find the value of k for which the constant function x(t) = k is a solution of the differential equation . 4t^3 dx/dt + 2x - 2 =0

The next string produced by the next subset algorithm will be 111101. This is achieved by adding one to the rightmost bit of the given string, which in this case is the last digit of 110101. This causes the last digit to change from a 0 to a 1, resulting in the new string 111101.

The next subset algorithm works by taking the given string, in this case 110101, and adding one to the rightmost bit of the string. This causes the rightmost bit to change from a 0 to a 1, and all of the digits to the left of this bit will remain unchanged. In the case of 110101, the rightmost bit is the last digit, so it will change from a 0 to a 1, resulting in the new string 111101. This process can be repeated for any given string, and the result will always be the string with one more 1 than the given string. For example, if the given string was 111000, the result would be 111001, and if the given string was 111111, the result would be 1000000.

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On solving the provided question we can say that since it is given that triangles are similar and 1/2 of each other so DE will be = 13

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

since it is given that triangles are similar and 1/2 of each other

so DE will be = 13

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The number of students in vans are 13 whereas in buses it is 31.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, the School A rented and filled 5 vans and 6 buses with 251 students, and School B rented and filled 6 vans and 14 buses with 512 students.

Let the number of student in vans be v and that of in buses be b, therefore, establishing the system of equations,

5v + 6b = 251.....(i)

6v + 14b = 512....(ii)

Multiplying eq(i) by 6 and eq(ii) by 5

30v + 36b = 1506...(iii)

30v + 70b = 2560....(iv)

Subtracting eq(iii) from (iv)

(30v + 70b = 2560) - (30v + 36b = 1506)

34b = 1054

b = 31

Put b = 31 in eq(i)

5v + 6×31 = 251

5v = 65

v = 13

Hence, the number of students in vans are 13 whereas in buses it is 31.

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The measures of those two angles are 105° and 135°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Two angles of a quadrilateral measure 110° and 10°.

And, The other two angles are in a ratio of 7 : 9.

Now, We know that;

The sum of all four interior angles of a quadrilateral are 360°.

Here, The other two angles are in a ratio of 7 : 9.

Hence, Measure of both angles are 7x and 9x.

So, We get;

⇒ 110° + 10° + 7x + 9x = 360°

⇒ 120 + 16x = 360

⇒ 16x = 360 - 120

⇒ 16x = 240

⇒ x = 15

Thus, Measure of both angles are;

⇒ 7x = 7 × 15 = 105°

⇒ 9x = 9 × 15 = 135°

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Answer:

8000 pounds

Step-by-step explanation:

1 ton is 2000 pounds

Therefore we can use the equation: 4x2000 which is:

8000 pounds

Answer:

4 tonnes =

8818.49 pounds

[tex]4 \: tones \: = \: 8818.49 \: pounds \\ \: is \: the \: answer \: of \: ur \: question[/tex]

The required function is y=11.047t + 199.12

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The given table shows the balance of a money market account over time.

Time (t)     Balance(y)

0                     200

1                      210

2                    220.5

3                    231.53

4                     243.1

5                   255.26

The function that represents the balance y(in dollars) after t years is a linear regression line because the value of y increased linearly.

The linear regression function is defined as y =bx +a

Where,

a= ∑y(∑x²)-∑x(∑xy) / n(∑x²)-(∑x)²

b= n(∑xy)-∑x(∑y) / n(∑x²)-(∑x)²

Put the values from the table attached below in the above formulas.

The value of b is 11.047 and the value of a is 199.12.

Here, the variable is t.

Therefore the required function is  y=11.047t + 199.12.

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Answer:

64 2s..?

Step-by-step explanation:

I sure as hell wouldn't trust this awnser bcz I got it from a friend-..

Step-by-step explanation:

The definite integral of the function (2x - 3) with respect to x can be found using the antiderivative, also known as indefinite integration.

The antiderivative of (2x - 3) is:x^2 - 3x + C, where C is the constant of integration.

For the definite integral, we need to find the antiderivative over a given interval. To calculate the definite integral, we need to evaluate the antiderivative at the limits of the interval and subtract the values.So, for example, if the interval is from a to b, the definite integral is given by:∫_a^b (2x - 3) dx = (x^2 - 3x) |_a^b = (x^2 - 3x) evaluated at b - (x^2 - 3x) evaluated at a.The definite integral of the function y³ (2y² – 3) with respect to y can be found in a similar way. The antiderivative of y³ (2y² – 3) can be found using power rule of integration.The antiderivative of y³ (2y² – 3) is:(1/4) y⁴ - 3y² + C, where C is the constant of integration.The definite integral of the function can then be found by evaluating the antiderivative at the limits of the interval and subtracting the values, as described above.

Credit to khalanopierra on brainly.

Answer:

Below

Step-by-step explanation:

Use triangle side length rule : any two sides must sum to greater than the remaining side

A  nope....   4 + 14 is not GREATER than 18

B  nope  27 + 39  in not greater than 39

C  nope   8 + 8 is not greater than 20

D Yes   13 + 32 > 44     and  13+44>32    and 44+ 32 > 13

By using the quadratic formula, the solution to this quadratic equation is equal to -0.5251 or -3.8081.

In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

From the information provided, we have the following values;

3x² + 13x + 4 = 0

Where:

a = 3

b = 13

c = 4

Substituting the values into the quadratic formula, we have the following;

[tex]x = \frac{-(13)\; \pm \;\sqrt{(13)^2 - 4(3)(13)}}{2(3)}\\\\x = \frac{-13\; \pm \;\sqrt{169 - 72}}{6}[/tex]

x = (-13 + √97)/6

x = -0.5251 or -3.8081.

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The angle opposite to the smallest angle is the smallest side. Thus,

TS < US < TU.

If you have the perimeter P and width w , its length can be found with h = P/2−w . If you have the diagonal d and width w , it's length is h = √(d²−w²). When we're trying to find the hypotenuse we substitute our two known sides for a and b. It doesn't matter which leg is a and which is b. Then we solve for c by adding the squared values of a and b and taking the square root of both sides.

The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.

Every triangle has three sides and three angles, some of which may be the same. The sides of a triangle are given special names in the case of a right triangle, with the side opposite the right angle being termed the hypotenuse and the other two sides being known as the legs.

In the given triangle the angle of interior angle is 180:

43z + z + 66 + z + 69 = 180

45z + 135 = 180

45z = 180 - 135

45z = 45

z = 1

The three angles are:

U = 43(1) = 43

T = 1 + 66 = 67

S = 1 + 69 = 70

The angle opposite to the smallest angle is the smallest side. Thus,

TS < US < TU

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A unit circle has a radius of 1, so r = 1. The point P(9/10, y) in the IV quadrant will have a positive x-value and a negative y-value.

Using the Pythagorean theorem we know that, x² + y² = r², in a Cartesian coordinate system. We can solve for y by rearranging the formula, r² - x2 = y², or y = ±√(r² - x²).

y = ±√(r² - x²)

y = ±√([1]² - [9/10]²)

Simplify the expression we have

y = ±√(1 - 81/100)

y = ±√(1-0.81)

y = ±√0.19, we choose the negative for quadrant IV.

y = -√0.19

y = -0.4359

Sin -0.4359 = 26 degrees in the IV quadrant, = 360-26 =334 degrees

CosA = 0.4359 in the Iv quadrant is positive we chose the positive figure 64 degrees

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Answer:

Account A:

$1,149.15

Account B

$1,906.80

Answer:

Around $174

Step-by-step explanation:

Correct me if I'm wrong

9x16=144

144+30=174

A: (a) A = [0 1; -1 0]. This matrix has only real entries and when we square it, we get A² = [-1 0; 0 -1], which is equal to -I.

(b) B = [0 1; 0 0]. This matrix is not 0, but when we square it, we get B² = [0 0; 0 0], which is equal to 0.

(c) C = [0 1; -1 0] and D = [1 0; 0 -1]. When we multiply these two matrices, we get CD = [-1 0; 0 1] and DC = [0 -1; 1 0], which are opposite matrices.

(d) E = [1 1; 1 1] and F = [-1 1; 1 -1]. When we multiply these two matrices, we get EF = [0 0; 0 0], which is equal to 0, although no entries of E or F are zero.

Here is explanation -

(a) A = [[0, -1], [1, 0]] is a 2x2 matrix with real entries that satisfies A^2 = -I. To see this, we can simply calculate the square of the matrix A:

A^2 = [[0, -1], [1, 0]] * [[0, -1], [1, 0]]

= [[00 + -11, 0*-1 + -10], [10 + 01, 1-1 + 0*0]]

= [[-1, 0], [0, -1]]

As we can see, A^2 = -I, where I is the 2x2 identity matrix.

(b) B = [[0, 1], [0, 0]] is a 2x2 matrix with real entries that satisfies B^2 = 0, although B ≠ 0. To see this, we can calculate the square of the matrix B:

B^2 = [[0, 1], [0, 0]] * [[0, 1], [0, 0]]

= [[00 + 10, 01 + 10], [00 + 00, 01 + 00]]

= [[0, 0], [0, 0]]

As we can see, B^2 = 0, although B ≠ 0.

(c) C = [[0, 1], [-1, 0]] and D = [[0, -1], [1, 0]] are 2x2 matrices with real entries that satisfy CD = -DC. To see this, we can calculate the product of matrices C and D:

CD = [[0, 1], [-1, 0]] * [[0, -1], [1, 0]]

= [[00 + 10, 0*-1 + 11], [-10 + 01, -1-1 + 0*0]]

= [[0, 1], [1, 1]]

DC = [[0, -1], [1, 0]] * [[0, 1], [-1, 0]]

= [[00 - 11, 01 + -10], [10 - 0-1, 11 + 00]]

= [[-1, 0], [1, 1]]

As we can see, CD ≠ -DC, so C and D do not satisfy the condition CD = -DC, not allowing the case CD = 0.

(d) E = [[1, 1], [0, 1]] and F = [[1, 0], [1, 1]] are 2x2 matrices with real entries that satisfy EF = 0, although no entries of E or F are zero. To see this, we can calculate the product of matrices E and F:

EF = [[1, 1], [0, 1]] * [[1, 0], [1, 1]]

= [[11 + 10, 11 + 11], [01 + 10, 01 + 11]]

= [[1, 2], [0, 1]]

As we can see, EF = 0, although no entries of E or F are zero.

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Step-by-step explanation:

x=15 i hope thats the right answer

Answer:

To calculate the speed of the car, you can use the following formula:

Speed = \frac{Distance}{Time}

In this case, the speed of the car is:

Speed = \frac{44 ft}{0.5 s} = 88 ft/s

To convert from feet per second to miles per hour, you can use the following formula:

Miles per hour = \frac{Feet per second}{1.467}

Therefore, the speed of the car is:

Miles per hour = \frac{88 ft/s}{1.467} = 59.89 mph

Answer:

60 miles per hour

Step-by-step explanation:

44ft/0.5 sec * 60sec/1min * 60min/1hr * 1 mile/5280ft =

(44*60*60*1)/(0.5*1*1*5280) =

158400 miles / 2640 hour =

158400÷2640 =

60 miles per hour .

Answer:

Option 3

Step-by-step explanation:

4(2) + 3(9)= 8+27=35

The answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

The equation x3 + y3 = 9 is a cubic equation and is a non-linear equation. As such, it does not have any tangent lines that are horizontal. A tangent line is a line that just touches a point on a curve and has the same slope as the curve at that point. Since the equation is non-linear, the slope of the curve changes at each point, meaning that there cannot be any horizontal tangent lines.

To calculate the slope of the curve at any point (x,y), we use the formula m = (dy/dx) or m = 3*(x2/y2). At these points, the slope of the curve will not be zero, meaning that there is no horizontal tangent line at any point on the curve.

Therefore, the answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

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Answer:

The lowest score was 80, because no student had gotten that grade.

7 students scored higher than 85.

The highest score there was, was 70, cause 4 student got that for a grade.

The range is 3, because the highest amount of studnets was 4 and the lowest was 1.

4 - 1 = 3

Step-by-step explanation:

Hope this helps! =D

The measure of the required angle is [tex]27^{0}[/tex].

The angle is the magnitude or measure of the turn between two lines or planes intersecting each other. It is measured in degrees, radians, or gradians. Angles are used to measure shapes, directions, distances, and other aspects of geometry. Angles can be classified into two types: acute angles and obtuse angles.

In the given figure there are two triangles in the figure:

As we know sum of all the angles of triangle is [tex]180^{0}[/tex],

therefore in the first triangle third angle will be:

[tex]75^{0} + 35^{0} + third angle = 180^{0}[/tex]

∴ Third angle = [tex]180^{0} - 75^{0} - 35^{0} = 70^{0}[/tex]

Using the triangle property third angle of one triangle is equal to its opposite angle in another triangle, we can find the third angle of another triangle also:

[tex]83^{0} + 70^{0} + third angle = 180^{0}[/tex]

∴ Third angle = [tex]180^{0} - 153^{0} =27^{0}[/tex]

Therefore, the required angle is [tex]27^{0}[/tex].

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The equation of the line that passes through the point (2, -3) and is parallel to the line y = 8 is y = -3.

What is the equation ?

The equation is a mathematical statement that shows the relationship between different values. It can be written using symbols, numbers and operations to describe the relationship between one or more variables. An equation usually consists of an equal sign (=) that separates two expressions which have the same value. For example, the equation 2+2=4 states that two plus two is equal to four.

The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Since the line is parallel to the line y = 8, they have the same slope, which is 0. Thus, the equation of the line that passes through the point (2, -3) is y = 0x + (-3). Simplifying this equation, we get y = -3.

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Expected Total Amount = $900

     The simple interest formula, I = PRT (P×R×T)

     where, P = principal amount

                 R = rate of interest

                 T = time period (years)

     so, I = PRT

     I = 500×0.04×20

     I = 400

 By adding the interest (400) to the principal amount (500) , hence she will have $900 in 20 years.

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The total area painted is 12 square inches, rounded to the nearest tenth.

The circumference of the base of the rod is 1 inch, so the diameter is 1/π inch. The radius of the rod is 1/2π inch.

The volume of the rod is the product of the height (4 inches) and the cross-sectional area (πr²), so it is 4πr² = 4π (1/2π)² = 4/4π = 1 cubic inch.

Each piece of the rod will have half the volume, or 0.5 cubic inches.

The surface area of one piece of the rod is the sum of the areas of the lateral surface (2πrh) and the top and bottom circles (2πr²), so it is 2πrh + 2πr² = 2πr (h + r) = 2π (1/2π) (4 + 1/2π) = 4 + 2 = 6 square inches.

Since both pieces of the rod have the same surface area, the total surface area of both pieces is 6 x 2 = 12 square inches.

So the total area painted is 12 square inches, rounded to the nearest tenth.

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Answer:

Step-by-step explanation:

if Suzy has 2 puppies that eat 60 cups of dog food per week

and 3 would eat 90 cups of dog food

and 4 would eat 120 cups per week

just add 60 more cups of food and you would get 180 cups of dog food because

each puppy eats 30 cups of dog food

(hopes this helps!)

Answer:

45 jeweled and 20 enameled music boxes.

Step-by-step explanation:

( j stands for jeweled and e stands for enameled )

j + e = 25        The equation for the original total of music boxes.

3j + 2e = 65    The equation for the current total of music boxes.

15{ j } + 10{e} = 25     Since the total is 25, I know that the variable will be a multiple of 5. (since that's the only way to get a number that ends in 5).

3(15) + 2(10) = 65  

45 + 20 + 65

The ratio of the number of children present to the number of beads is 1:24.

Define ratio.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.

Given,

Total number of student = 25

Total number of beads = 600

If one child is absent,

So, total number of student will be = 24

The ratio of the number of children present to the number of beads:

24:600

Simplifying,

1:25

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complete question

A cla of 25 children hare 600 bead. On a day when 1 child i abent, what i the ratio of the number of children preent to the number of bead?

Work Shown:

y = (1/2)x + 6

y-6 = (1/2)x

2(y-6) = x

x = 2(y - 6)

x = 2y - 12

Rounding to the nearest tenth of a foot, the ramp length is 150.7 feet.

To find the length of the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ramp) is equal to the sum of the squares of the other two sides (the rise and the run).

We have the rise (15 feet) and the run (150 feet), so we can use the formula: ramp length = √(rise^2 + run^2)

Plugging in the values, we have: ramp length = √(15^2 + 150^2) = √(225 + 22500) = √22725 = 150.7 feet

Therefore, rounding to the nearest tenth of a foot, the ramp length is 150.7 feet.

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