A. Solve the following initial value problem:
(t2−16t+60)dy/dt=y
with y(8)=1. (Find y as a function of t.)
y= .

B. On what interval is the solution valid?
Answer: It is valid for ?
C. Find the limit of the solution as t approaches the left end of the interval.
(Your answer should be a number or the word "infinite".)
Answer: .

D. Similar to C, but for the right end.
Answer: .

Answer: 0.0008

Please correct me if I'm wrong.

The probability of getting exactly two hearts from a well-shuffled standard deck of playing cards can be calculated as follows:Since there are 13 hearts in a standard deck of playing cards, the probability of getting a heart in one draw is 13/52

A heart card is one of the four suits in a standard deck of playing cards. The standard deck of playing cards has 52 cards, including 13 cards in each of the four suits: clubs, diamonds, spades, and hearts. The hearts suit is usually represented by a red heart symbol. Each suit has cards numbered from Ace to King.A standard deck of playing cards is a deck of playing cards that consists of 52 cards, including four suits: spades, hearts, diamonds, and clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. The cards in a standard deck are usually used for playing a variety of card games, such as poker, solitaire, bridge, blackjack, and many others. The standard deck of playing cards has been used for centuries and is still widely used for both casual and professional gaming.

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True statement about the kinetic energies between Daniel and Robert is that Daniel has more kinetic energy than Robert.

Kinetic energy will be greater if the speed and mass are large, otherwise the kinetic energy will be smaller if the speed and mass are small.

At the illustration, who has a faster speed is Daniel.

It is stated that the rowing device and its mass are the same. So a greater speed will also affect the kinetic energy which will also be greater. So it can be conclude that Daniel has more energy kinetic.

Your question is incomplete but most probably your full question was:

Daniel and Robert went rowing. While Robert was rowing at a speed of 8 km/h, Daniel was rowing at a speed of 10 km/h in the opposite direction. If the masses of the boats and their rowers are equal, which of the following is a true statement about their kinetic energies?

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The distance of the run is 11.67 miles.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Speed of first jogger = 5 mph

Speed of second jogger = 4 mph

Let d be the distance in miles of the run.

Time taken by first jogger be t hours.

Time taken by second jogger = t + (35 minutes) = t + (7/12) hours

Speed = Distance / Time

5 = d / t and 4 = d / (t + 7/12)

d = 5t and d = 4 (t + 7/12)

5t = 4 (t + 7/12)

5t = 4t + 7/3

t = 7/3 hours

d = 5t = 11.67 miles.

Hence the distance ran by both joggers is 11.67 miles.

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Answer:

18 3/4

Step-by-step explanation:

Answer:

18 3/4 or 75/4

Step-by-step explanation:

The simplified form of the given expression is 2a+b/2b+a.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is [tex]\frac{\frac{1}{a}+ \frac{2}{b} }{\frac{2}{a}+ \frac{1}{b} }[/tex].

The expression can be simplified as follows

[tex]\frac{\frac{b+2a}{ab} }{\frac{2b+a}{ab} }[/tex]

= 2a+b/2b+a

Therefore, the simplified form of the given expression is 2a+b/2b+a.

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Yes 12 inches converted to centimeters is around 30 cm

Answer:

the length of each side will b s.

Temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.

The physical concept of temperature indicates in numerical form how hot or cold something is.

A thermometer is used to determine temperature.

One variable that makes use of the scale interval is temperature.

Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.

The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes.

One of the seven base units in the International System of Units is the kelvin (SI). The lowest point on the thermodynamic temperature scale is absolute zero, or zero Kelvin, or 273.15 °C.

Therefore, the temperature is a variable that uses (2) the scale interval and, according to physical theory, represents in the numerical form how hot or cold something is.

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The statement that represents the ratio of cars to trains would be = 3 over 1. That is option C.

A ratio is defined as the expression that represents the comparison between two values.

The collection of vehicle models of Alex include the following:

The number of airplane = 8

The number of trains = 4

The number of cars = 12

Therefore, the ratio of cars to train = 12:4

This is further reduced to a simplest form;

= 12:4 ( divide through by 4)

= 3:1

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50%

since 98/2 = 49

Thats it

Answer:

see below

Step-by-step explanation:

r=2

arc = 3π

clock area = π r² =4π

circumference = 2πr =4π

subtended arc =3π = 75% of the clock

360° for a full circle so its central angle is 270°

The equation of the perpendicular line is y = -4/3 x + 12.

The equation of the parallel line is y = 3/4 x + 2.

Perpendicular lines are two lines that cross one other and create a 90-degree angle.

Consider the line y= (3/4)x+6.

To find the equation of the line that is perpendicular to the line y = (3/4)x + 6 and passes through the point (-8, -4), we need to find the slope of the perpendicular line.

Since the slope of a line perpendicular to another line is the negative reciprocal of the original line.

The slope of the line y = (3/4)x + 6 is m = 3/4.

Therefore, the slope of the perpendicular line is -4/3.

Plugging in the values we have, we get:

y - (-4) = -4/3 (x - (-8))

Simplifying, we get:

y + 4 = -4/3 x + 8

y = -4/3 x + 12

So the equation of the perpendicular line is y = -4/3 x + 12.

To find the equation of the line that is parallel to the line y = (3/4)x + 6 and passes through the point (-8, -4), we need to use the same slope, m = 3/4, as the original line.

Using the point-slope form of a line, we get:

y - (-4) = 3/4 (x - (-8))

Simplifying, we get:

y + 4 = 3/4 x + 6

y = 3/4 x + 2

So the equation of the parallel line is y = 3/4 x + 2.

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Answer: Answer: 475

Because i divided 500 by 5% and it gives u 475.

Answer:

equation A,C and E are true if w=100

The students who took notes by hand understood better than those who took lecture notes on laptop.

When students take notes by hand, during writing the notes they understand the concept, and their brains will store the information and they can memorize it easily. This is the best method for conceptual understanding and it will improve the analytical thinking and problem-solving skills of the student.

Instead of adopting the more conventional approach of concentrating on learning on topics, conceptual learning includes students engaging in high-quality learning experiences built around important concepts and essential ideas. Conceptual is a term used to describe ideas and mental constructs.

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The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral.

The trapezoidal rule is a strategy for approximating the definite integral in calculus. The trapezoidal rule works by computing the area of the region under the graph of the function f(x) that is approximated as a trapezoid. The trapezoidal rule is commonly used to calculate the area under curves. This is achievable if the overall area is divided into smaller trapezoids rather than rectangles. The Trapezoidal Rule integration determines the area by approximating the area under a function's graph as a trapezoid. The midway rule uses rectangular areas to approximate the definite integral, whereas the trapezoidal rule uses trapezoidal approximations to approximate the definite integral. Simpson's approach works by first approximating the original function with piecewise quadratic functions.

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Complete question:

The trapezoidal rule is a numerical integration method that frequently overestimates the real value of a function's definite integral. True/False

The solution is, by force wind move the sail.

As the boat is sailing, the wind will be faster than the boat. This fast wind is obstructed by the sail. That is, the fast wind gets slowed down by the sail because the sail pushes the wind backwards which slows down the wind. This will make the wind push the boat forward thereby accelerating the boat.

here, we have,

Gravity and buoyancy are the two key forces that operate on a stationary sailboat. The power of the wind pulls on the sail in order for the boat to move which allows the boat to move. The powers are now unbalanced, which is apparent from the acceleration of the ships.

The boat accelerates until the forward portion of the force from the sails is matched by the drag from the water.

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Answer: ok njnnnnnnnnnnnnnnnnnnnnnnnn

The equation that portrays the correct use of the distance formula is  6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² )

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the diagram;

Point A (5,6)

Point B (11,y₂)

Distance d = 6.71

Plug the given values into the distance formula.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² )

Therefore, the correct use of the formula is 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² ).

Option D) 6.71 = √( ( 11 - 5 )² + ( y₂ - 6 )² ) is the correct answer.

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The value of {r} is 64 and the value θ is 30°.

A complex number is a number of the form (a + bi), where [a] and [b] are real numbers and [i] is equal to [tex]\sqrt{-1}[/tex] . The general form of the complex number representation is (a + ib). In this, [a] is called real part and [ib] is called imaginary part.

Given is the complex number -

z = 4√3 - 4i

We can write the value of {r} as -

r = (4√3)² + (- 4)²

r = 16 x 3 + 16

r = 64

θ = tan ⁻¹(4/4√3)

θ = tan ⁻¹(1/√3)

θ = 30°

Therefore, the value of {r} is 64 and the value θ is 30°.

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Answer:

To find the solution of a linear system, we need to find the values of x and y that satisfy both equations. One method to solve a system of linear equations is substitution. We can use the first equation to find the value of y in terms of x, and substitute it into the second equation.

y = 1/2x + 1

y = 3/2x + 4

We substitute the first equation into the second equation:

3/2x + 4 = 1/2x + 1

Now we simplify:

2x = 3

x = 3/2

Finally, we substitute x = 3/2 into either equation to find y:

y = 1/2 * 3/2 + 1 = 2

So, the solution of the system is (3/2, 2). Out of the given options, only (3/2, 7/4) has the same values of x and y.

Therefore, the answer is (C) (3/2, 7/4).

Answer: A

If you plug in -3 into X on both equations you'd get -1/2, thus showing that (-3, -1/2) is a solution to both

Infinitely many solutions exist for a system with fewer equations than unknowns, yet there may be none. An underdetermined system is one that operates in this manner.

What in mathematics is a linear system?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

                          Equations with unknowns or variables that have powers of one are known as linear equations. Because the variables x, y, and z are linear, for instance, 3x - 4y + 5z = 3 is a linear equation, however xy + 3z = 7 is not because the phrase xy is a product of two variables.

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By using the formula for permutation, we can find that there are 2,598,960 possible combinations of 5 cards that can be dealt from a standard deck of 52 cards.

Poker is a popular card game that is played with a standard deck of 52 cards.

A permutation is the arrangement of objects in a specific order. In this case, the objects are the 52 cards in a standard deck, and the order is the 5 cards that are dealt to each player.

To find the number of possible 5-card hands, we can use the formula for permutation:

P(52, 5) = 52! / (52 - 5)!

Where "52!" is the factorial of 52, meaning the product of all positive integers from 1 to 52.

52! / (52 - 5)! = 806,368,039,360 / 47! = 2598960

The final answer is that there are 2,598,960 possible 5-card hands that can be dealt from a standard deck of 52 cards.

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Answer:

Step-by-step explanation:

is it possible to form a triangle with side lengths 3,3, and 4?

3 + 3 = 6 (greater then 4)

4 + 3 = 7 (greater then 3)

so, the answer is yes

in the picture your isosceles acute triangle

[tex]x^{2}[/tex] +[tex]y^{2}[/tex] = 801 is the equation of the circle in standard notation.

The equation of a circle with center at the origin (0, 0) can be written as:

, where r is the radius of the circle.

Since the circle passes through the point (5, -8), we can substitute these values into the equation of the circle to find the radius:

[tex](5-0)^{2} (-8-0)^{2}= r^{2}[/tex]

25 + 64 = r^2

[tex]r^{2}[/tex]= 89

r = sqrt(89) = 3 sqrt(89)

So, the equation of the circle with center at the origin and passing through (5, -8) is:

(x - 0)^2 + (y - 0)^2 = (3 sqrt(89))^2

[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 9 * 89

[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 801

This is the equation of the circle in standard notation.

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Answer:

To find the number of foxes after 22 years, we need to substitute x = 22/11 into the equation:

y = 50 * 4^(22/11)

Using a calculator or approximation, this expression evaluates to approximately 68,719.

So, after 22 years there will be approximately 68,719 foxes.

Step-by-step explanation:

The volume of the cube would be 5y√x cm^3.

A cube is a square shape, so both sides ( length and width) of a face would be the same.

Supposing that the considered cube has side length (also called edge length) of L units.

Then, its one side's area equals  L^2 sq. units (as each side is a square, so we used formula for area of a square).

We have to Find the length of the side by finding the square root of the area of the face:

Area = 75xy^2

Length = √75xy^2 =  y √5 x 5 x 3 x cm.

Volume is Length x Width X height.

Volume = 5y√x cm^3

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