Type the answers to these questions, in order, thank you.

a)The given differential equation is mdv/dt =−kvTo solve this differential equation, first, we will divide both sides by mv and rearrange to get the variables in separate terms. So, we have\($$\frac{dv}{v} = -\frac{k}{m}dt$$\)

Now, we will integrate both sides with limits. So, we getln\((v) = (-k/m)t + C1,\) where C1 is the constant of integration.

At time

\(t = 0, v = 1\\So, ln(1) = 0C1 = 0ln(v) = (-k/m)t\\So, we getv(t) = e^(-k/m)t.\)

b)Now, we will integrate v(t) to find the position x(t).\($$dx/dt = v(t)$$$$dx = v(t) dt = e^(-k/m)t dt$$\)

Now, we will integrate both sides with limits. So, we get \(x(t) = (-m/k)e^(-k/m)t + C2\), where C2 is the constant of integration.

At time

\(t = 0, x = 0.\\So, x(0) = (-m/k)e^0 + C2C2 \\= 0x(t) = (-m/k)e^(-k/m)t.\)

c)The limit position of the boat \(limt→[infinity]x(t)\) can be obtained by substituting the value of t→∞ in the above equation.

\(limt→[infinity]x(t) = (-m/k)limt→[infinity]e^(-k/m)t\)

Since k and m are constants, so

\(imt→∞e^(-k/m)t = 0limt→[infinity]x(t) = 0\)

So, the limit position of the boat is 0.It decreases with m.

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In geometry, a transversal is a line that intersects two or more other lines. When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .

It is given that <1 = <2

Then m<3 = m<4, since

Therefore, m<3 = m<4.

Answer:

1) 11\(\sqrt{3}\)

2) 2\(\sqrt{2}\)

3) \(20\sqrt{3} + 15\sqrt{2}\)

4) \(53 + 12\sqrt{10}\)

5) -2

6) \(7\sqrt{2} - 5\sqrt{3}\)

Step-by-step explanation:

1) 2\(\sqrt{12}\) + 3\(\sqrt{48}\) - \(\sqrt{75}\)

=(2 × 2\(\sqrt{3}\) )+ (3 × 4\(\sqrt{3}\)) - 5\(\sqrt{3}\)

= 4\(\sqrt{3}\) + 12\(\sqrt{3}\) - 5\(\sqrt{3}\)

= 11\(\sqrt{3}\)

2) 4\(\sqrt{8}\) -2\(\sqrt{98}\) + \(\sqrt{128}\)

= (4 × 2\(\sqrt{2}\)) - (2 × 7\(\sqrt{2}\)) + 8\(\sqrt{2}\)

= 8\(\sqrt{2}\) - 14\(\sqrt{2}\) +8\(\sqrt{2}\)

= 2\(\sqrt{2}\)

3) 5\(\sqrt{12\\}\) - 3\(\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}\)

= 5× \(2\sqrt{3}\) - 3×\(3\sqrt{2}\) + 4×\(6\sqrt{2}\) + 2×\(5\sqrt{3}\)

= \(10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}\)

= \(20\sqrt{3} + 15\sqrt{2}\)

4) \((2\sqrt{2} + 3\sqrt{5} )^{2}\)

= \(8 + 12\sqrt{10} + 45\)

= \(53 + 12\sqrt{10}\)

5) \((1+\sqrt{3} ) (1-\sqrt{3} )\)

= \(1 - 3\)

= -2

6) \((2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )\)

= \(2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}\)

= 2×\(3\sqrt{2}\) - 2×\(2\sqrt{3}\) - \(\sqrt{3} + \sqrt{2}\)

= \(6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}\)

= \(7\sqrt{2} - 5\sqrt{3}\)

Hope the working out is clear and will help you. :)

Step-by-step explanation:

please I solved the question in the diagram above

Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

Answer:

\(a^4\) Where (a) is the side length of the hypercube

Step-by-step explanation:

A dimension can be simply defined as a direction in which matter can move it.

We live in a 3-dimensional world, matter can move in three basic directions. The formula for finding the volume of a cube is the following: (\(a^3\)). In the second dimension, a flat world, the area for the volume of a square is as follows: (\(a^2\)). However, a hypercube is a paradox, as it exists in 4-dimensions, thus it cannot exist in our world. However, scientists propose "String theory" which requires that matter can move in more directs than the (3) we know of in our world. In essence, there can be more than 3 dimensions. A hypercube is the 4-dimensional version of a cube. If it follows the area pattern that a square-object follows in all preceding dimensions then the area of a hypercube is (\(a^4\)).

Bear in mind that the area patter for a square-object is generally the following:

\(a^n\)

Where (a) is the side length of the square-object

(n) is the dimension the object is in.

Please keep in mind, this answer was written in the June of 2021, as science keeps progressing and new discoveries are made, this theory can be disproven. Therefore, this answer might be considered correct now, but it can be proven incorrect in the future.

Answer:

Step-by-step explanation:

To solve for the measure of Angle N with the given side lengths, you need to find the inverse tangent (tan^-1). You use the tangent because you have the opposite and adjacent side lengths of the angle.

The step by step solution:

tan(<N)=1.7/6.7

<N=tan(^-1)1.7/6.7

<N=14 degrees

Answer:

The slope is -3/7 so B

Step-by-step explanation:

Just turn this into slope-intercept form.

what you do is subtract 3x so that it's moved to the right side.

It should look like this -7y = 12 - 3x

Then just divide all numbers by 7 so everything is simplified

It should look like this y = -3/7x - 12/7

pls mark brainliest because i didn't waste you time lol

We will have the following:

*We will determine the solution by replacing the pairs of values and calculating, that is:

*a. (-10, 6.5):

*b. (-2, 2.5):

*c. (5, -1):

So, the solution for the system is the point (5, -1).

Answer:

Step-by-step explanation:

8x^2 - 8x + 2

2(4x^2 - 4x + 1)

2(2x - 1)(2x - 1) or 2(2x - 1)^2

answer is C

The complete factorization of \(8x^2 - 8x + 2\) will be  \(2(2x-1)^2\) .

Factorization is a process consists of writing a number or another mathematical object as a product of several factors solving it into other factors.

We have,

\(8x^2 - 8x + 2\)

Using the mid term splitting method;

\(=8x^2-4x-4x+2\)

\(=4x(2x-1)-2(2x-1)\)

\(=(4x-2)(2x-1)\)

\(=2(2x-1)(2x-1)\)

\(=2(2x-1)^2\)

So, the factorization of the given expression is given in option \((c)\)  i.e.   \(2(2x-1)^2\) .

Hence, we can say that the complete factorization of \(8x^2 - 8x + 2\) will be  \(2(2x-1)^2\) .

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Hello!

3x² = 27

3x²/3 = 27/3

x² = 9

√x² = ±√9

x = ±3

The solution of the equation is :

Solution:

Our equation is: \(\sf{3x^2=27}\).

To solve it, we should isolate the x. So I begin by dividing each side by 3:

\(\sf{3x^2=27}\)

\(\sf{x^2=9}\)

Now, to get rid of the square on top of the x, I take the square-root of each side; the square-root and the square will cancel out on the left.

Keep in mind that once you take the square root of a number, you end up with TWO solutions.

So the result is:

\(\sf{x=3, x=-3}\), which can be rewritten as x = ± 3

Answer:

C. 13x^2 - 17x

Step-by-step explanation:

1. Collect like terms -

  4x^2 - 5x + 9x^2 - 12x

= 13x^2 - 5x - 12x

2. Collect like terms again -

   13x^2 - 5x - 12x

= 13x^2 - 17x

So, the answer is 13x^2 - 17x I hope this helps! :D

Answer:

-1 43/56

Step-by-step explanation:

Answer:

-99/56

Step-by-step explanation: i used my calc

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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Answer:

14 quarters and 1 nickel

Using the Pythagorean Rule we know that player A is 19.2 ft away from us.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

The Pythagorean Rule can be used to determine the distance between you and Player A since the distances between you, Player A, and Player B are in the shape of a right-angled triangle.

c² = a² + b²

Where;

c = hypotenuse = Distance between you and player A

a = Length of the triangle

b = Height of triangle

Then, calculate as follows:

c² = 12² + 15²

c² = 144 + 225

c = √369

c = 19.2 ft

Therefore, using the Pythagorean Rule we know that player A is 19.2 ft away from us.

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Correct question:

During a basketball game, you want to pass the ball to either Player A or Player B. You estimate that Player B is about 15 feet from you, as shown. How far away from you is Player A?

The surface area of just the base of the cone is approximately 314.16 cm^2.

The base of a cone is a circle, and the surface area of a circle can be calculated using the formula:

Surface Area of a Circle = π * radius^2

In this case, the radius of the base of the cone is given as 10 cm.

So, the surface area of just the base of the cone can be calculated as:

Surface Area of Base = π * (10 cm)²

Surface Area of Base = π * 100 cm²

∴ Surface Area of Base ≈ 314.16 cm²

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Answer:

17. 86 miles

Step-by-step explanation:

The fewest number of pieces you can receive in a fair exchange for 12 flats, 18 longs, and 17 units is 5 pieces.

To find the fewest number of pieces, we can exchange the smaller pieces for larger ones. For example, we can exchange 10 units for 1 long, and 10 longs for 1 flat. This way, we can reduce the number of pieces we have.

Starting with the 17 units, we can exchange 10 of them for 1 long, leaving us with 7 units. Then, we can add this 1 long to the 18 longs we already have, giving us a total of 19 longs.

Next, we can exchange 10 of the 19 longs for 1 flat, leaving us with 9 longs. We can add this 1 flat to the 12 flats we already have, giving us a total of 13 flats.

Finally, we can exchange 10 of the 13 flats for 1 thousand, leaving us with 3 flats.

So, in total, we have 1 thousand, 3 flats, 9 longs, and 7 units, which is a total of 5 pieces.

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According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.

The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.

By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.

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Answer:

Hello! Your answer would be, F)[1000, 10] AND C)[1000, 100]

Step-by-step explanation:

Hope I helped! Brainiest plz!♥ Have a nice afternoon. Hope you make a 100%! -Amelia

Yes, a baseball fit in box A.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.

Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Given:

The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.

So, the maximum value of Circumference

2πr = 9.5

r= 9.5/ 2 x 3.14

r = 1.472 inch

So, Volume of ball = 4/3 πr³

Volume of ball = 4/3 x 3.14 x (1.472)³

Volume of ball = 13.36 inch³ < 64 inch³

Hence, it will fit inside the box.

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Answer: 7

Step-by-step explanation:

The initial value is the same as what value it is when the independent variable is 0. Looking at the chart, when the input is 0, the output is y.

Answer:

7

Step-by-step explanation:

The answer is 7 because it is the y- intercept of the table.

I hope this helps.

Answer:

6 for senior and 7c for child

Step-by-step explanation:

The power required to operate the pump is approximately 0.0604 kilowatts

The power required to operate the pump, we need to consider the work done against gravity and the head loss in the system.

First, let's calculate the difference in elevation between the well and the tank:

Elevation difference = Height of the tank - Depth of the well

Elevation difference = 58 m - (-20 m)

Elevation difference = 78 m

Next, let's calculate the total head loss in the system, taking into account the head loss given as 34.3 m:

Total head loss = Elevation difference + Head loss

Total head loss = 78 m + 34.3 m

Total head loss = 112.3 m

Now, let's calculate the flow rate of water through the pipe using the given diameter:

Radius of the pipe = 5 cm / 2 = 2.5 cm = 0.025 m

Cross-sectional area of the pipe = π × (0.025 m)² = 0.00196 m²

Given that the water is pumped at a rate of 4 L/s, which is equivalent to 0.004 m³/s, we can calculate the velocity of water:

Velocity of water = Flow rate / Cross-sectional area

Velocity of water = 0.004 m³/s / 0.00196 m²

Velocity of water ≈ 2.041 m/s

Now, let's calculate the power required to operate the pump using the equation:

Power = (Flow rate × Total head loss) / Pump efficiency

Flow rate = 0.004 m³/s

Total head loss = 112.3 m

Pump efficiency = 75% = 0.75

Power = (0.004 m³/s × 112.3 m) / 0.75

Power ≈ 0.0604 kW

Therefore, the power required to operate the pump is approximately 0.0604 kilowatts.

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Answer:

3 kilometers

Step-by-step explanation:

If 6 laps around the lake is 18 kilometers, you divide 18 by 6 to get 3.

Answer:

-128/5 or - 25.6 will be ur answer.

I HOPE IT WILL HELP YOU.

Sry if it is wrong.

a) The family has to request €250,068.10 from the bank. b) The difference in price between the house and the car is €183,116.42.c) The family can save €25,406.91 by buying both things.

A family wants to request a loan from a bank to purchase a home that is worth €216,592.26 and a car that costs €33,475.84. a) The amount of money that this family has to request from the bank is the sum of the two costs:€216,592.26 + €33,475.84 = €250,068.10 The family has to request €250,068.10 from the bank. b) The difference in price between the house and the car is the absolute difference between the two prices:| €216,592.26 - €33,475.84 | = €183,116.42The difference in price between the house and the car is €183,116.42.c) They will be given a 10% discount if they buy both things.

Thus, they will pay only 9/10 of the total price:0.9 ( €216,592.26 + €33,475.84 ) = 0.9 €250,068.10 = €225,661.19If they buy both things, they will save the difference between the two prices and the new price they have to pay:€216,592.26 + €33,475.84 - €225,661.19 = €24,407The family can save €25,406.91 by buying both things.

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The event of Juan choosing at least one blue marker from the bag when randomly selecting 6 markers is certain.

In this scenario, Juan has a total of 7 markers in his bag, with 3 blue markers and 4 red markers. When he randomly chooses 6 markers from the bag, it is certain that he will select at least one blue marker. This is because there are more blue markers (3) than the number of markers he is selecting (6).

To understand why this event is certain, consider the worst-case scenario where Juan selects all 4 red markers first. Even in this case, there will still be 2 markers left in the bag, both of which are blue. Therefore, Juan is guaranteed to choose at least one blue marker when selecting 6 markers from the bag.

Since there are more blue markers available than the number of markers Juan is choosing, it is certain that he will select at least one blue marker. This makes the event of choosing at least one blue marker from the bag when randomly selecting 6 markers a certain event.

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