the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds, find the frequency when the tension is 72 pounds.
Answer:
when the tension is 72 pounds , the frequency is 900 hertz
Step-by-step explanation:
Hello, I think I can help you with this.
you can easily solve this by using a rule of three.
According to the question data:
the pitch, or frequency, of a vibrating string varies directly with the square root of the tension.in mathematical terms it is:
f ∝ √T
where f is the pitch or frequency and T is the tension
Step 1
if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds
300 hertz ∝ √8 pounds
300⇔√8
what is the frequency when the tension is 72 pounds
x⇔√72
Step 2
Let
300⇔√8
x⇔√72
the relation is
[tex]\frac{300}{\sqrt{8} } =\frac{x}{\sqrt{72} }\\\\ Now, solve\ for\ x\\\\\\\frac{300*\sqrt{72} }{\sqrt{8} } =x\\x=\frac{300*\sqrt{72} }{\sqrt{8} } \\x=\frac{300*\sqrt{8*9}}{\sqrt{8}} \\x=\frac{300*\sqrt{8}*\sqrt{9}}{\sqrt{8}} \\x=300*\sqrt{9}\\x=300*3\\x=900[/tex]
when the tension is 72 pounds , the frequency is 900 hertz
have a good day.
Effie's store has 10,908 more comic book than Brody's. Brody's store has 45,607 coming books. How many books do Effie's and Brody's store have together?
Show your work...
Farmer Jack needs 1,800 square feet of garden space to have enough corn for a year. His garden space is currently 10 5⁄6 feet by 18 feet. How much more land does farmer Jack need to plant the rest of his corn?
Farmer Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
Explanation:To find out how much more land Farmer Jack needs to plant the rest of his corn, we need to calculate the area of his current garden and subtract it from the required area of 1,800 square feet. Farmer Jack's garden is 10 5/6 feet by 18 feet, so we can multiply these two dimensions to get the area of his current garden. Then, we subtract this area from 1,800 to find out how much more land he needs:
Area of Farmer Jack's garden: 10 5/6 feet * 18 feet = 197 1/3 square feet
More land needed by Farmer Jack: 1,800 square feet - 197 1/3 square feet = 1,602 2/3 square feet
Farm Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
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The price of a technology stock was $ 9.69 yesterday. Today, the price fell to $ 9.58 . Find the percentage decrease.
The table shows the outputs y for different inputs x:
Input (x) 5 6 7 8
Output (y) 2 5 8 11
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?
Answer:
A. yes...it is a function because there is no repeating x values.
B. (5,2)(6,5)...slope = (5 - 2) / (6 - 5) = 3
y = mx + b
slope(m) = 3
(5,2)...x = 5 and y = 2
now we sub
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
so the equation is : y = 3x - 13
when x = 7
y = 3(7) - 13....y = 21 - 13....y = 8
f(x) = 2x + 13...when x = 7
f(7) = 2(7) + 13...f(7) = 14 + 13.....f(7) = 27
the function has a greater value
C. f(x) = 2x + 13....when f(x) = 75
75 = 2x + 13
75 - 13 = 2x
62 = 2x
62/2 = x
31 = x
Step-by-step explanation:
The price of a technology stock has risen to $9.73 today. Yesterday's price was $9.60 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Brianna built a rectangular flower garden. The garden is 10 feet long and 8 feet wide. What is the area of Briannas flower garden?.
A picture has a width that is 17 inches shorter than the length, and its total area is 480 square inches. Find the dimensions of the picture.
Final answer:
To find the dimensions of the picture, set up an equation using the length and width. Solve the equation to find the dimensions: length = 32 inches, width = 15 inches.
Explanation:
To find the dimensions of the picture, let's assume the length is x inches. According to the problem, the width is 17 inches shorter than the length, so the width would be (x - 17) inches. The total area of the picture is given as 480 square inches. We can set up an equation using the length and width: x(x - 17) = 480. Solve this quadratic equation to find the dimensions of the picture.
Expanding the equation, we get x^2 - 17x - 480 = 0. Factoring the quadratic equation, we find (x + 15)(x - 32) = 0. Therefore, the possible values for x are -15 and 32. Since the length cannot be negative, we discard -15. Thus, the length of the picture is 32 inches and the width is (32 - 17) = 15 inches.
Final answer:
The dimensions of the picture are 32 inches in length and 15 inches in width.
Explanation:
To find the dimensions of the picture, we need to establish equations based on the information provided. Let the length of the picture be L inches and the width be W inches.
Given that:
The width is 17 inches shorter than the length: W = L - 17.The total area of the picture is 480 square inches: L × W = 480.Plug the width expression from step 1 into the area equation from step 2 to form a quadratic equation:
L(L - 17) = 480
Solving this quadratic equation will give us the value of L. Once we have L, we can use the first equation to get W. Let's solve the quadratic equation:
L² - 17L - 480 = 0
Factoring the quadratic, we find that (L - 32)(L + 15) = 0. So L can be either 32 or -15. Since a length cannot be negative, L must be 32 inches, and W, therefore, is 32 - 17 = 15 inches.
The dimensions of the picture are therefore 32 inches by 15 inches.
Z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s , ∂z ∂t , ∂z ∂u when s = 1, t = 4, u = 5
If a drug has a concentration of 350 mg per 10 mL, how many milliliters are needed to deliver 2 grams of the drug? Express your answer rounded to the nearest milliliter.
To deliver 2 grams of a drug with a concentration of 350 mg per 10 mL, convert 2 grams to milligrams (2000 mg), and then divide this value by the concentration in mg/mL (350 mg/10 mL) to find the volume in milliliters. After calculation, this results in approximately 6 milliliters, when rounded to the nearest milliliter.
Explanation:To calculate how many milliliters are needed to deliver 2 grams of the drug when the concentration is 350 mg per 10 mL, we start with the conversion of grams to milligrams since the concentration is provided in milligrams. Remember, 1 gram equals 1000 milligrams:
Convert 2 grams to milligrams: 2 grams × 1000 = 2000 mg.Determine how many milliliters provide 350 mg: 10 mL corresponds to 350 mg.Calculate the proportion: (2000 mg) / (350 mg/mL) = Number of milliliters needed.Perform the calculation: 2000 / 350 = 5.71428571 mL.Round to the nearest milliliter: Approximately 6 mL.Therefore, approximately 6 milliliters of the drug are needed to deliver a dose of 2 grams.
What is the concentration of nitrate ions in a 0.125 M Mg(NO3)2 solution
We have that the concentration of the nitrate ions is mathematically given as
M= 0.250M
The concentration of the nitrate ionsQuestion Parameters:
Generally the equation for the Reaction is mathematically given as
Mg(NO₃)₂ --> Mg²⁺ + 2NO₃⁻
Each mole of the Mg(NO₃)₂ will dissociate into 2 moles of NO₃⁻.
the concentration of the nitrate ions is
M = (0.125M)(2)
M= 0.250M
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two hundred eighty-four thousand, one hundred eighty-seven in expanded form
Suppose an ant is sitting on the perimeter of the unit circle at the point (1,0). if the ant travels a distance of 2π3 in the counter-clockwise direction, then the coordinates of the point where the ant stops will be
After traveling a distance of 2π/3 on the unit circle in the counter-clockwise direction from (1,0), the ant stops at the coordinates (-1/2, √3/2), which are found using the unit circle's parametric equations.
Explanation:The question asks about finding the coordinates of a point on the unit circle after traveling a certain distance in the counter-clockwise direction. The distance given is 2π/3, which, when considering the circumference of the unit circle (2π), represents an arc that is a third of the full circle. The unit circle is centered at the origin (0,0) and has a radius of 1, with points on it defined by cos(θ) and sin(θ) for any angle θ measured in radians from the positive x-axis.
Traveling 2π/3 radians from (1,0) in the counter-clockwise direction lands us at an angle of 2π/3 radians from the positive x-axis. The coordinates of the point on the unit circle at this angle can be found using the circle's parametric equations x = cos(θ) and y = sin(θ). Substituting θ with 2π/3, we obtain:
x = cos(2π/3) = -1/2y = sin(2π/3) = √3/2Therefore, the coordinates of the point where the ant stops are (-1/2, √3/2).
Use this equation to find dy/dx. 9y cos(x) = x2 + y2
Final answer:
The derivative dy/dx for the equation 9y cos(x) = x² + y² is found by applying implicit differentiation. Rearranging terms after differentiation, dy/dx is obtained as the fraction (9y sin(x) + 2x) / (9 cos(x) - 2y).
Explanation:
The question asks for the derivative of dy/dx using the equation 9y cos(x) = x2 + y2. To find dy/dx, we can apply implicit differentiation, which implies taking the derivative of both sides with respect to x while treating y as a function of x (y(x)).
Let's differentiate both sides:
The left side: d/dx [9y cos(x)] = d/dx [9y] cos(x) + 9y d/dx[cos(x)] = 9(dy/dx) cos(x) - 9y sin(x)
The right side: d/dx [x2 + y2] = 2x + 2y(dy/dx)
Equating both the derivatives, we have:
9(dy/dx) cos(x) - 9y sin(x) = 2x + 2y(dy/dx)
Now, solving for dy/dx gives us:
dy/dx = (9y sin(x) + 2x) / (9 cos(x) - 2y)
If the pattern continues, how many cups of milk does George need to make 6 batches of muffins? Explain how you found your answer.
To make 6 batches of muffins, George needs 3 cups of milk, which is found by multiplying the ratio of 1/2 cup of milk per batch by 6.
Explanation:The question is asking to determine the quantity of an ingredient needed for a recipe, specifically milk for pancakes, according to a given ratio. The question is based on a proportion where 1/2 cup of milk is needed for one batch of pancakes. To find out how many cups of milk are needed for 6 batches of muffins (assuming muffins and pancakes require the same amount of milk which appears to be a minor typo in the scenario), we multiply the 1/2 cup required for one batch by 6.
Thus, the calculation is: 1/2 cup of milk × 6 batches = 3 cups of milk.
To find out how many cups of milk George needs to make 6 batches of muffins, we first need to determine the number of cups needed for one batch. Let's assume that each batch requires 3 cups of milk. Therefore, to make 6 batches, George would need 3 cups x 6 batches = 18 cups of milk
Find tanθ exactly if sinθ=-9/41, and θ is in the fourth quadrant
"suppose we are comparing the implementations of algorithm a and algorithm b on the same machine. for inputs of size n, algorithm a runs in 2n steps, and algorithm b runs in 5√n steps. for which values of n does algorithm a beat algorithm b?"
The solution is : n = 9
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Explanation:
To find the answer we need to check at what point the running time of algorithm A is equal the running time of B:
1000*n*n = n*n*n*n*n
1000 = n*n*n = n^3
n = ∛(1000) = 10 (when n equals ten A equal B)
For any integer greater than ten B > A and for any integer smaller than ten B < A.
The greatest integer for which B < A is nine, therefore nine is our answer.
A B
1000n^2 n^5
n = 8 64000 < 32768
n = 9 81000 < 59049
n = 10 100000 = 100000
n = 11 121000 > 161051
n = 12 144000 > 248832
therefore nine is our answer.
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For [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex], Algorithm A (which runs in [tex]\( 2n \)[/tex] steps) beats Algorithm B (which runs in [tex]\( 5\sqrt{n} \)[/tex] steps).
To determine for which values of [tex]\( n \)[/tex] Algorithm A beats Algorithm B in terms of running time, we compare their complexities:
Algorithm A runs in [tex]\( 2n \)[/tex] steps.
Algorithm B runs in [tex]\( 5\sqrt{n} \)[/tex] steps.
Algorithm A beats Algorithm B if [tex]\( 2n < 5\sqrt{n} \)[/tex].
Let's solve this inequality step by step:
1. Square both sides to eliminate the square root (valid since [tex]\( n \geq 0 \)[/tex]):
[tex]\[ (2n)^2 < (5\sqrt{n})^2 \][/tex]
[tex]\[ 4n^2 < 25n \][/tex]
2. Bring all terms to one side to form a quadratic inequality:
[tex]\[ 4n^2 - 25n < 0 \][/tex]
3. Factorize the quadratic inequality if possible:
[tex]\[ n(4n - 25) < 0 \][/tex]
4. Find the values of [tex]\( n \)[/tex] that satisfy the inequality:
[tex]\( n(4n - 25) < 0 \)[/tex] holds when one factor is negative, and the other is positive:
[tex]\( n < 0 \)[/tex] and [tex]\( 4n - 25 > 0 \)[/tex]: No valid solutions since [tex]\( n \geq 0 \)[/tex].
[tex]\( n > 0 \)[/tex] and [tex]\( 4n - 25 < 0 \)[/tex]:
[tex]\[ 4n < 25 \Rightarrow n < \frac{25}{4} = 6.25 \][/tex]
[tex]\( n < 0 \) and \( 4n - 25 < 0 \)[/tex]: All [tex]\( n \geq 0 \)[/tex] satisfy this condition.
5. Determine the integer values of [tex]\( n \)[/tex]:
Since [tex]\( n \)[/tex] must be non-negative, the integer values of [tex]\( n \)[/tex] that satisfy [tex]\( 4n^2 - 25n < 0 \)[/tex] are [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex].
Let f(X)=1/x+1
Use the limit definition of the derivative to find:
i) f(-4)
ii) f(-3)
iii) f(1)
iv) f(3)
A cube has an edge if 4 feet. The edge is increasing at a rate of 2 feet per minute. Express the volume of the cube as a function
To find the volume of a cube with an edge length that is increasing with time, express the edge length as a function of time and substitute this into the volume formula. In the given problem, the edge length is increasing 2 feet per minute, thus the volume V of the cube at any given time can be expressed as V = (4 + 2t)³.
Explanation:The volume of a cube is calculated by raising the edge length to the power of three (V = e³). For this problem, we know that the edge e is increasing at a rate of 2 feet per minute. Therefore, we can express e as a function of time t, where e = 4 + 2t. Substituting this back into our volume equation, we receive the volume V of the cube as a function of time t: V = (4 + 2t)³.
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Name the property of equality that justifies: If x = 3 and y = x + 5, then y = 8
Mr. River's car averages 25 3/4 miles per gallon. Express the miles per gallon as a decimal
how do you solve 3 - 1 3/4
Keith has p pennies, n nickels, and d dimes in his pocket. The total number of coins is 9. The expression 0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.44. He has one more dime than nickels. How many pennies does Keith have? Keith has _____ pennies.
he has 4 pennies
2 nickels=10 cents
3 dime=30 cents
20 cents
40 +4 pennies =44 cents
Answer:
Keith has 4 pennies, 3 dimes and 2 nickels.
Step-by-step explanation:
Let the pennies be = p
Let the nickels be = n
Let the dimes be = d
Total coins Keith has = 9
So, 1st equation form :
[tex]p+n+d=9[/tex] ....(1)
Keith has one more dime than nickels, means [tex]d=n+1[/tex] .....(2)
Total value of these coins is $0.44
So, third equation forms:
[tex]0.01p+0.05n+0.10d=0.44[/tex] .....(3)
Substituting (2) in (1)
[tex]p+n+n+1=9[/tex]
[tex]p+2n=8[/tex] .....(4)
Similarly substitution (2) in (3)
[tex]0.01p+0.05n+0.10(n+1)=0.44[/tex]
[tex]0.01p+0.05n+0.10n+0.10=0.44[/tex]
[tex]0.01p+0.15n=0.34[/tex] ....(5)
Now multiplying (4) by 0.01 and subtracting by (5)
[tex]0.01p+0.02n=0.08[/tex] subtracting this from (5) we get
[tex]0.13n=0.26[/tex]
So, we get n = 2
[tex]p+2n=8[/tex]
[tex]p+2(2)=8[/tex]
[tex]p+4=8[/tex]
p = 4
[tex]p+n+d=9[/tex]
[tex]4+2+d=9[/tex]
[tex]6+d=9[/tex]
d = 3
-------------------------------------------------------------------------------------
Therefore, Keith has 4 pennies, 3 dimes and 2 nickels.
The local home improvement store wants to increase their inventory. Last year 40 lawn mowers cost them $4,776.
At the same cost, how much would 120 lawn mowers cost them this year?
Answer:14,328
Step-by-step explanation:
PLEASE ANSWER
Solve the Equation
-2=3x/5+1
which of the following are the factors of 4b^2-16?
The width of a rectangle is 3 4 the length. The perimeter is 252 cm. What is the width of the rectangle? A) 36 cm B) 48 cm C) 54 cm D) 72 cm
Which item would most likely appear on a culturally fair test?
Ursula bought 9 dozen rolls of first aid tape for the health office. The rolls were divide equally into 4 boxes. How many rolls are in each box?
Explain why you think slope-intercept form makes sense as a name for y = mx +
b. explain why you think point-slope form make sense as a name for y - y1 = m(x - x1)
The slope-intercept form y = mx + b shows how the slope and y-intercept values are used in the equation, while the point-slope form y - y₁ = m(x - x₁) defines a line using a point and the slope.
Explanation:The slope-intercept form, y = mx + b, makes sense as a name because it explicitly shows how the slope and y-intercept values are used in the equation.
The 'm' represents the slope, which describes the steepness of the line, and the 'b' represents the y-intercept, which indicates where the line intersects the y-axis.
For example, in the equation y = 2x + 3, the slope is 2 and the y-intercept is 3.
The point-slope form, y - y₁ = m(x - x₁), is called so because it defines a line using a single point (x₁, y₁) and the slope 'm'. This form makes it easier to determine the equation of a line when given a point and the slope.
For instance, in the equation y - 2 = -3(x - 4), the point (4, 2) and the slope -3 are used to specify the line equation.