spherical water tank of radius R = 5m is emptied through a small circular hole of radius r = 0.03 m at the bottom. The top of the tank is open to the atmosphere. The instantaneous water level h in the tank (measured from the bottom of the tank, at the drain) can be determined from the solution of the following ODE:
dh /dt =r²(2gh)^0.5/ 2hR-h²
where g = 9.81 m/s². If the initial (t = 0) water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.

[tex] \frac{3}{10 } = 0.3[/tex]

[tex]0.25 < 0.3 < 0.333[/tex]

[tex] \frac{32}{100} = \frac{8}{25} = 0.32[/tex]

[tex]0.25 < 0.32 < 0.333[/tex]

[tex] \frac{26}{100} = \frac{13}{50} = 0.26[/tex]

[tex]0.25 < 0.26 < 0.333[/tex]

[tex] \frac{28}{100} = \frac{7}{25} = 0.28[/tex]

[tex]0.25 < 0.28 < 0.333[/tex]

[tex] \frac{252}{1000} = \frac{63}{250} = 0.252[/tex]

[tex]0.25 < 0.252 < 0.333[/tex]

[tex] \frac{ \frac{ - 2}{5} + \frac{1}{2} }{2} = \frac{ \frac{ - 4 + 5}{10} }{2} = \frac{ \frac{1}{10} }{2} = \frac{1}{20} [/tex]

19.99 + 15= 34.99

40-34.99 = 12.51

Jenny received $5.01 change.

4 ( b + 5 )- 2b = 100

____________________

B  =  40

Answer:

[tex]\tt b=40[/tex]

Step-by-step explanation:

[tex]\tt 4 ( b + 5 )- 2b = 100[/tex]

[tex]\bf Expand\; (Apply\; Distributions\; Law) :-[/tex]

[tex]\tt 2b+20=100[/tex]

[tex]\tt 2b+20-20=100-20\;\; (Subtract \;20\; from\; both \;sides)[/tex]

[tex]\tt 2b=80[/tex]  [tex]\tt (Simplify)[/tex]

[tex]\tt \cfrac{2b}{2}=\cfrac{80}{2}\;\;( Divide\; both \;sides\: by\; 2)[/tex]

[tex]\tt b=40[/tex]

~

Answer:

Step-by-step explanation:

All the three sides are equal. So, it is an equilateral triangle.

Each angle in an equilateral triangle = 60°

7x + 4 = 60

    7x  = 60 -4

    7x   = 56

      x = 56/7

x = 8

✿————✦————✿

Answer: D

✿————✦————✿

Answer:

Center: (2, -11)

Radius: 10

Step-by-step explanation:

(x - 2)² + (y + 11)² = 100

(x - h)² + (y - k)² = r²

-------------------------------

x - 2 = 0

  +2   +2

x = 2

------------

y + 11 = 0

   -11    -11

y = -11

------------------------------

r² = 100

r = √100

r = 10

----------------------------

Center: (h, k)

Radius: r

-------------------------------

Center: (2, -11)

Radius: 10

I hope this helps!

We are given the equation of circle (x - 2)² + (y + 11)² = 100 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

[tex]{:\implies \quad \sf (x-2)^{2}+(y+11)^{2}=100}[/tex]

Can be further written as ;

[tex]{:\implies \quad \sf (x-2)^{2}+\{y-(-11)\}^{2}={10}^{2}}[/tex]

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

The error made by Tnaya in constructing the box plot is the first quartile and third quartile depicited is wrong.

A box plot is used to study the distribution and level of a set of data. The box plot consists of two lines known as whiskers and a box. The first whisker represents the minimum value and the last whisker represents the maximum value.

On the box, the first line to the left represents the first quartile. 25% of the score represents the lower quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the third quartile. 75% of the scores represents the third quartile.

For the data given, the:

To learn more about median, please check: https://brainly.com/question/20434777

Answer: b = -0.5

Step-by-step explanation:

Given

-3b + 2.5 = 4

Subtract 2.5 on both sides

-3b + 2.5 - 2.5 = 4 - 2.5

-3b = 1.5

Divide -3 on both sides

-3b / -3 = 1.5 / -3

[tex]\boxed{b=-0.5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]\Longrightarrow: \boxed{\sf{b=-0.5}}[/tex]

Step-by-step explanation:

To solve this problem, all you have to do is isolate the term of b from one side of the equation.

First, you have to subtract by 2.5 from both sides.

→ -3b+2.5-2.5=4-2.5

Solve.

Add or subtract the numbers from left to right.

→ -3b=1.5

Then, you divide by -3 from both sides.

→ -3b/-3=1.5/-3

Solve.

Divide the numbers from left to right.

→ 1.5/-3=-0.5

b=-0.5

I hope this helps! Let me know if you have any questions.

The similar circles P and Q can be made equal by dilation and translation

From the figure, we have the centers to be:

P = (-5,4)

Q = (6,8)

The distance is then calculated using:

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have:

d = √(6 + 5)^2 + (8 - 4)^2

Evaluate the sum

d = √137

Evaluate the root

d = 11.70

Hence, the horizontal distance between the center of circles P and Q is 11.70 units

We have their radius to be:

P = 2

Q = 5

Divide the radius of Q by P to determine the scale factor (k)

k = Q/P

k = 5/2

k = 2.5

Hence, the scale factor of dilation from circle P to Q is 2.5

Read more about dilation at:

https://brainly.com/question/3457976

D. 40 ft.

Based on the given conditions, formulate:

[tex]30\times20\div15[/tex]

Calculate

[tex]\frac{30\times20}{15}[/tex]

Cross out the common factor

[tex]2\times20[/tex]

Calculate the product or quotient

[tex]40[/tex]

___________________________________________________

C. Yes, Right Triangle Similarity Theorem

[tex]-\ If\ an\ altitude\ is\ drawn\ to\ the\ hypotenuse\ of\ a\\ right\ triangle,\ then\ the\ two\ triangles\ formed\ are\\ similar\ to\ the\ original\ triangle\ and\ to\ each\ other.[/tex]

____________________________________________________

D. 23.40 ft.

[tex]height\ of\ tree:x[/tex]

[tex]\frac{x}{s_0-d_0}=\frac{39}{50}[/tex]

[tex]x=\frac{30.39}{50}[/tex]

[tex]=23.40ft[/tex]

[tex]\left \{ {{calculate\}[/tex]

I hope this helps you

:)

Answer:

88 scoops

Step-by-step explanation:

Hello!

If 25% of 352 scoops were strawberry, we find 25% of 352

Solve:

This means 88 scoops of strawberry were sold.

Image attatched for conversion of decimals, percents, and fractions.

Answer:

The lines of symmetry in the wheel is infinite.

Explanation:

Since there are an infinite number of lines through the center, a circle has an infinite number of lines of symmetry.

Answer:

1/8

Step-by-step explanation:

So he had 1/4 of a candy box and he ate 1/2 of it. 1/2 of 1/4 is 1/8 because 1/4 × 1/2 =1/8

Answer:

12

Step-by-step explanation:

The answer is 12 because if 1/3 of the log is buried then 2/3 of the log is 8 meters. 8 divided by 2 is 4 so you know that 1/3 of the log is 4 meters. Then you just multiply 4 times 3 or add 4 and 8.

Answer:

12 meters

Step-by-step explanation:

see image. If 1/3 log is buried, then 2/3 (the rest of it) log is above ground. If 8meters of log is 2/3 of the log, that is 8 meters is 2 parts, then each part is 4 meters.

2 parts (thirds!) above ground:

8 meters

1 part (one-third) below ground:

4 meters

Total is 8 + 4 =12

or 3×4 = 12

The whole log is 12 meters.

Answer:

6

Step-by-step explanation:

Divide the amount of eggs by the amount of people this gives you the amount of eggs needed for one person then times by 9

(4÷6) x9

Answer:

nasa pic yung answer

Step-by-step explanation:

hope its help

correct me if im wrong

Answer:

Two angles whose sides are opposite rays are called vertical angles. Two coplanar angles with a common side, a common vertex, and no common interior points are called adjacent angles.

Further explanation

Adjacent Angles are two angles that share a common vertex, a common side, and no common interior points. They share a vertex and side, but do not overlap. The example is shown in the picture below.  

Where ∠1 and ∠2 are adjacent angles, ∠ABC and ∠1 are NOT adjacent angles because ∠ABC overlaps ∠1.

Vertical Angles are two angles whose sides form two pairs of opposite rays (straight lines). Vertical angles are located across from one another in the corners of the "X" formed by the two straight lines.  The example is shown in the picture below.

Where ∠1 and ∠2 are vertical angles, ∠3 and ∠4 are vertical angles, Vertical angles are not adjacent.  ∠1 and ∠3 are not vertical angles (they are a linear pair) and Vertical angles are always equal in measure.

Step-by-step explanation:

Answer:

Tata oil

Step-by-step explanation:

Per 0.1 L

Tata oil is the better buy

Answer:

n = 7

Step-by-step explanation:

simplify the logs according to their bases

Answer:

n = 7

Step-by-step explanation:

[tex]\sf \log_4(64)^{n+1}=log_5(625)^{n-1}[/tex]

Change 64 to an exponent with base 4 and 625 to an exponent with base 5:

[tex]\implies \sf \log_4(4^3)^{n+1}=log_5(5^4)^{n-1}[/tex]

Using exponent rule [tex](a^b)^c=a^{bc}[/tex]

[tex]\implies \sf \log_4(4)^{3(n+1)}=log_5(5)^{4(n-1)}[/tex]

Using log rule:  [tex]\log_a(b^c)=c \log_a(b)[/tex]

[tex]\implies \sf 3(n+1)\log_4(4)}=4(n-1)log_5(5)[/tex]

Using log rule: [tex]\sf \log_a(a)=1[/tex]

[tex]\implies \sf 3(n+1)=4(n-1)[/tex]

[tex]\implies \sf 3n+3=4n-4[/tex]

[tex]\implies \sf 3+4=4n-3n[/tex]

[tex]\implies \sf n=7[/tex]

The only common factor between these two numbers will be 1.

Remember that any number can be decomposed as a product of prime numbers. For example for 18 we have:

18 = 2*3*3

There 18 is written as a product of its prime factors.

Now, for our case of p^n and q^m we will have:

p^n = P = p*p*p...*p     n times.

q^m = Q = q*q*q*...*q     m times.

Now, notice that because q and p are primes, there is no common factor in these two decompositions. (and we can't decompose it furthermore). Then we conclude that the only factor that these numbers share is the trivial one, which is 1.

If you want to learn more about prime numbers, you can read:

https://brainly.com/question/145452

Answer:

A

Step-by-step explanation:

Remember domain is input and range is output.

Input: All real numbers

Output: [0, infinity)

A

Answer:

20sq in

Step-by-step explanation:

h x b / 2

20 x 2 / 2

40/2

20

Answer:

at first write the equation in correct order y=Mx+b. 2y=5x=10

y= 5x/2+5.

Step-by-step explanation:

the slope is 5/2. as we know slope is rise over run. so you go up 5 units and go right 2 unit.

the graph picture is added below click on the PNG. hope it helps. have a great day.

Step-by-step explanation:

6y×100=24

600y=24

600y/600=24/600

y=4/100

y=0.04

Answer:

In a right triangle, the leg adjacent to an angle of 25° is 13 cm long. How long is the leg opposite the 25° angle, to the nearest tenth?

Step-by-step explanation:

Answer:

Jack is 31

Lacy is 10

Step-by-step explanation:

x - 9 = 22

since jack is 3 times as old as lacy,

the formula is

3x - 9 = 22

3x = 31

x = 10.3

So Jack is 31

And Lacy is 10

To prove this, subract 9 (years) from both ages

It will give you an approximate sum of 22 years for both their ages, as the question states

Since Lacy is a little over 10 years old, Jack is 31 instead of 30

The formula was taken from someone elses answer so sorry if it`s wrong

The  rectangles have the same areas but greater perimeters are 12 ft by 3 ft, 9 ft by 4 ft and 18 ft by 2 ft.

Area is the amount of space occupied by a two dimensional shape or object.

A rectangle is shown with a length and height of 6 ft. Hence:

Area = (6 * 6) = 36 ft²

Perimeter = 2(6 + 6) = 24 ft

For 12 ft by 3 ft:

Area = (12 * 3) = 36 ft²

Perimeter = 2(12 + 3) = 30 ft

For 9 ft by 4 ft:

Area = (9 * 4) = 36 ft²

Perimeter = 2(9 + 4) = 26 ft

For 8 ft by 3 ft:

Area = (8 * 3) = 24 ft²

Perimeter = 2(8 + 3) = 24 ft

For 7 ft by 4 ft:

Area = (7 * 4) = 28 ft²

Perimeter = 2(7 + 4) = 26 ft

For 18 ft by 2 ft:

Area = (18 * 2) = 36 ft²

Perimeter = 2(18 + 2) = 40 ft

The  rectangles have the same areas but greater perimeters are 12 ft by 3 ft, 9 ft by 4 ft and 18 ft by 2 ft.

Find out more on area at: https://brainly.com/question/25292087

Answer:

3+1.20c > 13.50

Step-by-step explanation:

hope this helps