3 nail polish bottles.

Let x be the number of lip gloss tubes purchased by Max and y be the number of nail polish bottles purchased by Max. Then we have:

\(x + y = 7\)(Max bought a total of 7 items)

\(5.32x + 6.89y = 41.95\) (Max spent $41.95 in total)

To solve for x and y, we can use the first equation to express one variable in terms of the other and substitute that expression into the second equation. For example, we can solve for y in terms of x as follows:

\(y = 7 - x\)

Substituting this into the second equation, we get:

\(5.32x + 6.89(7 - x) = 41.95\)

Simplifying and solving for x, we have:

\(5.32x + 48.23 - 6.89x = 41.95\\-1.57x = -6.28\\x = 4\)

So Max purchased 4 lip gloss tubes. Substituting this back into the first equation, we get:

\(4 + y = 7\\y = 3\)

Therefore, Max purchased 4 lip gloss tubes and 3 nail polish bottles.

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Answer:

-4x-32

Step-by-step explanation:

This is a quadratic expression with no real roots. Hence, there are no vertical asymptotes for this function. So, the horizontal asymptote is y = 3/2 and there are no vertical asymptotes.

To determine the horizontal and vertical asymptotes of the given function f(x) = 3x − 5/2x² + 1, we need to consider the limits as x approaches infinity and negative infinity respectively.
The limits help us understand the behavior of the function at extremely large positive or negative values of x.Let's find the horizontal asymptotes:
Horizontal asymptotes: If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is y = 0.If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote is y = p/q where p is the leading coefficient of the numerator and q is the leading coefficient of the denominator.
If the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote.
So, in the given function, the degree of the numerator and denominator are 1 and 2 respectively. Hence, the horizontal asymptote is given by the ratio of the leading coefficients of the numerator and denominator. The ratio is 3/2. Hence, the horizontal asymptote is given by y = 3/2.Now, let's find the vertical asymptote(s).
Vertical asymptotes: To find the vertical asymptotes of the given function, we need to find the values of x that make the denominator equal to zero. These are the values that the function cannot take as it becomes infinite at these points. In the given function, the denominator is 2x² + 1.
This is a quadratic expression with no real roots. Hence, there are no vertical asymptotes for this function. So, the horizontal asymptote is y = 3/2 and there are no vertical asymptotes.

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This is a quadratic expression with no real roots. Hence, there are no vertical asymptotes for this function. So, the horizontal asymptote is y = 3/2 and there are no vertical asymptotes.

To determine the horizontal and vertical asymptotes of the given function f(x) = 3x − 5/2x² + 1, we need to consider the limits as x approaches infinity and negative infinity respectively.
The limits help us understand the behavior of the function at extremely large positive or negative values of x.Let's find the horizontal asymptotes:
Horizontal asymptotes: If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is y = 0.If the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote is y = p/q where p is the leading coefficient of the numerator and q is the leading coefficient of the denominator.
If the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote.
So, in the given function, the degree of the numerator and denominator are 1 and 2 respectively. Hence, the horizontal asymptote is given by the ratio of the leading coefficients of the numerator and denominator. The ratio is 3/2. Hence, the horizontal asymptote is given by y = 3/2.Now, let's find the vertical asymptote(s).
Vertical asymptotes: To find the vertical asymptotes of the given function, we need to find the values of x that make the denominator equal to zero. These are the values that the function cannot take as it becomes infinite at these points. In the given function, the denominator is 2x² + 1.
This is a quadratic expression with no real roots. Hence, there are no vertical asymptotes for this function. So, the horizontal asymptote is y = 3/2 and there are no vertical asymptotes.

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Answer:

The Answer To Your To Your Question Is SAS (Side-Angle-Side) Theroem

Answer:

Side angle side Theorem

Step-by-step explanation:

Answer:

its 15 ur counting by 3's

Step-by-step explanation:

Answer:

it is 15

Step-by-step explanation:

just go by 3's 3,6,9,12,15,18,21,24,27,30

Answer:

see in the picture, we have:

P is the midpoint of AB

Q is the midpoint of CD

=> PQ is the median line of the trapezoid ABCD

=> PQ = (BC + AD)/2 = (54 + 33)/2 = 43.5

Step-by-step explanation:

To find the Area of a Trapezium, we use 1/2(a+b)*h

where a=2.8 and b=4.4, Height=3.5

1/2(2.8+4.4) *3.5

1/2(7.2)*3.5

3.6*3.5

12.6cm2

Answer:

Step-by-step explanation:

Area of a trapezium = 1/2(a + b) x h

1/2 (2.8 + 4.4) x 3.5

1/2 x 7.2 x 3.5

12.6

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

Answer:

x = 8

Step-by-step explanation:

the exterior angles of a triangle sum to 360° , that is

20x + 8x + 17x = 360

45x = 360 ( divide both sides by 45 )

x = 8

Write the equation in slope-intercept form.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Substituting the slope and the y-intercept values into the equation, we get: y = 16x + 0.

Simplifying the equation, we get: y = 16x.

Therefore, the equation in slope-intercept form for Nathan's gym membership is y = 16x, where y represents the total cost of Nathan's gym membership and x represents the number of weeks of membership.

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Answer: =12x

Step-by-step explanation:

=3x+4x+5x

=(3x+4x+5x)

=12x

Answer:

7×3

Step-by-step explanation:

option b

i hope it is helpful for you

Answer:  B. 7x3

This is because 7 times 3 = 21. The other answer choices do not multiply to 21.

Think of it like having 7 rows and 3 columns to give 21 squares overall to make this larger rectangle.

A circle is a curve that is made by a moving point in a plane. The perimeter of a circle is equal to the length of the circle's defining line and is commonly referred to as the circle's circumference.

What is a circle?

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We can see here that:

A cube is a three-dimensional geometric shape that has six square faces, all of which are congruent (equal in size) and perpendicular to each other. It is a special type of rectangular prism where all edges have the same length, and all angles are right angles (90 degrees).

Cubes are commonly encountered in everyday life, such as dice, boxes, and Rubik's Cube puzzles. They have precise and uniform geometry, making them useful in various mathematical and engineering applications.

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(1+i) ^18 ≈ 4.766×10^6 - 1.632×10^7i. a. To solve (e^-4-2i) ^2, we first need to simplify e^-4-2i. Using Euler's formula, we can rewrite e^-4-2i as e^-4 * e^-2i, which is equivalent to e^-4(cos (-2) +i*sin (-2)). Simplifying further, we get e^-4(cos(2)-i*sin(2)).

Now, we can square this expression to get (e^-4(cos (2)-i*sin (2))) ^2. Using the formula (a+bi)^2 = a^2 - b^2 + 2abi, we get:

(e^-4*cos(2))^2 - (e^-4*sin(2))^2 + 2*e^-4*cos(2)*i*sin(2)

Simplifying, we get:

e^-8 - e^-8*sin^2(2) + 2*e^-4*cos(2)*i*sin(2)

This is the form a+bi, so our final answer is:

a = e^-8 - e^-8*sin^2(2) ≈ 0.0153
b = 2*e^-4*cos(2)*sin(2) ≈ -0.0565

Therefore, (e^-4-2i)^2 ≈ 0.0153 - 0.0565i.

b. To solve (1+i)^18, we can use the binomial theorem, which states that (a+b)^n = Σ(n choose k)a^(n-k)*b^k, where Σ is the sum from k=0 to n. Applying this to (1+i)^18, we get:

(18 choose 0)1^18*i^0 + (18 choose 1)1^17*i^1 + (18 choose 2)1^16*i^2 + ... + (18 choose 18)1^0*i^18

Simplifying the coefficients using the formula (n choose k) = n!/((n-k)!k!), we get:

1 + 18i - 1530 - 3060i + 18564 + 145152i - 437580 - 947736i + 1352078 + 1081664i - 587863.5 - 575784i + 203887.5 + 405528i - 88749 + 35064i - 5400 + 304i

Adding up the real and imaginary parts separately, we get:

a = 4766436 ≈ 4.766×10^6
b = -16318512 ≈ -1.632×10^7

Therefore, (1+i)^18 ≈ 4.766×10^6 - 1.632×10^7i.

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Answer:

536 cars can park along one side of this parking lot.

Step-by-step explanation:

First, divide the parking lot's area by 2 to have an even length and width (since the parking lot is a square, each side haas the same length).

9640 ÷ 2 = 4820 ft

Now divide 4820 by 9 (the width of each parking space) to see how many parking spaces, cars, can fit into one side

4820 ÷ 9 = 535.56 ≈ 536 parking spaces for cars

536 cars can park along one side of the parking lot.

The quadratic function that satisfies the given conditions is f(x) = (-1/6)(x - 6)(x + 4). Option C is correct.

We can start by using the fact that the roots of the quadratic function are 6 and -4. If a quadratic function has roots of r₁ and r₂, then it can be written in factored form as:

f(x) = a(x - r₁)(x - r₂)

Using this formula, we can write the quadratic function in factored form as:

f(x) = a(x - 6)(x + 4)

Now we can use the given point (2,4) to solve for the value of a. Substituting x = 2 and y = 4 into the equation gives:

4 = a(2 - 6)(2 + 4)

a = -1/6

Therefore, the quadratic function that satisfies the given conditions is:

f(x) = (-1/6)(x - 6)(x + 4). Option C is correct.

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Answer:

A is the correct answer

Step-by-step explanation:

Answer:

129

Step-by-step explanation:

2*2+x(100-15x)

2*2+5(100-15*5)

2*2+5(100-75)

2*2+5*25

4+125

129ans

M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.

Example :

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\(33 + 1 \times 12\)

\(33 + 12\)

\(45\)

To build a garden of 4 feet Deja needs 12 small bricks.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The first garden is 4 feet long the bricks Deja is using are each 1/3 of a foot long.

Therefore, the number of bricks required is,

= 4/(1/3).

= 4×(3/1).

= 12 bricks.

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The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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Answer:

\(\rm\displaystyle \theta = \frac{\pi}{4} \)

Step-by-step explanation:

we want to find the acute angle θ (as θ is between (0,π/2)) formed by the line y=-2x+4 and y=3x-3 to do so we can consider the following formula:

\( \displaystyle\tan( \theta) = \bigg| \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | \)

\( \rm \displaystyle \implies\theta = \arctan \left( \bigg | \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | \right)\)

From the first equation we obtain that \(m_1\) is -2 and from the second that \(m_2\) is 3 therefore substitute:

\( \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 2) (3)} \bigg | \right)\)

simplify multiplication:

\( \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 6)} \bigg | \right)\)

simplify Parentheses:

\( \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 + 2 }{1 + ( - 6)} \bigg | \right)\)

simplify addition:

\( \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 5 }{ - 5} \bigg | \right)\)

simplify division:

\( \rm\displaystyle \theta = \arctan \left( | - 1| \right)\)

calculate the absolute of -1:

\(\rm\displaystyle \theta = \arctan \left( 1\right)\)

calculate the inverse function:

\(\rm\displaystyle \theta = \frac{\pi}{4} \)

hence,

the angle θ which is formed by the line y = -2x+4 and y = 3x-3 is π/4

(for more info about the formula refer the attachment thank you!)

Consider two vector-valued functions,

\(\vec r(t) = \left\langle t, -2t+4\right\rangle \text{ and } \vec s(t) = \left\langle t, 3t-3\right\rangle\)

Differentiate both to get the corresponding tangent/direction vectors:

\(\dfrac{\mathrm d\vec r(t)}{\mathrm dt} = \left\langle1,-2\right\rangle \text{ and } \dfrac{\mathrm d\vec s(t)}{\mathrm dt} = \left\langle1,3\right\rangle\)

Recall the dot product identity: for two vectors \(\vec a\) and \(\vec b\), we have

\(\vec a \cdot \vec b = \|\vec a\| \|\vec b\| \cos(\theta)\)

where \(\theta\) is the angle between them.

We have

\(\langle1,-2\rangle \cdot \langle1,3\rangle = \|\langle1,-2\rangle\| \|\langle1,3\rangle\| \cos(\theta) \\\\ 1\times1 + (-2)\times3 = \sqrt{1^2 + (-2)^2} \times \sqrt{1^2+3^2} \cos(\theta) \\\\ \cos(\theta) = \dfrac{-5}{\sqrt5\times\sqrt{10}} = -\dfrac1{\sqrt2} \\\\ \implies \theta = \cos^{-1}\left(-\dfrac1{\sqrt2}\right) = \dfrac{3\pi}4\)

Then the acute angle between the lines is π/4.

Answer:

.6x=540, x= number surveyed

Step-by-step explanation:

.6×=540

x=number surveyed

60% of number surveyed is 540

multiply where "of" is and "is" is the equal sign