A silo composed of a cylinder topped by a half-sphere. The height of the cylinder is 6.2 meters and the radius of both the cylinder and the half-sphere is 1.6 meters. Use 3.14 for pi. Find the volumes of the half-sphere, the cylinder, and the entire silo to the nearest tenth. Explain how you found the volume of the silo.

The differential equation for the amount of salt a(t) in the tank at time t > 0 is dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t).

To find the differential equation for the amount of salt a(t) in the tank at time t > 0, we need to consider the rate of change of the salt concentration in the tank.

Let A(t) represent the amount of salt in the tank at time t. The salt entering the tank each minute is given by the concentration (4 lb/gal) multiplied by the rate of inflow (3 gal/min), which is 12 lb/min.

The salt leaving the tank each minute is given by the concentration in the tank (A(t)/V(t)) multiplied by the rate of outflow (2 gal/min), which is 2A(t)/(35 + (3 - 2)t).

Therefore, the rate of change of the salt in the tank is given by the difference between the rate of inflow and the rate of outflow: dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t). This is our differential equation for the amount of salt in the tank.

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Final answer:

The slope of a line in general form can be found by rearranging the equation to solve for y. The x-intercept is obtained by setting y = 0 and solving for x, while the y-intercept is obtained by setting x = 0 and solving for y.

Explanation:

The slope of a line defined in general form by the equation Ax+By = C can be found by rearranging the equation to solve for y, resulting in y = (-A/B)x + (C/B). The coefficient of x, -A/B, represents the slope of the line. The x-intercept can be found by setting y = 0 and solving for x, resulting in x = C/A. Similarly, the y-intercept can be found by setting x = 0 and solving for y, resulting in y = C/B.

First calculate the total amount of liters consumed:

Volume gas consumed = (6 L / 100 km) * 2000 km = 120 L

Then calculate the total cost:

Cost = ($1.20 / L) * 120 L = $144

Since there are three of them, so each must pay:

Payment of each = $144 / 3 = $48 per person

Answer:

$48 per person

Final answer:

The amount of salt in the tank at the end of 40 minutes is still 50 pounds.

Explanation:

To find the amount of salt in the tank at the end of 40 minutes, we need to calculate the change in the amount of salt in the tank over that time period.

The tank contains 200 gallons of brine with 50 pounds of salt in solution. Brine containing 2 pounds of salt per gallon is entering and exiting the tank at a rate of 4 gallons per minute.

Since the rate of flow in and out of the tank is the same, the amount of salt in the tank remains constant. Therefore, the amount of salt in the tank at the end of 40 minutes is still 50 pounds.

Final answer:

To make the lengths the same, she would have to cut 0.3 feet from the longer piece.

Explanation:

To find the amount she would have to cut to make the two lengths the same, we need to subtract the smaller length from the larger length.

The first length is 3 4/5 feet, which can also be written as 3 + 4/5 = 3 + 0.8 = 3.8 feet.

The second length is 3 1/2 feet, which can also be written as 3 + 1/2 = 3 + 0.5 = 3.5 feet.

Subtracting the smaller length (3.5 feet) from the larger length (3.8 feet), we get:

3.8 feet - 3.5 feet = 0.3 feet.

So she would have to cut 0.3 feet from the longer piece to make the lengths the same.

The value of c in the equation y = x² + c, given the point (4,7) lies on the graph, is found to be -9 after substituting the point's coordinates into the equation and solving for c.

To find the value of c in the equation y = x² + c, where the point (4,7) is on the graph, we substitute the x and y values from the point into the equation. This gives us:

7 = 4² + c

7 = 16 + c

Now, we subtract 16 from both sides to solve for c:

c = 7 - 16

c = -9

Therefore, the value of c is -9.

The equation of the line passing through the point (-3,6) with a slope of a third is y = 1/3x + 7. The graph of this line can be drawn by plotting the y-intercept at (0,7) and using the slope to plot other points.

The provided point through which the line passes is (-3,6) and the slope is a third. The general slope-intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept. That is, it represents the point where the line intersects the y-axis.

Let's use this information to find the equation of the line. We know that y = mx + b. We can substitute the slope (m=1/3) and the point (-3, 6) into this equation: 6 =(1/3)(-3) + b.

Solving this for b gives us b = 6 + 1 = 7. Therefore, the equation of the line in slope-intercept form is y = 1/3x + 7.

To graph the line, you can start by plotting the y-intercept at (0,7) on the y-axis, then rise 1 unit and run 3 units (since the slope = rise/run = 1/3) from the y-intercept point to plot the second point. Connect these points to draw the line.

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I hope you got satisfied

Final answer:

Larry's new solution has an approximate salt concentration of 11.33%. This was calculated by adding the initial mass of salt in the solution (10.5 g) to the extra salt added (15 g), resulting in a new total mass of salt (25.5 g), then dividing by the total mass of the new solution (225 g), and finally multiplying by 100%.

Explanation:

To find the percent of salt in Larry's new solution, we first need to calculate the total mass of the solution and how much of that mass is salt. Initially, we have 210 grams of a 5% salt solution. To find out how much salt that is, we use the percentage:

210 g × 0.05 = 10.5 g of salt

Now, Larry adds 15 grams of salt to this solution, so we add that amount to the initial salt mass:

10.5 g + 15 g = 25.5 g of salt

The total mass of the new solution is the sum of the mass of the original solution and the added salt:

210 g + 15 g = 225 g

Finally, to find the mass/mass percent concentration of the new solution, we divide the total mass of salt by the total mass of the solution and multiply by 100%:

((25.5 g / 225 g) × 100% = 11.33%

So, the percent of salt in Larry's new solution is approximately 11.33%.

To calculate the property taxes on a townhouse valued at $73,000, divide the value by $100 to find the number of $100 increments, and then multiply this by the tax rate of $1.15.

To find the property taxes on a townhouse valued at $73,000, we need to calculate the tax amount based on the given tax rate. The tax rate is $1.15 for every $100 of home value.

First, we need to find how many $100 increments are there in the home value.

Divide $73,000 by $100:

$73,000 ÷ $100 = $730

Now, multiply the number of $100 increments by the tax rate:

$730 × $1.15 = $839.50

Therefore, the property taxes on a townhouse valued at $73,000 would be $839.50.

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To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2. The two points are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2.

First, we find the derivative of the function:

dy/dx = 3x^2 - 12x - 34

Next, we set the derivative equal to 2 and solve for x:

3x^2 - 12x - 34 = 2

3x^2 - 12x - 36 = 0

Using the quadratic formula, we find the solutions for x:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values a = 3, b = -12, and c = -36 into the quadratic formula, we get:

x = (-(-12) ± √((-12)^2 - 4(3)(-36)))/(2(3))

x = (12 ± √(144 + 432))/6

x = (12 ± √(576))/6

x = (12 ± 24)/6

x = 12/6 ± 24/6

x = 2 ± 4

So the two points where the slope of the tangent line is 2 on the curve are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

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