a rectangular well is 6 feet long, 4 feet wide, and 10 feet deep. if water is running into the well at the rate of 3 ft3 /min , how fast is the water rising?
Answers
The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
To calculate this, we can use the following formula:
Rate of Water Rising = Volume of Water Added Per Minute / Total Volume of Well
Rate of Water Rising = 3 ft3/min / 240 ft3
Rate of Water Rising = 1/80 ft per minute
Therefore, The volume of water in the well is 6 x 4 x 10 = 240 ft3. Since water is running into the well at the rate of 3 ft3 per minute, the water is rising at the rate of 3/240 ft per minute or 1/80 ft per minute.
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Related Questions
Apply the Law of Exponents to write an equivalent expression of -4x³y2 - 3x5y6
Answers
The equivalent form of 4x³y³ - 3x⁵y⁶ is ,
⇒ \(x^{3} y^{3}( 4 - 3x^{2}y^{3})\)
The given expression is.,
4x³y³ - 3x⁵y⁶
Here we have to write the equivalent form of the given expression by using exponent law,
Since we know that,
Exponent is defined as the method of expressing large numbers in terms of powers.
That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times,
i.e. 6 × 6 × 6 × 6.
This can be written as 64. Here, 4 is the exponent and 6 is the base. This can be read as 6 is raised to power 4.
Therefore,
Applying exponent law of product,
\(x^{a} x^{b} = x^{a+b}\)
So we can write the given expression as
⇒ \(4x^{3} y^{3} - 3x^{5} y^{6}\)
⇒ \(4x^{3} y^{3} - 3x^{3+2} y^{3+3}\)
⇒ \(4x^{3} y^{3} - 3x^{3} x^{2} y^{3}y^{3}\)
⇒ \(x^{3} y^{3}( 4 - 3x^{2}y^{3})\)
Hence the expression,
\(x^{3} y^{3}( 4 - 3x^{2}y^{3})\) is equivalent to the given expression.
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David has a coin collection. He keeps 11 of the coins in his box, which is 5% of the
collection. How many total coins are in his collection?
Insert the values given in the problem then scale up or down
to find the missing value.
coins
percent
100
Answers
Scaling up, David has 220 coins in his collection with 5% of 11 of the coins kept in his box.
What is a scale up?A scale up represents an increase or growth.
Scale factors are ratios comparing two quantities or values.
Proportionately, if 5% represent 11 coins, 100% will be 220 coins.
The number of coins David keeps in his box = 11
The percentage of the coins kept in the box = 5%
Thus, proportionately, 11 = 5%; therefore, 100% = 220 (11 ÷ 5%).
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Multiple choice question
Answers
Answer:
35b is the answers for the question
Step-by-step explanation:
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Sasha needs to write a division expression for the fraction 9/14. She is not sure which number goes where. Help Sasha understand how to write a division expression from a fraction
Answers
To write a division expression from a fraction, identify the numerator, which is the dividend, while the denominator is the divisor.
What is a division expression?A division expression is an algebraic expression using the division operand (÷).
Algebraic expressions involve the combination of numbers, constants, values, and variables with mathematical operands.
The result of a division operation, which is one of the four basic mathematical operations, is known as the quotient.
Thus, we can conclude that the dividend is related to the numerator of the fraction just as the divisor is related to the denominator of the fraction.
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a real estate agent sold a house for $718,000. He makes a 5.5% commission. How much did he make?
Answers
Answer:
$39490
Step-by-step explanation:
0.055 × 718000 = $39490
Denise is using a ladder to clean the outside of her second story windows. The ladder she is using is 24 feet long, and she puts the base of the ladder 13 feet away from the house in order to avoid her flower garden. How high up the side of her house does the ladder reach? Round to the nearest tenth.
Answers
Answer:
72 ft
Step-by-step explanation:
What is the y - intercept of the line perpendicular to 5x - 3y = 8 through the point (-5, 2)?
Answers
Answer:
Let's see what to do buddy..
Step-by-step explanation:
_________________________________
STEP (1)
We have to first find the slope of the given line. To do that we must write the given line to slope-intercept form.
\(5x - 3y = 8\)
Subtract the sides of the equation minus 5x :
\( - 3y = 8 - 5x \\ - 3y = - 5x + 8\)
Divided the sides of the equation by -3 :
\( \frac{ - 3}{ - 3}y = \frac{ - 5x + 8}{ - 3} \\ \\ y = \frac{5}{3}x - \frac{8}{3} \)
We know that the slope-intercept form of the linear functions is like this :
\(y = a \: x + b\)
Where a is the slope and b is width of origin.
So the slope of the given line is 5/3.
_________________________________
STEP (2)
The slopes of two lines perpendicular to each other are symmetrical and inverse to each other.
In other words, the product of the slopes of two lines perpendicular to each other is -1 .
So :
\( \frac{5}{3} \times (t) = - 1 \\ \)
Divided the sides of the equation by 5/3 :
\( \frac{ \frac{5}{3} }{ \frac{5}{3} } \times t = \frac{ - 1}{ \frac{5}{3} } \\ \\ t = - \frac{3}{5} \)
((t)) is the slope of the line which we want to find.
_________________________________
STEP (3)
We have this equation to find the slope-intercept form of the linear functions :
\(y - y(given \: point) = (slope) \times ( \: x - x(g \: p) \: ) \\ \)
Now Just need to put the slope and the given point in the equation:
given point = ( -5 , 2 )
slope = -3/5
\(y - 2 = - \frac{3}{5}(x - ( - 5)) \\ y - 2 = - \frac{3}{5}(x + 5) \\ y - 2 = - \frac{3}{5}x - 3 \\ \)
Subtract the sides of the equation plus 2 :
\(y = - \frac{3}{5}x - 1 \\ \)
And we're done.
Thanks for watching buddy good luck.
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in class, we proved that the number of ways of tiling a $1 \times n$ rectangle with $1 \times 1$ and $1 \times 2$ tiles is $f {n 1}.$ (a) use a tiling argument to give a combinatorial proof that \[f 1 f 2 f 3 \dots f n
Answers
Here is a straightforward recursion you may employ to calculate the value.
let's use rectangles with integer aspects to represent the quantity of tilings of a $2 instances n$ rectangle as $T(n)$. There are $22n-2$ techniques to accomplish this if no rectangles of height $2$ are hired, wherein case we lessen to two wonderful times of the $1 times n$ state of affairs. If no longer, we set a situation based at the top-proper rectangle's $2 height. With the preliminary conditions $T(0)=1$ and $T(1)=2$, this results in $$T(n)=22n-2+sum k=0n-1 T(okay)+sum 0leq k ell leq n-1T(ok)22(n-ell-1)$. The center term inside the recursion corresponds to the case where the rightmost rectangle of top $2$ is absolutely the rightmost rectangle inside the tiling.It should be noted that the formula $2n-1$ for the $1 times n$ case is incorrect if $n=0$.
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Simplify: 9y(-3y to the eighth power)
Answers
Felipe calculated that he uses about 545 gallons of fuel each year. His car's owner's manual says that it is approved to use regular fuel. How much money can he save each year by switching from premium fuel, at $4.59 per gallon, to regular fuel at $4.18 per gallon?
$0.41
$2,501.55
$223.45
$2,278.10
$4,779.65
Answers
Answer:
$223.45
Step-by-step explanation:
premium fuel: 4.59 x 545
= 2501.55
regular fuel: 4.18 x 545
=2278.1
2501.55-2278.1 = 223.45
If the discriminant of a quadratic equation is 4, which statement describes the roots?
There are two complex roots.
There are two real roots.
There is one real root.
There is one complex root.
Answers
Answer: There are two real roots
Step-by-step explanation: Terms in this set (6) If the discriminant of a quadratic equation is 4, which statement describes the roots? B. There are two real roots.
As of discriminant of the quadratic equation is 4, then we find that there two real and distinct roots.
In a quadratic equation, the discriminant of the quadratic formula indicates the nature of the two roots of the polynomial. Main characteristics are described below:
If discriminant is greater than zero, then roots are real and distinct.If discriminant is zero, then roots are real and equal.If discriminant is less than zero, then roots are complex.According to the statement, the discriminant of the quadratic equation is 4, then we find that there two real and distinct roots.
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Tamar's house is greater than 472 and less than 500 which number can be on Tamar's house?
Answers
490
472 <490<500
it fits the criteria
A ball is thrown downward from the top of a 200 foot building with an initial velocity of 24 ft. /s.  The height of the ball H in feet after tea seconds is given by the equation H equals -16 T^2-24t+200. How long after the ball is thrown will it strike the ground?
Answers
The time it takes the ball to strike the ground after it is thrown, found using the kinematic equation, H = -16·t² - 24·t + 200 is approximately 2.86 seconds
What is a kinematic equation?A kinematic equation is an equation of the motion of an object moving with a constant acceleration.
The direction in which the ball is thrown = Downwards
Height of the building = 200 foot
Initial velocity of the ball = 24 ft./s
The kinematic equation that indicates the height of the ball after t seconds is, H = -16·t² - 24·t + 200
At ground level, H = 0, therefore;
H = 0 = -16·t² - 24·t + 200
-16·t² - 24·t + 200 = 0
-2·t² - 3·t + 25 = 0
t = (3 ± √((-3)² - 4 × (-2)×25))/(2×(-2))
t = (3 ± √(209))/(-4)
t = (3 + √(209))/(-4) ≈ -4.36 and t = (3 - √(209))/(-4)) ≈ 2.86
The time it takes the ball to strike the ground after it is thrown is approximately 2.86 seconds.Learn more about kinematic equations in mathematics here:
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A 74.0 kg sprinter starts a race with an acceleration of 1.36 m/s
2
. If the sprinter accelerates at that rate for 34 m, and then maintains that velocity for the remainder of the 100 m dash, what will be his time (in s) for the race?
Answers
Given DataMass, m = 74.0 kg, Acceleration, a = 1.36 m/s²
Initial velocity, u = 0
Distance covered before constant velocity, s = 34 m
Distance remaining, s' = 100 - 34 = 66 m
Formula Used The equation for calculating distance is given by: s = ut + (1/2)at²
Where,s = Distance
u = Initial velocity
a = Acceleration
t = Time , The equation for calculating time is given by:t = √((2s)/
a)Calculation Acceleration remains constant, so the equation for calculating time will be:
t = √((2s)/a)t = √((2(34))/1.36)t = 5.11 s
Now, for calculating the remaining time taken by the sprinter to complete the race, we need to find the final velocity of the sprinter. The equation used is given by:v² - u² = 2as'
Where,v = Final velocity, u = Initial velocity, a = Accelerations' = Distance remaining
v² = u² + 2as'v² = 0 + 2(1.36)(66)v² = 179.52v = 13.4 m/sNow, we can calculate the time taken by the sprinter for the remainder of the race.t' = s'/vt' = 66/13.4t' = 4.93 s
The total time taken by the sprinter for the race is given by:Total time taken, t_total = t + t' = 5.11 + 4.93 ≈ 10.04 s
Therefore, the time taken by the sprinter to complete the race is approximately 10.04 seconds.
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(a) Verify that y tan (x c) is a one-parameter family
of solutions of the differential equation y 1 y2. (b) Since f(x, y) 1 y2 and fy 2y are continuous everywhere, the region R in Theorem 1. 2. 1 can
be taken to be the entire xy-plane. Use the family of
solutions in part (a) to find an explicit solution of
the first-order initial-value problem y 1 y2
,
y(0) 0. Even though x0 0 is in the interval
(2, 2), explain why the solution is not defined on
this interval. (c) Determine the largest interval I of definition for the
solution of the initial-value problem in part (b)
Answers
The expression y tan(xc) is a one-parameter family of solutions of the differential equation y' = 1/y^2.To verify that y tan(xc) is a solution of the differential equation, we need to find its derivative and substitute it into the differential equation.
Taking the derivative of y tan(xc) with respect to x, we use the product rule:(dy/dx) tan(xc) + y sec^2(xc) * c = 1/y^2. Now we simplify the equation: (sec^2(xc) + c) y = 1/y^2. We know that sec^2(xc) + c is a constant, let's call it k. So we have:
\(k * y = 1/y^2.\)
Dividing both sides by y and rearranging, we get:
\(ky^3 - 1 = 0.\)
This equation is satisfied for any real value of k, which means that y tan(xc) is a one-parameter family of solutions. (b) The explicit solution of the initial-value problem y' = 1/y^2, y(0) = 0, using the family of solutions \(y = tan(xc), is y = 0.\)
Given the initial condition y(0) = 0, we can substitute x = 0 into the equation y = tan(xc). This gives us y = tan(0 * c) = tan(0) = 0. Therefore, the solution to the initial-value problem is y = 0. Even though x0 = 0 is in the interval (-2, 2), the solution is not defined on this interval because the function y = tan(xc) has vertical asymptotes at x = ±π/2c. For the solution to be defined, x must be outside the intervals where these vertical asymptotes occur. (c) The largest interval of definition, I, for the solution of the initial-valueproblem in part (b) is (-∞, ∞).Since the solution y = 0 is a constant function, it is defined for all real values of x. Therefore, the largest interval of definition for the solution is the entire real line, (-∞, ∞). The solution is valid for any value of x.
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Liz is using the distributive property to evaluate the expression 27 (36) by using friendlier numbers. Her work is shown below.
Liz’s Work
27(36)
Step 1
27 (3 + 12)
Step 2
27 (3) + 27 (12)
Step 3
81 + 324
Step 4
405
What was the first error that Liz made?
Answers
Answer:
the first error she made was that she used the wrong numbers to multiply by
Step-by-step explanation:
Answer:
Error: she replaced 36 with the unequaled value of 3+12.
Step-by-step explanation:
The first error made is 36 cannot be substituted with 3+12 because 36 doesn't equal 3+12. She might have been thinking 3(12)=36. She could have done 10+10+10+5+1 for 36 and did the following:
27(10+10+10+5+1)
270+270+270+135+27
(270+270)+(270+135)+27
(540)+(405)+27
972
Describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. Look at image for example. Let’s do problem number 11f(x)=2(x-1)^2 + 1h(x) = f(x-5)
Answers
1) Note that we can see the following function:
\(f(x)=2\left(x-1\right)^2+1\)Note that we can see that this function f is vertically stretched, translated 1 unit to the side, and vertically shifted one unit
2) Now, let's visualize h(x):
\(\begin{gathered} h(x)=f(x-5)=2((x-5)-1))^2+1 \\ h(x)=2\left(x-6\right)^2+1 \end{gathered}\)Note that the difference between the graph of f and the graph of h(x) is h(x) is translated 5 units to the right.
So h(x) is horizontally translated 5 units to the right
Prove algebraically that (image). Trigonometric Identities. Please help.
Answers
Answer:
Step-by-step explanation:
jayce travels 30 miles per hour in her car.how many miles does she travel in 4 hours
Answers
Answer:
120 miles
Step-by-step explanation:
30 miles per hour * 4 hours
120 miles
Answer:
She travels 120 miles in 4 hours.
Step-by-step explanation:
She travel in 4 hours = 30 miles × 4 = 120 milesShe travels 120 miles in 4 hours
Write the prime factorization: 52
Answers
Answer:
2² * 13
Step-by-step explanation:
Prime Factorization refers to the representation of the number as the product of prime numbers.
Dividing it by 2 until it reaches a point that it cannot be divided by 2 (since 2 is a prime number):
52/2 = 26/2 = 13
Since 13 is a prime number:
13/13 = 1
Hence,
52 = 2 * 2 * 13
= 2² * 13
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What is the conversion of 70f to celcius?
Answers
The conversion of 70°F is equal to 21.1°C.
A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).
Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.
To convert 70°F (degrees Fahrenheit) to Celsius (°C), you can use the following formula:
°C = (°F - 32) / 1.8
Substituting 70°F for °F in the formula, we get:
°C = (70 - 32) / 1.8
Simplifying the calculation, we get:
°C = 38 / 1.8
°C ≈ 21.1
Therefore, the conversion of 70°F is nearly equal to 21.1°C.
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I will give you BRAINLIEST for the correct answer
Answers
Answer:
If I got this wrong pls dont get mad but I think the answer 150
what is the rule for finding the sum of two negative integers
Answers
adding two negative integers always yields a negative sum
What is the value of x in this triangle?
38
53
Enter your answer as a decimal in the box. Round only your final
answer to the nearest hundredth.
Answers
Answer:
x = 45.79°
Step-by-step explanation:
You can use sin Θ to find the value of x.
Let us find it now.
Sin x = Opposite / Hypotenuse
Sin x = 38 / 53
Sin x = 0.7169
x = Sin ⁻¹ 0.7169
x = 45.79°
A square flower garden is surrounded by a brick walkway that is 1.8 m wide. The area of the walkway is equal to the area of the garden. Determine the dimensions of the garden to the nearest tenth of a metre.
Answers
The length of the garden is 4.3 m while the width is 4.3 m
Let x represent the length of the garden. Therefore:
The area of the garden = x × x = x²
The width of the walkaway is 1.8 m, hence the length of the garden and walkaway = x + 1.8. The width of the garden and walkaway = x + 1.8.
Hence the area of the garden and walkaway = (x + 1.8) × (x + 1.8) = x² + 3.6x + 3.24
The area of walkaway = (x² + 3.6x + 3.24) - x² = 3.6x + 3.24
Since the area of the walkway is equal to the area of the garden, hence:
3.6x + 3.24 = x²
x² -3.6x - 3.24 = 0
x= 4.34 m or -0.74 m
Since the length cannot be negative, hence x = 4.3 m
Therefore the garden is 4.3 m by 4.3 m
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In a circle centered at point O, the ratio of the area of sector AOB to the area of the circle is . What is the approximate measure, in radians, of the central angle corresponding to
Answers
In a circle centered at point O, the ratio of the area of sector AOB to the area of the circle is given. To find the approximate measure, in radians, of the central angle corresponding to this ratio, we can use the formula for the area of a sector:
Area of sector = (central angle / 360°) * π * r^2
We are given the ratio of the area of sector AOB to the area of the circle, which is. Let's denote this ratio as x:
x = (central angle / 360°) * π * r^2 / (π * r^2)
Simplifying the equation, we get:
x = (central angle / 360°)
To find the measure of the central angle, we can rearrange the equation as:
central angle = x * 360°
So, the approximate measure, in radians, of the central angle corresponding to the given ratio is x * 360°.
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a bin contains 21 balls, numbered 1 through 21. how many ways are there to pick a set of six balls from the bin in which at least one ball has an odd number?
Answers
To find the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number, we can use the principle of inclusion-exclusion.
First, we find the total number of ways to pick a set of six balls from the bin, which is 21 choose 6 (written as C(21,6)) = 54264.
Next, we find the number of ways to pick a set of six balls from the bin in which all the balls have even numbers. There are only 10 even-numbered balls in the bin, so the number of ways to pick a set of six even-numbered balls is 10 choose 6 (written as C(10,6)) = 210.
Therefore, the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number is:
C(21,6) - C(10,6) = 54264 - 210 = 54054.
So there are 54054 ways to pick a set of six balls from the bin in which at least one ball has an odd number.e
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Suppose that a volcano is erupting and readings of the rate r(f) at which solid materials are spewed into the atmosphere are given In the table. The time t is measured in seconds and the units for r(t) are tonnes (metric tons) per second. (a) Give upper and lower estimates for the total quantity Q(6) of erupted materials after 6 seconds using 6 subintervals. Q(6) = _____ tonnes (lower estimate) Q(6) = _____ tonnes (upper estimate) (b) Use the Midpoint with three subintervals to estimate Q(6). Q(6) = _____ tonnes
Answers
We can give upper and lower estimates using the Trapezoidal Rule with 6 subintervals and use the Midpoint Rule with 3 subintervals to obtain a more accurate estimate.
Explanation:
To estimate Q(6) using the Trapezoidal Rule with 6 subintervals, we divide the interval [0, 6] into 6 subintervals of equal width. Then, we use the formula for the Trapezoidal Rule:
Q(6) ≈ h/2 * [f(0) + 2f(h) + 2f(2h) + ... + 2f(5h) + f(6h)]
where h is the width of each subinterval (h = 1 in this case), and f(t) is the rate at which materials are spewed into the atmosphere at time t. Using the values in the table, we can calculate the lower and upper estimates for Q(6) using this formula.
For the Midpoint Rule with 3 subintervals, we divide the interval [0, 6] into 3 subintervals of equal width. Then, we use the formula for the Midpoint Rule:
Q(6) ≈ h * [f(1.5h) + f(4.5h) + f(7.5h)]
where h is the width of each subinterval (h = 2 in this case). Again, using the values in the table, we can calculate an estimate for Q(6) using this formula.
The upper and lower estimates for Q(6) using the Trapezoidal Rule with 6 subintervals are 12.45 tonnes and 16.25 tonnes, respectively. The estimate for Q(6) using the Midpoint Rule with 3 subintervals is 15.82 tonnes. The Midpoint Rule gives a more accurate estimate since it uses the midpoint of each subinterval, which can reduce the error introduced by the linear approximation of the Trapezoidal Rule.
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Describe the relationship between the number of "at bats" and the number of hits using the data in the scatter plot.
A.)For these data, as the number of at bats increases, the number of hits tend to increase.
B.) For these data, the number of at bats and hits do not appear to be related.
C.)For these data, as the number of hits increase, the number of at bats tend to stay the same.
D.) For these data, as the number of at bats increases, the number of hits tend to decrease.
Answers
Answer: A.) For these data, as the number of at bats increases, the number of hits tend to increase.
This is because the points seem to trend upward as we move from left to right. This makes sense because the more attempts you get, the more hits you're expected to get.
Assume that someone has a batting average of 0.300; this means that if they got 1000 attempts, then we expect about 0.300*1000 = 300 hits. Now if they got 2000 at bats this time, then we expect about 0.300*2000 = 600 hits.
Of course things won't fit this perfectly since everything in life has random statistical error, but this gives a good idea of the upward trending data. The two variables (at bats and hits) are strongly related. We can say the variables have strong positive correlation.
A survey was done that asked people to indicate whether they preferred to ride a
street bike or a mountain bike. The results of the survey are shown in the two-way
table.
Amjed is making a relative frequency table from this data.
What operation should Amjed perform to determine the relative frequency of a
person over 30 years old who prefers to ride a mountain bike? 1) Subtract 25 from 462, then divide by 462. 2) Divide 25 by 462. 3) Add 180 to 462, then divide by 463. 4) Divide 180 by 462
Answers
The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:
2) Divide 25 by 462.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.
The total number of people is given as follows:
58 + 164 + 215 + 25 = 462.
Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:
25/462.
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