Find the EXACT values for a, b, and c.
(Picture attached)

The position of a mass oscillating on a spring is given by

x = (3.8 cm)cos[2πt/(0.32 s)].

The position equation becomes:

x = (3.8 cm)cos(19.6 t)

The position of a mass oscillating on a spring is given by

x = (3.8 cm)cos[2πt/(0.32 s)].

The amplitude is the maximum displacement from equilibrium, which is 3.8 cm.

The angular frequency, ω, is equal to 2π/T

Where T is the period.

Therefore,

ω = 2π/0.32

= 19.6 rad/s.

The mass on the spring is in simple harmonic motion since its position can be defined by a sinusoidal function of time.

The period, T, is the time taken for one complete oscillation or cycle.

Therefore,

T = 0.32 s.

The position equation can be expressed in terms of displacement, x, as follows:

x = Acos(ωt + φ),

Where A is the amplitude and φ is the phase angle.

The phase angle is zero in this case because the mass is at maximum displacement when t = 0.

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The trigonometric values are:

\(cos(\frac{3\pi}{4})=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=\frac{1}{\sqrt{2} }\)

The given trigonometric identities are:

\(cos(\frac{3\pi}{4} )\\\\sin(\frac{3\pi}{4})\)

Note that:

\(\pi=180^o\\\\\frac{3\pi}{4}=135^0\)

Therefore, using the calculator for the given expressions:

\(cos(\frac{3\pi}{4})=cos135^0=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=sin135^0=\frac{1}{\sqrt{2} }\)

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Answer: Dome Fuji, in Antarctica, is the coldest place in the world with a record low of –92 degrees.

Step-by-step explanation:

Answer:

Lines 1 and 4 are parallel

Step-by-step explanation:

The image below shows the four lines graphed, and proves that lines 1 and 4 are parallel.

Hope this helps! :)

Answer:

if you want to solve for x=1.5

if you want to solve for y=3

Answer:

y = -3 + 2x

x = 3/2 + 1/2y

x = 3/2

Step-by-step explanation:

If you need what y is equal to:

10x - 5y = 15

-10x           -10x

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

-5y = 15 - 10x

-----     ----------

-5           -5

y = -3 + 2x

If you need what x is equal to:

10x - 5y = 15

       +5y   +5y

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

    10x = 15 + 5y

    -----    ----------

     10         10

       x = 15/10 + 5/10 y

Simplify by 5:

x = 3/2 + 1/2y

10x + (-3 + 2x) = 15

12x - 3 = 15

      +3    +3

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

  12x = 18

  -----   -----

    12     12

      x = 9/6 = 3/2

Hope this helped.

hypotenuse of a right triangle is always the side opposite the right angle.

In geometry, a right triangle is a type of triangle that contains one angle measuring 90 degrees, known as the right angle. Right triangles have several distinguishing properties, and one of the fundamental concepts associated with them is the identification of the sides relative to the right angle. In this detailed explanation, we will explore the term that describes the specific side of a right triangle that is always opposite the right angle.

In a right triangle, there are three sides: the hypotenuse, the adjacent side, and the opposite side. The hypotenuse is the side opposite the right angle and is the longest side of the triangle. The adjacent side is the side that forms the right angle with the hypotenuse, while the opposite side is the side that is opposite the right angle. The term that refers to the side of a right triangle that is always opposite the right angle is the "hypotenuse."

To better understand the concept, let's consider the Pythagorean theorem, which is a fundamental relationship in right triangles. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be expressed as:

\(c^2 = a^2 + b^2\)

In this equation, "c" represents the length of the hypotenuse, while "a" and "b" represent the lengths of the other two sides (adjacent and opposite). By rearranging the equation, we can solve for the hypotenuse (c):

\(c = \sqrt(a^2 + b^2)\)

From this equation, we can see that the hypotenuse is determined by the lengths of the other two sides of the right triangle. The relationship expressed by the Pythagorean theorem highlights the importance of the hypotenuse in determining the overall shape and size of the right triangle.

Furthermore, the hypotenuse is significant because it provides the longest side of the right triangle. Its length directly influences the triangle's shape and can be used to calculate various properties, such as the triangle's area or the lengths of the other sides.

In trigonometry, the hypotenuse is also crucial for defining trigonometric ratios, such as sine, cosine, and tangent, which are used to establish relationships between the sides and angles of a right triangle.

In conclusion, the side of a right triangle that is always opposite the right angle is called the "hypotenuse." It is the longest side of the triangle and is directly related to the lengths of the other two sides through the Pythagorean theorem. Understanding the concept of the hypotenuse is essential for working with right triangles, as it plays a fundamental role in determining the triangle's properties, shape, and trigonometric relationships.

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Ishmael can use a screen capture tool and screen recording software to achieve this.

Ishmael should learn more about the selected screen capture software and its features. After installing and launching the software, he can select the specific area of the screen he wants to capture. Once the desired portion is selected, he can start the screen recording feature and perform the actions he wishes to capture. The software will record everything within the selected area, including the actions performed. After completing the actions, he can stop the recording, save the video file, and review it as needed.

How to use screen capture software and its features, Ishmael can refer to the software's documentation, online tutorials, or user forums. These resources can provide detailed instructions on selecting specific screen areas, starting and stopping recordings, and saving the captured footage. Additionally, exploring the software's settings and options can help customize the recording experience to meet Ishmael's specific needs.

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The amount needed in the account is 182,713.25 dollars then the correct option is B.

The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.

Then the formula of monthly payment (MP) will be

\(\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\\)

The formula can be written as

\(\rm P = MP \times \dfrac{(1+r)^n-1}{r(1+r)^n}\\\)

You plan on supplementing your income. you would like to withdraw a semiannual salary of $6,951.20 from an account paying 1.75% interest, compounded semiannually.

The amount needed in the account is such that you can withdraw the needed amount at the end of each period for 15 years will be

MP = $6951.20

r = 0.00875

n = 30

Then we have

\(\rm P = 6951.20 \times \dfrac{(1+0.00875)^{30}-1}{0.00875(1+0.00875)^{30}}\\\\P = \$182713.25\)

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Answer:

60x8=6x8=48x10=480

Step-by-step explanation:

Answer: 55

Step-by-step explanation:

lets say dads age is y

lets look at the first sentence and set up an equation... with ana's age meaning x

\(x = \frac{1}{5}y + 7\)

ok now the second sentence

\(y+19=(x+19)2\)

so now lets actually work these problems out and aim to get a number without any variables on one side.

lets start with the first equation

\(x-\frac{1}{5}y=7\)

and now the next equation, distribute the 2.

\(y+19=2x+38\)

\(y-19=2x\)

now just switch 2x and 19 but remember do the opposite on both sides of the equal sign

\(y-2x=19\)

ok so now we have our final two equations here to solve our System of Equations™ just rearrange the second equation so that the x and y line up with the first equation

\(x-\frac{1}{5}y=7\)

\(-2x+y=19\)

lets MULTIPLY THE FIRST EQUATION BY 2 because then that will make the x's OPPOSITES.

\(2(x- \frac{1}{5}y=7)\\2x- \frac{2}{5}y=14\)

now we can add them

\(2x- \frac{2}{5}y=14\)

\(-2x+y=19\)

just literally add the x and ys together and the constants

\(\frac{3}{5}y = 33\)

divide 33 by 3/5

dads age is 55

The sampling probability refers to the property of an element of a given population in its given probability to become a part of a sample during the drawing of a single sample.

It is a defined and distinguished technique that is based on the principle of random selection to study a certain part of a concerning population. Furthermore, in this specific method, every member of the population has the possibility of having an equal chance of being chosen for the sample.

One backlash in the field of using sampling probability is it's very time-consuming and has a higher expenditure in comparison to other methods.

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9514 1404 393

Answer:

Step-by-step explanation:

The limit of any polynomial function at a point is the value of the polynomial at that point. A polynomial is defined and continuous for all values of the independent variable.

The limit of a rational function at a "hole" is the value of the simplified function at that point.

1a) lim = 4+3+2-2 = 7

1b) lim = (3)(-3)(3) = -27

1c) lim = 3^2+9 = 18

1d) lim = (x+4) = 4+4 = 8

1e) lim = 3x+1 = 3(1/3) +1 = 2

1f) lim = x^2/x^2 = 1

_____

The expressions of (e) and (f) can be simplified by factoring the difference of squares: a^2 -b^2 = (a -b)(a +b). In each case, one of the factors cancels the one in the denominator, so the remaining function can be evaluated at the limit point.

As x approaches infinity, the only terms of a rational expression that matter are those of the highest degree in numerator and denominator. (There's a little more to it if the numerator has a higher degree than the denominator.)

We are given the solid e bounded by the surfaces y = 4 - x^2 z^2 and y = 0. We need to express the integral ∭e f(x, y, z) dV as an iterated integral in the order dz dy dx.

To set up the limits of integration, we need to find the bounds for z, y, and x. Since the solid is bounded below by the xy-plane (y = 0) and above by the surface y = 4 - x^2 z^2, we have 0 ≤ y ≤ 4 - x^2 z^2.

Since we are integrating with respect to z first, we need to find the bounds for z in terms of x and y. Solving for z in the equation y = 4 - x^2 z^2, we get z = ±√(4 - y)/x^2. Since the solid is bounded by the surfaces y = 4 - x^2 z^2 and y = 0, we only need to consider the positive square root, so we have 0 ≤ z ≤ √(4 - y)/x^2.

Finally, since we are integrating with respect to y next, we need to find the bounds for y in terms of x. The solid is symmetric about the yz-plane, so we can integrate over the half of the solid where x ≥ 0 and multiply by 2.

We have 0 ≤ y ≤ 4 - x^2 z^2, and since 0 ≤ z ≤ √(4 - y)/x^2, we have 0 ≤ y ≤ 4x^2.

Thus, the integral becomes:

∫∫∫e f(x, y, z) dV = ∫0^∞ ∫0^(4x^2) ∫0^√(4 - y)/x^2 f(x, y, z) dz dy dx

where e = {(x, y, z) | 0 ≤ z ≤ √(4 - y)/x^2, 0 ≤ y ≤ 4 - x^2 z^2, x ≥ 0}.

Note that we have integrated in the order dz dy dx.

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Answer:

No, no es

Step-by-step explanation:

Answer:

first blank is 55

second blank is 121

Step-by-step explanation:

Hope this helped :)

Answer:

55 and 121

Step-by-step explanation:

22/11 =2  55/11=5   121/11=11

Hope this helped and if you can can i have a brainliest  thank you

Answer:

240

Step-by-step explanation:

1 foot=12 inches.

12 inchest times 20=240

In 1 square feet there will be  0..0025 inches on the scaled diagram.

Conversion of one unit to another unit of measurement for the same quantity using multiplication/division by conversion factors is known as unit conversion of measurement.

For example,

1 kg = 1000g

⇒ 1 gm = 1/1000kg

According to the given question.

1 inch = 20 feet.

⇒ \(1 feet = \frac{1}{20} inch\)

⇒\(1^{2} (feet)^{2} = (\frac{1}{20} )^{2} (inch)^{2}\)

⇒ 1 square feet = 1/400 square inches

⇒ 1 square feet = 0.0025 square inches

Hence, in 1 square feet there will be  0..0025 inches on the scaled diagram.

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The expression for the above statement =  (7x + 5)/(- 2x + 11)

The correct option is C.

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout nearly all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.

let a number be x

Consequently, the result of seven times a number plus five is

7x + 5

Moreover, add the negative sums of two times the number and eleven.

- 2x + 11

Now, you can write the sentence "the total of seven times a number and five, divided by the sum of negative two times the number and eleven" as

(7x + 5)/(- 2x + 11)

The expression for the above statement =  (7x + 5)/(- 2x + 11)

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I understand that the question you are looking for is :

Write the expression "the sum of seven times a number and five, divided by the sum of negative two times the number and eleven" using algebra. choose the correct phrase below.

A. (–2x + 11) ÷ (7x + 5)

B. (–2x + 11) (7x + 5)

C. (7x + 5) (–2x + 11)

D. (7x + 5) ÷ (–2x + 11)

Answer:

the answer is (7x+5)/(-2x+11)

Step-by-step explanation:

the other answer is correct

A. By the given conditions, the function f has a root in the interval [a, b].

B. The given conditions provide information about the function f and its derivatives.

Let's analyze the conditions step by step:

1. f(a) < 0 and f(b) > 0: This implies that function f takes negative values at the left endpoint a and positive values at the right endpoint b.

In other words, the function changes the sign between a and b.

2. f'(x) > 0 for all x in (a, b): This condition states that the derivative of f, denoted as f'(x), is always positive in the open interval (a, b).

This indicates that the function is increasing within this interval.

3. f''(x) > 0 for all x in (a, b): This condition states that the second derivative of f, denoted as f''(x), is always positive in the open interval (a, b).

This indicates that the function is concave up within this interval.

By combining these conditions, we can conclude that the function f is continuous, increasing, and concave up within the interval (a, b).

Since f(a) < 0 and f(b) > 0, and the function changes sign between a and b, by the Intermediate Value Theorem, there exists at least one root of the function f in the interval [a, b].

Therefore, the main answer is that the function f has a root in the interval [a, b].

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The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

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Answer:

The percent decrease in the price of shirt is 27.78%

Step-by-step explanation:

The percent decrease is the decrease in the price of a product or good.

Given

Original Price = $45

Decreased price = $32.50

Percentage decrease is calculated by using the formula

\(Percentage\ decrease = \frac{decrease}{Original\ price} *100\\\)

And the decrease is calculated as:

\(Decrease = Original\ price - Reduced\ price\)

So,

\(Decrease = 45-32.50 = 12.5\)

Putting the values in the formula for percent decrease

\(Percent\ decrease = \frac{12.50}{45} *100\\=0.2777..*100\\= 27.77..\)

Rounding off to nearest hundredth: 27.78%

Hence

The percent decrease in the price of shirt is 27.78%

Answer:

Step-by-step explanation:

Let the line 4x-y+k=0

Now 4×(-2)-4+k=0

K=12

So, the line will be 4x -y +12

Answer:

The answer is

\(k = 48\)

The required area under the whole probability density curve is given by option C. 1.

The area under the entire probability density curve is equal to,

As the probability density function (pdf) represents the probability of a continuous random variable.

And continuous random variable taking on a specific value within a certain range.

Since the total probability of all possible outcomes must be equal to 1.

This implies that the area under the entire probability density function (pdf) curve must also be equal to 1.

Therefore, the area under the entire probability density curve function is equal to option c. 1.

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Answer:

A. B.

Step-by-step explanation:

Answer:

To solve this problem, we need to use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.

Step 1: We know that the radius of the tank is 2 feet and that it is being filled at a rate of 4 cubic feet per minute. We also know that the tank is half full, so we can assume that the height of the water in the tank is half the height of the tank itself.

Step 2: We can use the volume formula to find the volume of the tank when it is half full.

V = πr^2h

V = π(2^2)(h/2)

V = 4πh/2

Step 3: We can divide the rate of fill by the volume of the tank when it is half full to find the rate of change of the height of the water.

dh/dt = 4/(4π/2)

dh/dt = 2/π ft/min

Final Answer: The level of the water in the tank is rising at a rate of 2/π feet per minute when the tank is half full.

The estimated measure of the angle formed by Nuuk, the North Pole, and the Prime Meridian is approximately 25.825° in terms of latitude and 51.738° in terms of longitude.

To estimate the measure of the angle formed by Nuuk, Greenland, the North Pole, and the Prime Meridian, we need to consider the geographic coordinates of Nuuk, as well as the concept of latitude and longitude.

Nuuk, Greenland is located at approximately 64.175°N latitude and 51.738°W longitude. The North Pole is located at 90°N latitude, and the Prime Meridian runs through Greenwich, London, at 0° longitude.

The angle formed by these three points can be estimated by considering the difference in latitude and longitude between Nuuk and the North Pole, as well as between Nuuk and the Prime Meridian.

In terms of latitude, the difference between Nuuk (64.175°N) and the North Pole (90°N) is approximately 25.825°. Similarly, in terms of longitude, the difference between Nuuk (51.738°W) and the Prime Meridian (0°) is approximately 51.738°.

Therefore, the estimated measure of the angle formed by Nuuk, the North Pole, and the Prime Meridian is approximately 25.825° in terms of latitude and 51.738° in terms of longitude.

It is important to note that this is an estimated value and not an exact calculation. The actual angle formed may vary slightly due to the curvature of the Earth and the specific location of the points.

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Answer:

C.) 7√2/2

Step-by-step explanation:

tan¤ = opp/adj

tan 45° = y/7√2/2

1 = y/7√2/2

1 = 2y/7√2

7√2 = 2y

2y = 7√2

y = 7√2/2

NOTE: ¤ = Theta

Answer: 11

Step-by-step explanation:

The type of transformation is described by (x, y) --> (x + 9, y - 3) is a translation transformation

The transformation is described by (x, y) --> (x + 9, y - 3)

Write out the transformation rule

So, we have

(x, y) --> (x + 9, y - 3)

There are four types of transformation, and they are:

The representation of the types of transformation are:

By comparing the rules of the above types of transformation, we can see that (x, y) --> (x + 9, y - 3) has the same format as the translation transformation

Hence, the type of transformation is described by (x, y) --> (x + 9, y - 3) is a translation transformation

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The correct option is option D

The total number of Yogs used for a bonfire, if 5 new logs are added each hour​