what is the answer for this maths watch question?

The value of k such the the solution of differential equation of dx/dt = kx is k = ln(3).

By multiplying the original exponential function by the derivative of its power, one can differentiate an exponential.

The rule for differentiating an exponential function is  f(x)=a^u = a^t ln(t).

The given function is:

x(t) = 3^t

Using the differential rule for the exponential function we have:

d/ dt (3^t) = 3^t ln(3)

Substituting the value of x(t) in the equation with 3^t ln(3) we have:

3^t ln(3) = k 3^t

Since 3^t is a non-zero expression the value of k corresponding to the given value is:

ln(3) = k

Hence, the value of k such the the solution of differential equation of dx/dt = kx is k = ln(3).

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For Deepa to find his yearly balance in a single step, he must multiply his money by 1.01

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period. Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The following calculation must be done in order to determine what Deepa should multiply his current balance by in order to find his total balance in a year in one step if no money will be added to or removed from the investment. Deepa invests money in an account that pays a simple interest rate of 1% per year.

Current balance = X

Interest = 1% = 1/100 = 0.01

Interest + principal = 1.01

1.01X = Total balance in a year

Deepa must therefore multiply her money by 1.01 in order to determine it in a single step.

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The table can be written as,

Minutes   Gallons

9                   1

18                 2

27                3

36                4

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

At the end of 18 minutes, it has filled 2.

This can be written as

y = kx

Where x is minutes and y is the number of gallons.

So,

2 = 18k

k = 2/18 = 1/9

Now,

The equation is y = (1/9)x

The table can be written as,

Minutes   Gallons

9                   1

18                 2

27                3

36                4

       
Thus,

The table that represents the relationship between the number of minutes and the number of gallons of water in the pool is given above.

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Answer:$45.60

Step-by-step explanation:

p=%w

69.8(.60)w

/.6 /.6

116. =w

-69.8

46.5

Answer:

349/5/5

Step-by-step explanation:

(69,8) % of 60x$

simplify the expression

Answer:

the angle of SQR = 40°

Step-by-step explanation:

in any triangle, the sum of all angles will be equal to 180°

by adding RSQ and QRS you get 140°

180°-140°=40°

The measurement of angle ∠SQR is 40 degrees

We are given that  triangle QRS the measure of angle RSQ is 117°, and the measure of angle QRS is 23°.

Since we know that in any triangle, the sum of all angles will be equal to 180°

To find the total angle of any polygon, use the formula = 180(n-2)

The "n" is number of sides a polygon have. Triangle has 3 sides.

Hence,substitute as n=3 in the formula above.

Total angle in a triangle =180(3-2)= 180(1)

= 180 degrees

∠QRS+∠RSQ+∠SQR=180°

180°-140°=40°

The angle SQR= 40°

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$6273.04 have to deposit at the end of each of the next 5 years to fund this liability

PV of Annuity = P*[1-{[tex]{1+i}^{n}[/tex]}]/i

Where, P = Annuity = 12000, i = Interest Rate = 0.08, n = Number of Periods = 4

PV at 6 years from today = 12000*[1-{(1+0.08)^-4}]/0.08 = 12000*0.26497/0.08 = $39745.52

PV at 5 years from today = PV at 6 years from today/[1+Interest Rate] = 39745.52/[1+0.08] = $36801.41

FV of Annuity = P*[{[tex]1+i^{n}[/tex]}-1]/i

Where, FV = 36801.41, i = Interest Rate = 0.08, n = Number of Periods = 5

Therefore,

36801.41 = P*[{(1+0.08)^5}-1]/0.08

2944.1127 = P*0.469328

Therefore, Amount to be deposited =

                                 P = 2944.1127/0.469328 = $6273.04

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Answer: It is approximately 49.2126 or 49, for short.

Step-by-step explanation:

For a more approximate result, multiply the length value by 3.281

49.21 feet or 15 meters are the same.

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Answer: the answer is 189

Step-by-step explanation:

At 2:30 AM,

the pool will be full.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

At 9:30 AM,

Sean started filling a 4,500-gallonswimming pool.

At 11:30 AM,

he had filled 1,800 gallons.

The unit rate = 1800/2 = 900 gallons per hour.

The pool completely filled in 5 hours.

Therefore, the pool be full at 2:30 AM.

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The complete question:

At 9:30 AM,

Sean started filling a4,500-gallonswimming =~ pool. At 11:30 a.m., he had filled 1,800 : gallons. At what time will the pool be full? :

Answer:

1.725

Step-by-step explanation:

1/4 or .25 multiplied by the total of 6.9

Eloise correctly determined the volume of this prism by multiplying the three dimensions, She got a product of  (3×8×4) unit³.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

The given figure is a cuboid made up of unit cubes.

We know the volume of a cuboid is (length×width×height).

By observing the figure we have 3 unit cubes of width, 8 unit cubes of length, and 4 unit cubes of height.

Therefore, The volume of the cuboid is,

= (3×8×4) unit³.

= 96 unit³.

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The area of the trapezoid is 24 square units.

What is the area of the trapezoid?

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. In British and other dialects of English, it is referred to as a trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. Its parallel sides serve as its bases.

The area of a trapezoid can be calculated by using the formula:

Area = (a + b)h / 2,

where a and b are the lengths of the parallel sides and h is the height.

By the given figure, we can find the area of the trapezoid

Area = (a+b)h/2
Area = (4.3 + 7.7)*4/2
Area = 12*4/2
Area = 24 Square units.

Hence, the area of the trapezoid is 24 square units.

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Answer:

Reflexive Property

Answer:

reflexive property

Step-by-step explanation:

We can use the reflexive property to state that LN = LN.

It states that a value is equal to itself.

Answer:

2) 1885 km

3) 795 h 46 m 29 s

Step-by-step explanation:

2)

C = 2πr

C = 2 × 3.14159 × 300 km

C = 1885 km

3)

(1000000 km)/ (1885 km/tour) = 530.16477 tours

1 tour = 1 h 30 m = 1.5 h

530.16477 tours = 530.16477 × 1.5 h = 795.7747155 h = 795 h 46 m 29 s

Answer: (-3,6)

Step-by-step explanation:

The point is 3 spaces to the left in the second quadrant on the x-axis which is negative

Then it is 6 spaces up on the y-axis which is positive

The formula for the sum of cubes of the first n natural numbers is:

(1^3 + 2^3 + 3^3 + ... + n^3) = (1 + 2 + 3 + ... + n)^2

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The value of x is 6

The possible error could your friend have made to get x​ = -2 is Your friend should have added 5x and 4x to get a sum of 9​x, but instead got a sum of 8x. Option C

Algebraic expressions are described as expressions that are composed of variable, terms, coefficients, factors and constants.

These expressions are also made up of mathematical or arithmetic operations. These operations include;

From the information given, we have the equation;

5x + 4x - 68 = 34 - 8x

collect like terms

5x + 4x + 8x = 34 + 68

Add or subtract the like terms

17x = 102

Divide both sides by the coefficient of the variable, we get;

17x/17 = 102/17

x = 6

Hence, the value is 6

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The slope is:

Work/explanation:

To find the slope, I use the slope formula

[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m = slope.

Plug in the data

[tex]\sf{m=\dfrac{-2-4}{14-(-1)}[/tex]

Simplify

[tex]\sf{m=\dfrac{-6}{14+1}}[/tex]

Simplify the denominator

[tex]\sf{m=-\dfrac{6}{15}}[/tex]

Finally, reduce the fraction to its lowest terms.

[tex]\sf{m=-\dfrac{2}{5}}[/tex]

The inverse of the cosecant function is the secant function so option A is correct.

In mathematics, the inverse of a function "f" is another function "g" such that when "f" is applied to an input "x", the result is "x". And when "g" is applied to the result, the original input "x" is recovered. This relationship can be expressed as: f(g(x)) = x and g(f(x)) = x.

The cosecant function is defined as the reciprocal of the sine function, so csc(x) = 1/sin(x). The inverse of the cosecant function is the secant function, which is defined as the reciprocal of the cosine function, so sec(x) = 1/cos(x).

In other words, when the cosecant function is applied to an angle "x", the result is 1/sin(x), and when the secant function is applied to the result, the original angle "x" is recovered. This relationship can be expressed as: sec(csc(x)) = x and csc(sec(x)) = x.

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The two possible answer is  3(5.5a - 2.4b + 12) that Laine could have written for expression 16.5a - 77.2b + 36 .

Laine could just just used another common number to write it down as,

LCM(165, 36, 72) = 3960

Prime factorization of the numbers:

165 = 3 × 5 × 11

36 = 2 × 2 × 3 × 3

72 = 2 × 2 × 2 × 3 × 3

LCM(165, 36, 72)

= 2 × 2 × 2 × 3 × 3 × 5 × 11

= 3960

GCD(165, 36, 72) = 3

So we get three as a common multiple of them so after removing 3 common from them we can write 16.5a - 7.2b + 36 as

3(5.5a - 2.4b + 12)  

Hence, The two possible answer is  3(5.5a - 2.4b + 12) that Laine could have written for expression 16.5a - 77.2b + 36.

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1 pound is approximately equal to 0.45359237 kilograms. Therefore, 1.5 pounds is approximately equal to 0.45359237 x 1.5 = 0.68 kg

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According to VSEPR (Valence Shell Electron Pair Repulsion) theory, the electron domains around an atom will arrange themselves in a trigonal bipyramidal geometry based on the number of domains in the valence shell.

If there are five electron domains in the valence shell, they will be arranged in a trigonal bipyramidal geometry. In this geometry, the five domains occupy the positions of three axial domains (120 degrees apart) and two equatorial domains (90 degrees apart). This arrangement minimizes the repulsion between the electron domains, leading to a more stable molecule.

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An equivalent expression of 3(2x + 11y) is 6x + 33y.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

3(2x + 11y).

The distributive property:

a(b + c) = ab + ac.

So,

3(2x + 11y) = 6x + 33y

Therefore, 6x + 33y is an equivalent expression.

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The number of performances which the company must put on in order to break even is equal to 10 performances.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-axis, which is given by the ordered pair (10, 4,000).

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Therefore, when the triangle's perimeter is 38 meters and its two sides are 18 meters and 13 meters, respectively, the opposite side of the perimeter is 7 meters.

An isolated path that surrounding, delimits, or embraces a two-dimensional shape or a single-dimension length sometimes referred to as the boundary. The perimeter of either an ellipse or circle refers itself to outermost area. The perimeter measurement has many legitimate applications. This perimeter of a form is its edge's circumference. Discover how to determine the perimeter by adding the lengths of such sides of various forms. Your can always find the perimeter of a polygon by multiplying its multiplicative inverse. The perimeter of an object is the space it around. At your house, a contained garden is one illustration. The perimeter of anything is the area encircling it. For a 50 feet x 50 feet yard, a 200 foot fence is required.

given

The distance surrounding a closed-plane figure is its perimeter, or P.

P is equal to a plus b plus c, where a, b, and c are the lengths of the three sides, and let c be the third side's undetermined length.

P = 38 m, a = 13 m, and b = 18 m are the values provided. Now, to determine the third side's length c,

P = a + b + c

38m = 13m, 18m, and c

38 m = 31 m + c

38 m minus 31 m Equals 31 m minus 31 m plus c

7 m = 0 + c

7 m = c

Therefore, when the triangle's perimeter is 38 meters and its two sides are 18 meters and 13 meters, respectively, the opposite side of the perimeter is 7 meters.

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Check the picture below.

Step 1: limx→0[f(x)+g(x)] .Rule or Limit Law used: Sum Rule for Limits.

Step 2: limx→0f(x)+limx→0g(x) .Rule or Limit Law used: Limit of a Sum Rule.

Step 1: limx→0[f(x)+g(x)]

This first step is using the sum Rule for Limits. This rule states that the limit of the sum of two functions is equal to the sum of the limits of the individual functions. So in this case, the limit of the sum of f(x) and g(x) is equal to the sum of the limits of f(x) and g(x) individually.

Step 2: limx→0f(x)+limx→0g(x)

This second step uses the Limit of a Sum Rule. This rule states that the limit of the sum of two functions is equal to the sum of the individual limits of the functions. So in this case, the limit of the sum of f(x) and g(x) is equal to the sum of the individual limits of f(x) and g(x). This is the same result as in the first step, but using a different rule.

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Answer: Quotient is 3.6*10^10/5 and the standard form is 7.2*10^9

Step-by-step explanation:

Answer:

Step-by-step explanation:

3.6×10∧10÷5=0.72×10∧10

standard form=7.2×10∧9

The tip of the pendulum travels 22.33 inches in a singles swing.

A pendulum is a weight suspended from a pivot so that it can swing back and forth under the influence of gravity. Pendulums are commonly used as timekeepers in clocks, but they also have other applications, such as in seismology, where they can be used to detect earthquakes.

Each swing does an angle of 40° in each direction, so we have a total angle of 80°.

Then, we want to get the length of an arc defined by an angle of 80° on a circle with a radius of 16 in, this is:

L = (80°/360°) * 3.14 * (2 * 16 in)

   = 22.33 in.

The distance that the tip of the pendulum travels on each swing is 22.33 inches.

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The tip of the pendulum travels approximately 28.3 inches in a single swing through an angle of 40 degrees.

To calculate how far the tip of the pendulum travels in a single swing through an angle of 40 degrees, we will use the formula:

Distance = 2 * PI * Length * (angle / 360)

Where PI is approximately 3.14 and Length refers to the length of the pendulum.

In this case, the length of the pendulum is 16 inches. Therefore, we can substitute these values into the formula:

Distance = 2 * 3.14 * 16 * (40 / 360)

Distance = 2 * 3.14 * 16 * 0.111

Distance = 28.3 inches

Therefore, the tip of the pendulum travels approximately 28.3 inches in a single swing through an angle of 40 degrees.

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The distance from the base's center at that time is 18 feet.

What is function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

A function is typically represented as y = f. (x).

h(x) = 16 ft x is the distance from the base when

h(x) = 16 h(x) = -IxI + 34

when a raindrop falls from the end of the roof.

16 = -IxI + 34

IxI = 34 – 16 = 18

It might land on the roof's opposite end.

The distance from the base's center at that time is 18 feet.

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