To find the rate of change of height with respect to time, we use the formula dh/dt = dV/dt / (πr²) and substitute the given values for the rate of volume change and the radius.
We have the rate of volume change as 23 cm³/sec and the cylinder has a radius of 12 cm. Note that the typo '2323 cm³/sec' and '1212 cm' should be read as '23 cm³/sec' and '12 cm,' respectively.
The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To find the rate at which the height h changes over time, we can take the derivative of the volume with respect to time, which gives us dV/dt = πr² dh/dt. We can solve this equation for dh/dt (the rate of change of height with respect to time) by dividing both sides by πr² and substituting the given values. Therefore, dh/dt = dV/dt / (πr²).
Substituting the values, we get:
dh/dt = 23 cm³/sec / (π * (12 cm)²)
Upon simplifying, we will obtain the rate at which the height of the water is decreasing in cm/sec.
When combining functions, what operation requires that you restrict the domain of one or both functions?
At a grocery store, an uncooked beef roast is on sale for $4.99/lb. At the same store, prepared roast beef is at the deli for $2.99/100g. How many times more expensive is the deli roast compared to the uncooked roast?
The cost of a service call to fix a washing machine can be expressed by the linear function y = 45x + 35, where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
the cost for each hour it takes to repair the machine
the cost for coming to look at the machine
the total cost for fixing the washing machine
the amount of time that it takes to arrive at the home to make the repairs
Answer:
A
Step-by-step explanation:
simplify (2 (radical 5) - 4) (3 (radical 5) +2)
Find all solutions in the interval [0, 2π). 7 tan^3x - 21 tan x = 0
To solve this problem, the first thing we can do is to take out 7 tan (x) from the whole equation, this results in simplification:
7 * tan (x) * (tan (x)^2 - 3) = 0
Therefore the initial roots are taken from:
tan (x) = 0
Calculating for x:
x = 0, pi
The other roots can be taken from:
(tan (x)^2 - 3) = 0
Calculating for x:
tan (x)^2 = 3
tan (x) = ± sqrt (3)
x = pi/3 , 2pi/3 , 4pi/3 , 5pi/3
Therefore the solutions are:
0 , pi, pi/3 , 2pi/3 , 4pi/3 , 5pi/3
Rectangle 800 feet long and 700 feet wide. if fencing costs $13 per yard, what will it cost to place fencing around the playground
The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. find the length of the median of the trapezoid.
Final answer:
The length of the median of the trapezoid with perpendicular diagonals of lengths 8 and 10 is 9 units. This is calculated using properties of the median and the Pythagorean theorem.
Explanation:
The question you've asked regarding the median of a trapezoid with perpendicular diagonals of lengths 8 and 10 can be resolved by recognizing a property of the median in a trapezoid. The median (also known as the mid-segment) of a trapezoid is parallel to the bases and its length is equal to the average of the lengths of the bases. Since the diagonals are perpendicular, they would form right triangles with the two bases and the median line, dividing the trapezoid into four right triangles.
Let's denote the lengths of the bases as a and b, and the median as m. We know the diagonals intersect at their midpoints, thus splitting each into segments of lengths 4 and 5. Now we can form two right triangles sharing the median as a common side. Applying the Pythagorean theorem, we get two equations: m² + 4² = a² for the first right triangle and m² + 5² = b² for the second right triangle.
Since the median is the average of the bases, we have m = (a + b) / 2. Using the equations above, after some algebraic manipulations, we find that a² - b² = 16. With more manipulation, eventually, we find that (a - b)(a + b) = 16, and, since m is the average, 2m = a + b. Hence, we derive that 2m - b = (a - b), which simplifies to give us m = 9. This gives us the length of the median of the trapezoid as 9 units.
if a mixture of a 6% acid solution with an 11% acid solution is to be made, how much of each solution is needed to make 10 liters of an 8% acid solution
Given the function f (x) = 10x + 4, find each of the following. f(8), f(-4), f (0)
f(8)=?
f(-4)=?
f(0)=?
mary and jolene are both growing tomatoes in thier backyards to sell.jolene had 3 times as many as mary.but birds had eaten 6 before she picked them all.for the season they have a total of 54 tomotoes.how many did mary grow?
Mary grew 15 tomatoes. A simple algebraic equation was formulated and solved to determine the quantity: m + 3m - 6 = 54, where m represents the number of tomatoes grown by Mary.
Given that Jolene had 3 times as many tomatoes as Mary and birds ate 6 of Jolene's tomatoes, and together they have 54 tomatoes, we need to set up an equation to solve for the number of tomatoes Mary grew.
Let's denote the number of tomatoes Mary grew as m. Therefore, Jolene grew 3m tomatoes. Since birds ate 6 of Jolene's tomatoes, we have 3m - 6 for the number of tomatoes left with Jolene. The equation representing the total number of tomatoes then becomes m (Mary's tomatoes) + (3m - 6) (Jolene's remaining tomatoes) = 54. Simplifying this equation:
m + 3m - 6 = 54
4m - 6 = 54
4m = 60
m = 15
Therefore, Mary grew 15 tomatoes.
Please solve. best answer gets rewarded! show step by step.
help plzzzzzzzz this is hard
Answer:
A is correct!
Step-by-step explanation:
Complete the multiplication: AB.
A.
B.
C.
D.
Solve the triangle. B=36 a=41 c=20
In the triangle with B = 36°, a = 41, c = 20, b ≈ 45.3, C ≈ 29.5, A ≈ 114.5.
To solve the triangle, we can use the Law of Sines and the fact that the sum of angles in a triangle is 180 degrees.
Given:
[tex]- Angle \( B = 36° \)[/tex]
[tex]- Side \( a = 41 \)[/tex]
[tex]- Side \( c = 20 \)[/tex]
First, we need to find angle [tex]\( A \)[/tex]. We can use the fact that the sum of angles in a triangle is 180 degrees:
[tex]\[ A = 180 - B - C \][/tex]
We can find angle [tex]\( C \)[/tex] using the Law of Sines:
[tex]\[ \frac{\sin C}{c} = \frac{\sin B}{b} \][/tex]
Solving for [tex]\( C \):[/tex]
[tex]\[ \sin C = \frac{c \times \sin B}{b} \][/tex]
[tex]\[ \sin C = \frac{20 \times \sin 36°}{b} \][/tex]
[tex]\[ \sin C = \frac{20 \times 0.5878}{b} \][/tex]
[tex]\[ \sin C = \frac{11.756}{b} \][/tex]
Now we can find angle [tex]\( C \)[/tex] using the inverse sine function:
[tex]\[ C = \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
Now, we can substitute [tex]\( C \) i[/tex]nto the equation for [tex]\( A \)[/tex] and solve for [tex]\( b \):[/tex]
[tex]\[ A = 180 - B - C \][/tex]
[tex]\[ A = 180 - 36 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
[tex]\[ A = 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
Since we know all three angles of the triangle, we can find [tex]\( b \)[/tex] using the Law of Sines again:
[tex]\[ \frac{\sin A}{a} = \frac{\sin B}{b} \][/tex]
[tex]\[ \sin A = \frac{a \times \sin B}{b} \][/tex]
[tex]\[ \sin A = \frac{41 \times \sin 36}{b} \][/tex]
[tex]\[ \sin A = \frac{41 \times 0.5878}{b} \][/tex]
[tex]\[ \sin A = \frac{24.0678}{b} \][/tex]
Now, we can find [tex]\( b \)[/tex] using the inverse sine function:
[tex]\[ b = \frac{24.0678}{\sin A} \][/tex]
Finally, we'll use the given values and calculate the closest option:
[tex]\[ A \approx 144 - \sin^{-1}\left(\frac{11.756}{b}\right) \][/tex]
[tex]\[ b \approx \frac{24.0678}{\sin A} \][/tex]
[tex]\[ c \approx 20 \][/tex]
B = 36°
[tex]\[ a = 41 \][/tex]
After the calculation, the closest option is:
[tex]\[ b \approx 45.3, \ C \approx 29.5, \ A \approx 114.5 \][/tex]
Complete Question:
Solve the triangle.
B = 36°, a = 41, c = 20
choices:
b ≈ 27.5, C ≈ 115.5, A ≈ 28.5
b ≈ 45.3, C ≈ 25.5, A ≈ 118.5
b ≈ 45.3, C ≈ 29.5, A ≈ 114.5
b ≈ 27.5, C ≈ 25.5, A ≈ 118.5
what is the value of y?
Answer:
The correct option is D) 60°
Step-by-step explanation:
Consider the provided triangle.
From the provided figure it is given that one angle is 60° and we need to find the value of y.
As we know the sum of all interior angle in a triangle is 180°.
y°+y°+60°=180°
Now solve the above equation to find the value of y.
2y°+60°=180°
2y°=180°-60°
2y°=120°
y°=120°÷2
y°=60°
Hence, the value of y is 60°.
Thus, the correct option is D) 60°
A gutter at the edge of a roof drops 2 inches for every 30 feet of length. The measure of the angle to the nearest tenth of a degree that the gutter makes with the roof is ____ degrees. (Enter only the number.)
Marla swims twice a week. her equipment cost her $32.85 and she has a membership to the pool for $35 plus #3.50 per visit. she can walk to the pool, so transportation is free. how much will swimming cost her for the year?
the answer to the triangle the hexagon and the Diamond
Find the missing term. If y = 1 + i, then y3 − 3y2 + (-3y) (-3y + 1) (3y) (3i ) − 1 = -i .
Answer:3y is the answer
Step-by-step explanation:
The cost of a long-distance phone call is $0.46 for the first minute and $0.37 for each additional minute. if the total charge for a long-distance call is $6.75, how many minutes was the call?
1st minute = 0.46
additional minutes = 0.37
6.75 -0.46 = 6.29
6.29/0.37 =17
17 +1 = 18 total minutes
A jet flies at a rate of 1.3 x 10^ 6 feet per hour. Written in scientific notation, which is the best estimate of how many feet the jet will travel in 2.8 x 10^ 3 hours?
What is the solution to the system of linear equations?
The point of intersection of lines represents the common solution of the system of linear equations. The solution of linear equations given in the graph is (0,2).
Linear equation represents a line on the graph. The system of linear equations represents couple/s of linear equations or lines.
The solution of system of linear equations means the common point satisfying the different linear equations.
Graphically, the point of intersection of two lines represents the common solution of these two lines or simply the solution of the system of linear equations.
So, the point of intersection from the given graph is (0,2).
Therefore, the solution of linear equations given in the graph is (0,2).
For more details, refer to the link:
https://brainly.com/question/16515610
Alexandra Romar has a previous balance at Porter Pharmacy of $68.42. She had payments and credits of $18.25. The monthly finance charge is 1.85% of the unpaid balance. After the finance charge was calculated, she made $34.00 in new purchases. What is her new balance?
Answer:
Her new balance is $85.10.
Step-by-step explanation:
Alexandra Romar has a previous balance at Porter Pharmacy = $68.42
She had payments and credits = $18.25
Now the unpaid balance = 68.42 - 18.25 = $50.17
The monthly finance charge on unpaid balance = 1.85% × 50.17
= [tex]\frac{1.85}{100}[/tex] × 50.17
= 0.928145 ≈ $0.93
So the balance with finance charge = 50.17 + 0.93 = 51.10
She made a new purchase = $34.00
Her new balance = 51.10 + 34.00 = $85.10
Her new balance is $85.10.
Find the angular size of a circular object with a 3-inch diameter viewed from a distance of 4 yards.
Final answer:
To determine the angular size of an object with a diameter of 3 inches from 4 yards away, one can use the formula θ = d / D to calculate θ in radians, which is then converted to degrees, resulting in an angular size of approximately 1.19°.
Explanation:
To find the angular size of a circular object with a 3-inch diameter viewed from a distance of 4 yards, one can use the following formula for angular size θ (in radians): θ = d / D, where d is the diameter of the object and D is the distance to the object.
First, we convert the diameter and the distance to the same units. There are 36 inches in a yard, so 4 yards is 144 inches:
Diameter (d): 3 inchesDistance (D): 4 yards = 144 inchesThen, we calculate the angular size in radians:
θ = d / D = 3 inches / 144 inches = 0.0208333...
This can be converted to degrees by multiplying with 180/π:
θ(in degrees) = 0.0208333... * (180/π) = 1.19° (approximately).
Thus, the angular size of the object is approximately 1.19° when viewed from a distance of 4 yards.
Pick the geometric term that matches the real-word object: a lip-gloss tube.
Answer: Cylinder.
Step-by-step explanation: Lip-gloss tubes may have different shapes, but the usual form of a lip-gloss tube is, as the name says, a tube.
This means that it has a circular base and a circular top, and a given height that connects the base and the top, the geometrical shape that has this shape is called a cylinder.
The table below shows four systems of equations: System 1 System 2 System 3 System 4 4x − 5y = 2 3x − y = 8 4x − 5y = 2 10x − 7y = 18 4x − 5y = 2 3x − 8y = 4 4x − 5y = 2 10x + 3y = 15 Which pair of systems will have the same solution?
Answer:
System 1 and System 2 are equivalent.Step-by-step explanation:
The first and second system have the same solutions, the are equivalent systems of equations. Let's calculate solutions to demonstrate it:
System 1.[tex]\left \{ {{4x - 5y = 2} \atop { 3x - y = 8}} \right.[/tex]
If we multiply the second equations by -5, we can eliminate one variable and find the first solution:
[tex]\left \{ {{4x - 5y = 2} \atop { -15x +5y = -40}} \right.\\-11x=-38\\x=\frac{38}{11}[/tex]
Now, we use this value to find the other solution:
[tex]3x - y = 8\\3(\frac{38}{11})-y=8\\\frac{114}{11}-8=y\\ y=\frac{114-88}{11}=\frac{26}{11}[/tex]
The solution of the first system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]
System 2.[tex]\left \{ {{4x - 5y = 2} \atop { 10x - 7y = 18}} \right.[/tex]
We do the same process than we did before, but this time we have to multiply by [tex]-\frac{5}{7}[/tex]:
[tex]\left \{ {{4x - 5y = 2} \atop { -\frac{50}{7}x + 5y = \frac{90}{7} }} \right.\\\frac{28x-50x}{7}=\frac{-90+14}{7}\\-22x=-76\\x=\frac{38}{11}[/tex]
Then,
[tex]4x - 5y = 2\\4(\frac{38}{11})-5y=2\\\frac{152}{11}-2=5y\\ 5y=\frac{152-22}{11}\\y=\frac{130}{5(11)}=\frac{26}{11}[/tex]
The solution of the second system is [tex](\frac{38}{11} ;\frac{26}{11} )[/tex]
Therefore, system 1 and system 2 are equivalent.
f={(x,y)| y=x+3} find f(3.6) & f(-0.2)
Three subtracted from x is less than or equal to -17
What is the distance between -14 and 5
What is the value of theta , if tan theta = -1/squareroot3