Using implicit differentiation, it is found that the water level is rising a rate of 0.001 ft/sec.
The volume of a pool of length l, width w and height h is given by:
[tex]V = lwh[/tex]
Applying implicit differentiation, the rate of change of the volume is given by:
[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]
Neither the width nor the length changes, hence [tex]\frac{dl}{dt} = \frac{dw}{dt} = 0[/tex], and:
[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]
We are given that:
[tex]\frac{dV}{dt} = 0.3, l = 20, w = 40[/tex], hence:
[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]
[tex]0.8 = 20(40)\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{0.8}{800}[/tex]
[tex]\frac{dh}{dt} = 0.001 [/tex]
Water level is rising at rate of 0.001 ft/sec.
A similar problem is given at https://brainly.com/question/9543179
A car is travelling at a constant speed until the car’s brakes are applied. The car’s speed changes at a rate given by -0.08t ms^{-2} after the brakes are applied, where t s is the time since the brakes were applied. 3 seconds after the brakes are applied, the speed of the car is 5 ms^{-1} . How far will the car travel with the brakes applied before it stops?
The car will travel a distance of 52.08 seconds will the brakes applied before it stops
The acceleration of the car after t seconds that the brake was applied is given as:
[tex]a=-0.08t m/s^2[/tex]
The speed of the car after 3 seconds that the brake was applied, u = 5 m/s
The speed of the car when it eventually stops, v = 0m/s
3 seconds after the brake was applied:
The time, t = 3 seconds
substitute t = 3 into the acceleration [tex]a=-0.08t m/s^2[/tex]
[tex]a=-0.08(3)m/s^2\\\\a = -0.24m/s^2[/tex]
To calculate the distance traveled by the car after the brakes are applied, use the equation below
[tex]v^2=u^2+2as[/tex]
Substitute u = 5, a = -0.24, and v = 0 into the equation above in order to calculate the distance
[tex]0^2=5^2+2(-0.24)s\\\\0=25-0.48s\\\\0.48s = 25\\\\s = \frac{25}{0.48}\\\\s = 52.08 m[/tex]
The car will travel a distance of 52.08 seconds will the brakes applied before it stops
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16.12 divided by 52 QUICK
0.31
Ok Hope it’s correct ;)
at edgars bakery one customer buys 4 donuts and 10 muffins for $32. Another customer buys 12 donuts and 5 muffins and pays $21.
x=price of donut
y=price of muffin
1. Write an equation to represent the first customer
2.write an equation to represent the 2nd customer
3.solve system of equations
Based on the information given, the price of donut will be 1.5 and the price of muffin is 3.8.
The equation to represent the first customer is 4x + 10y = 32
The equation to represent the 2nd customer is 12x + 5y = 21
Solving the equations will be:
4x + 10y = 32 ...... i
12x + 5y = 21 ......ii
Multiply equation i by 12
Multiply equation ii by 4
48x + 120y = 384
48x + 20y = 84
100y = 380
y = 380/100 = 3.8
Therefore, we'll find the value for x which will be:
4x + 10y = 32
4x + 10(3.8) = 32
4x = 32 - 38
4x = -6
x = -1.5
Therefore, the price of donuts will be 1.5 and the price of muffin is 3.8.
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Just number three pls give right answer and will give brainless
Answer:
i think 34
Step-by-step explanation:
because thats the answer i got on calculator
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $160 and first class tickets for $1020. She used her total budget for airfare for the trip, which was $8480. How many first class tickets did she buy? How many coach tickets did she buy?
Answer: 6 coach class tickets and 2 first class tickets
Step-by-step explanation:
a coin is flipped 3 times and lands on heads each time. What is the probability of it landing on tails on the fourth flip?
Answer:
1/4
Step-by-step explanation:
since the dice would be rolled 4 times, and the dice rolled heads 3 times, the probability of the coin land8ng of tail on the 4th flip is 1/4
The probability of it landing on tails on the fourth flip will be 1/4.
What is probability?
Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that a coin is flipped 3 times and lands on heads each time. The probability of getting head on the fourth flip will be:-
Probability = Number of favorable outcomes / Number of sample
Number of favorable outcomes = tails = 1
Number of samples = 4
Probability = 1 / 4
Therefore, the probability of it landing on tails on the fourth flip will be 1/4.
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#SPJ2
help me please guys! for the most brain lol
Answer:
-3<-1
-3[tex]\leq[/tex]-1
Step-by-step explanation:
[tex]\leq[/tex] Means less than or equal to
< Means less than
How do the expressions 5h2−3g and 3(g+h)h compare when g = 10 and h = 3?
Drag a symbol into the box to correctly complete the statement.
5h2−3g Response area 3(g+h)h when g = 10 and h = 3.
Answer:
the answer is >
Step-by-step explanation:
I took the test
what is the greatest number of obtuse angles that a right triangle can contain
Step-by-step explanation:
i think this is the answer
Answer:
ZeroStep-by-step explanation:
Obtuse angle is the angle greater than 90°.
A right triangle has one 90° and the sum of remaining angles is 90°.
It means a right triangle can't have an obtuse angle.
Does anyone know this?
Answer: 8.6?
Step-by-step explanation:
Use the elimination method to solve the system of equations. Choose the correct orderly pair.
2x+4y=16
2x-4y=0
A. (2,-4)
B. (4,-2)
C. (2,4)
D. (4,2)
(2x+4y=16).....1
(2x-4y=0).....2
then take equation 1 plus 2
4x=16
x=4
then take equation 2 to solve for y
2x-4y=0
(2×4)-4y=0
y=2
therefore answer is D. (4,2)
One non-negative number is the reciprocal of another number. The sum of the two numbers is a minimum. What are the two numbers
The two numbers are 1 and 1.
Let the non-negative number be x and its reciprocal be y = 1/x
The sum of the two numbers is f(x,y) = x + y
= x + 1/x
= f(x)
For f(x) to be minimum, we differentiate it with respect to x and equate it to zero to find the value of x at which irt is minimum.
So, df(x)/dx = d(x + 1/x)/dx
= dx/dx + d(1/x)/dx
= 1 - 1/x²
Equating it to zero, we have
1 - 1/x² = 0
1 = 1/x²
x² = 1
Taking square-root of both sides, we have
x = ±√1
x = ±1
Since x is non-negative x = + 1
We differentiate f(x) again to determine if this value gives a minimum for f(x).
So, d²f(x)/dx² = d(1 - 1/x²)/dx
= d1/dx - d(1/x²)/dx
= 0 - × (-2/x³)
= 2/x³
Substituting x = 1 into the equation,
d²f(x)/dx² = 2/x³
= 2/1³
= 2 > 0.
So x = 1 is a minimum point for f(x)
Since x = 1 and y = 1/x, y = 1/1 = 1
So, the two numbers are 1 and 1.
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Is there a proportional relationship between x and y? Explain.
Answer:
c
Step-by-step explanation:
14-11=3
12-9=3
10-7=3
8-5=3
Answer:
A
Step-by-step explanation:
It isn’t proportional because when you graph the coordinates, it doesn’t pass the origin, so it isn’t equivalent. Therefore, making the answer A.
what is the answer for number 2?
Answer:
7/3
Step-by-step explanation:
integral of equation is x^3/3-6x^2/2+5x/1
the answer will be
7^3/3-3*7^2+5*7-0= 343/3-147+35= 7/3
What is 11% of 96 students
Answer:
8.7
Step-by-step explanation:
8.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.7
Bạn dự định đi học thêm vào mùa hè này. Nếu đi học bạn sẽ không thể đi làm với thu nhập là 5 triệu đồng và không thể ở nhà nghỉ ngơi. Học phí là 2 triệu, tiền mua giáo trình 300 ngàn, sinh hoạt phí là 1.5 triệu. Hãy xác định chi phí cơ hội của việc đi học thêm vào mùa hè này.
Answer:
4 better inbox
Step-by-step explanation:
geomtry plzzzzz help. me
Answer:
N=3.5
Step-by-step explanation:
it is 3.5 because it said line p is the perendicular bisector so the triangle has to be equal. so the line ZY=XY
14/4=3.5
If Brianna spent $65 on necklaces and bracelets at a crafts fair.
She spent $23 on bracelets and the rest on necklaces.
If the necklaces all cost the same and Brianna bought 3, how much did each necklace cost?
help plsssssssssssss
Answer:
with what
Step-by-step explanation:
Answer:
help with? there's nothing there
Someone help me on PART B:
Step-by-step explanation:
given expression,
4(3x - 1) - 2(6 + 2x)
given,
x = 12.5
so q/q
→ 4[3(12.5) - 1] - 2[6 + 2(12.5)]
→ 4(37.5 - 1) - 2(6 + 25)
→ 4 × 36.5 - 2 × 31
→ 146 - 62
→ 84
therefore, 84 articles store received last Thursday.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE.
Answer:
84
Step-by-step explanation:
1,200 miles; 5% increase
Answer:
5%equals 5 divided by 100 equals 600
calc 3 iiiiiiiiiiiiiiiiiiiiiiiiiiii
Take the Laplace transform of both sides:
L[y'' - 4y' + 8y] = L[δ(t - 1)]
I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :
(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]
s²Y - 4sY + 8Y = exp(-s)
(s² - 4s + 8) Y = exp(-s)
Y = exp(-s) / (s² - 4s + 8)
and complete the square in the denominator,
Y = exp(-s) / ((s - 2)^2 + 4)
Recall that
L⁻¹[F(s - c)] = exp(ct) f(t)
In order to apply this property, we multiply Y by exp(2)/exp(2), so that
Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)
Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)
Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)
Then taking the inverse transform, we have
L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]
L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]
L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]
Next, we recall another property,
L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)
where F is the Laplace transform of f, and u(t) is the unit step function
[tex]u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}[/tex]
To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is
L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)
Then we find
L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))
and so we end up with
y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)
Whats the area and the perimeter of this shape. show calculations
Answer:
The answer is 15 cm
Step-by-step explanation:
as one square is 1 cm and there are 15 squares used for this shape then it is 15 cm
If X is a factor of Y and Y is a factor of Z then X is a factor of Z. If so then how
PLS HELP HELP HELP HELP HELP HELP HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
then z is a factor of x??? huh??
at the fish market, a whole fish costs $4.20. If the body costs $1 more than the tail, and the body costs $2 more than the head, how much does the head cost?
Answer:
$ 0.4
Step-by-step explanation:
if we assume head costs $ x then,
body will cost $x + 2 (2 more than head)
and tail will cost $x+1
x+x+2+x+1 = $ 4.20
or, 3x = 4.20-3
or, x= 1.20/3
therefore, x=0.4
Answer:
$ 0.4
Step-by-step explanation:
.45 is 1/10 of what?
Answer:
The answer is 4.5
consider the following :
[tex]f(x) = {x}^{2} - x + 2 \div x - 2 = x + 1 + 4 \div x - 2[/tex]
which polynomials do you think we should call the divisor,dividend,quotient and remainder ?
Step-by-step explanation:
remainder=4
quotient=x+1
divisor=x-2
dividend=x^2 -x +2
Pls help. The question is on the picture
Volume of the square part" 20 x 20 x 37 = 14,800 m^3
Volume of a cone ( round part): PI x r^2 x h/3 = 3.14 x 10^2 x 37/3 = 3,872.67 m^3
The1/4 of the circle is inside the square so multiply the volume of the cone by 3/4:
3872.67 x 3/4 = 2904.50m^3
Total volume = 14,800 + 2904.50 = 17,704.50
Round to nearest m = 17,705 m^3
Which expression finds the length of side y in this right triangle?
Answer:
y = [tex]\sqrt{19^2} + \sqrt{8.2^2}[/tex]
Step-by-step explanation:
Pythagorean Theorem : a² + b² = c²
19² + 8.2² = c²
c = [tex]\sqrt{19^2 + 8.2^2}[/tex]
c = [tex]\sqrt{19^2} + \sqrt{8.2^2}[/tex]
-Chetan K
Write 2 over 5 as a percent.
Answer:
40%
Step-by-step explanation:
2/5 = 40/100 = 40%
