Answer: There will 486 bacteria in 31 hours.
Step-by-step explanation:
The population decay in bacteria is exponential.
Exponential function : [tex]y=Ab^x[/tex], where A = initial population, b multiplication decay factor, t= time:
As per given:
Initial population: [tex]A=120,000[/tex]
After 36 hours, population = [tex]120000(b^{36})=200[/tex]
Divide both sides by 120,000 we get
[tex]b^{36}= 0.00167[/tex]
Taking natural log on both sides , we get
[tex]36\ln b=\ln 0.00167\\\\\Rightarrow\ b=e^{\left(\frac{\ln0.00167}{36}\right)}=0.83724629\approx0.8372[/tex]
At x= 31,
[tex]y=120000(0.8372)^{31}=120000\times0.00405234\approx486[/tex]
Hence, there will 486 bacteria in 31 hours.
Triangle ABC has vertices A(0, 6) , B(−8, −2) , and C(8, −2) . A dilation with a scale factor of 12 and center at the origin is applied to this triangle. What are the coordinates of B′ in the dilated image? Enter your answer by filling in the boxes. B′ has a coordinate pair of ( , )
Answer:
[tex]B' = (-96,-24)[/tex]
Step-by-step explanation:
Given
[tex]A(0,6)[/tex]
[tex]B(-8,-2)[/tex]
[tex]C(8,-2)[/tex]
Required
Determine the coordinates of B' if dilated by a scale factor of 12
The new coordinates of a dilated coordinates can be calculated using the following formula;
New Coordinates = Old Coordinates * Scale Factor
So;
[tex]B' = B * 12[/tex]
Substitute (-8,-2) for B
[tex]B' = (-8,-2) * 12[/tex]
Open Bracket
[tex]B' = (-8 * 12,-2 * 12)[/tex]
[tex]B' = (-96,-24)[/tex]
Hence the coordinates of B' is [tex]B' = (-96,-24)[/tex]
Answer:
Bit late but the answer is (-4,-1)
Step-by-step explanation:
Took the test in k12
At the age of 10, Edgar received an inheritance of $10,000. His father wants to invest the money in an account that will double in value in 8 years. Approximately what interest rate does the father need to find in order to reach his goal?
Answer:
9%
Step-by-step explanation:
Use the rule of 72. If you want the money to double in 8 years, it will need to be at 9 percent interest rate to reach this goal.
what is the diameter of a circular swimming pool with a radius of 9 feet? enter only the number
Answer:
The answer is 18 feet
Step-by-step explanation:
To find the diameter of a circle given it's radius we use the formula
diameter = radius × 2
From the question
radius = 8
So the diameter is
diameter = 9 × 2 = 18 feetHope this helps you
Answer:
18
Step-by-step explanation:
Hey there!
Well radius is half the diameter so,
D = r*2
Plug in 9
D = 9*2
D = 18
Hope this helps :)
you pick a card at random from an ordinary deck of 52 cards. If the card is an ace, you get 9 points; if not, you lose a point
Answer: a = 9, b = 48, c = -1
Step-by-step explanation:
"a" represents the points you receive if an Ace is picked. It is given that you get 9 points ----> a = 9
"b" represents the number of cards that are Not an Ace. 4 cards in the deck are Aces so 52 - 4 = 48 cards are Not an Ace -----> b = 48
"c" represents the points you receive if Not an Ace is picked. It is given that you lose 1 point ----> c = -1
Answer:
Here is the rest of the page
Step-by-step explanation:
1
1 point
mZABD = 79
D
C
V
(5x + 4)
(8x - 3)
В B.
A
x= type your answer...
2
1 point
Answer:
x = 6
Step-by-step explanation:
∠ DBC + ∠ ABC = ∠ ABD , substitute values
5x - 4 + 8x - 3 = 79
13x + 1 = 79 ( subtract 1 from both sides )
13x = 78 ( divide both sides by 13 )
x = 6
What is the value of the mean from the following set of data: 12,10, 11, 8, 6, 5, 3, 7, 9. Round to the nearest hundredth.
Answer:
7.88 or 7.9
Step-by-step explanation:
To find the mean, we need to do:
=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9
=> 71/9
=> 7.88 or 7.9
I divided the sum of all numbers by 9 because we added 9 numbers.
Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that σ is in the neighborhood of .5 pH and that you want your estimate to lie within .1 of µ with probability near .95. Approximately how many rainfalls must be included in your sample (one pH reading per rainfall)? Would it be valid to select all of your water specimens from a single rainfall? Explain.
Answer:
The number of rainfalls is [tex]n =96[/tex]
The answer to the second question is no it will not be valid this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid.
Step-by-step explanation:
from the question we are told that
The standard deviation is [tex]\sigma = 0.5[/tex]
The margin of error is [tex]E = 0.1[/tex]
Given that the confidence level is 95% then we can evaluate the level of significance as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha =0.05[/tex]
Next we will obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} * \sigma }}{ E} ]^2[/tex]
substituting values
[tex]n = [\frac{1.96 * 0.5 }{ 0.1} ]^2[/tex]
[tex]n =96[/tex]
The answer to the second question is no the validity is null this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid
Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans.
Plan A: Raise the price by $0.05 each week until the price reaches $8.00.
Plan B: Raise the price by 10 percent each week until the price reaches $8.00.
Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00.
Plan D: Raise the price by $0.25 each week until the price reaches $8.00.
The Answer is:
B.) Plan B
The right plan for Him is Plan B which is; Raise the price by 10 percent each week until the price reaches $8.00.
We have Bagel Emporium sells a dozen bagels for $5.00.
A plan should be kind of an arrange that is done as a parts of any given idea or layout.
We conclude that the right plan result in the price of the bagels reaching $8.00. fastest is Plan B that is Raise the price by 10 percent each week until the price reaches $8.00 as it doubles the rate as the percentage is increased.
The correct plan is B.
Learn more about plan from;
brainly.com/question/10528412
#SPJ7
The time is 8:08 and subract that to 27 minutes ago what time was it?
Answer:
7:41
Step-by-step explanation:
8:08 - 7 Minutes = 8:01
8:01 - 20 Minutes = 7:41
HELP PLEASE!! I have been working on this for about three hours!!
Answer:
see below
Step-by-step explanation:
First we need to find the slope
m = ( y2-y1)/ ( x2-x1)
= (60-64)/( 10-0)
= -6/10
= -2/5
The y intercept is (0,64)
The slope intercept form of the equation is
y = mx+b where m is the slope and b is the y intercept
y = -2/5 x + 64 where y is in the thousands of feet
m = -2/5 * 1000 = -400 ft / minute
The height decreases since the sign is negative
The height decreases 400 ft per minute
The y intercept is (0,64)
64 is in the thousands of ft
64*1000 = 64,000 ft
When it starts, it is at 64,000 ft
The descent starts at a cruising altitude of 64,000 ft
PLEASE HELP !! (2/5) -50 POINTS-
Answer:
[tex]X=\begin{bmatrix}5\\ 14\\ -10\end{bmatrix}[/tex]
Step-by-step explanation:
Our approach here is to isolate X, and simplify this solution. We want to begin by subtracting matrix 2, as shown below, from either side - the first step in isolating X. Afterwards we can multiply either side by the inverse of matrix 1, the co - efficient of X, such that X is now isolated. We can then simplify this value.
Given,
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ \:\:\:3&-2&-1\end{bmatrix}[/tex] : Matrix 1
[tex]\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}[/tex] : Matrix 2
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X+\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}=\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}[/tex] ( Subtract Matrix 2 from either side )
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X=\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}-\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}[/tex] ( Simplify )
[tex]\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}-\begin{bmatrix}3\\ -1\\ 8\end{bmatrix} = \begin{bmatrix}6-3\\ 4-\left(-1\right)\\ 5-8\end{bmatrix}=\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}[/tex] ( Substitute )
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X=\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}[/tex] ( Multiply either side by inverse of Matrix 1 )
[tex]X=\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}^{-1}\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}=\begin{bmatrix}5\\ 14\\ -10\end{bmatrix}[/tex] - let's say that this is Matrix 3. Our solution would hence be Matrix 3.
If 2^x =30 find 2^(x+3) A)8 B)5 C)240 D)200 E)250 (Good Luck! Plz solve fast!)
Answer:
C
Step-by-step explanation:
So we already know that:
[tex]2^x=30[/tex]
And we want to find the value of:
[tex]2^{x+3}[/tex]
So, what you want to do here is to separate the exponents. Recall the properties of exponents, where:
[tex]x^2\cdot x^3=x^{2+3}=x^5[/tex]
We can do the reverse of this. In other words:
[tex]2^{x+3}=2^x\cdot 2^3[/tex]
If we multiply it back together, we can check that this statement is true.
Thus, go back to the original equation and multiply both sides by 2^3:
[tex]2^x(2^3)=30(2^3)\\[/tex]
Combine the left and multiply out the right. 2^3 is 8:
[tex]2^{x+3}=30(8)\\2^{x+3}=240[/tex]
The answer is C.
Answer:
the answer is c
Step-by-step explanation:
What is the rate of change from x = 0 to x = pi over 2 ? (6 points) trig graph with points at (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4)
Answer: [tex]\dfrac{8}{\pi}[/tex] .
Step-by-step explanation:
We know that the rate of change of function f(x) from x=a to x= b is given by :-
[tex]k=\dfrac{f(b)-f(a)}{b-a}[/tex]
The given points on graph : (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4).
The rate of change from x = 0 to x = pi over 2 will be :-
[tex]\dfrac{0-(-4)}{\dfrac{\pi}{2}-0}=\dfrac{4}{\dfrac{\pi}{2}}[/tex] [By using points (0, -4) and (pi over 2, 0) ]
[tex]=\dfrac{8}{\pi}[/tex]
Hence, the rate of change from x = 0 to x = pi over 2 is [tex]\dfrac{8}{\pi}[/tex] .
please answer this question please
Step-by-step explanation:
C = Amount (A) - Principal (P)
Where
C is the compound interest
To find the amount we use the formula
[tex]A = P ({1 + \frac{r}{100} })^{n} [/tex]
where
P is the principal
r is the rate
n is the period / time
From the question
P = Rs 12, 000
r = 5%
n = 3 years
Substitute the values into the above formula
That's
[tex]A = 12000 ({1 + \frac{5}{100} })^{3} \\ A = 12000(1 + 0.05)^{3} \\ A = 12000 ({1.05})^{3} [/tex]
We have the answer as
Amount = Rs 13891.50Compound interest = 13891.50 - 12000
Compound interest = Rs 1891.50Hope this helps you
PPPLLLEEEEAAAASSSSEEEEE ANSWER FAST
The following shape is based only on squares, semicircles, and quarter circles. Find the area of the shaded part.
Answer:
36.53 cm²
Step-by-step explanation:
Picture this repeated four times to make a circle. The circle would have a radius of 8. [tex]\pi[/tex]r² would give us 201.06. One quarter of that would be 50.265.
The area of the square is length times width, or 8X8=64.
64-50.265=13.735. That would be ONE of the non shaded sections of the square. If you take that away twice, the leftover part would be the shaded area.
64-13.735-13.735=36.53 cm²
Round 3.1 to the nearest whole number
Answer:
3.1 rounded off to the nearest whole number is 3.
Step-by-step explanation:
A box of nails weighs 1-5/6 pounds. What is the weight of 12 boxes?
Step-by-step explanation:
for finding the weight of 12 boxes multiply 12 with the weight of first box and then you will get your answer. Tell me the answer which you found and if it will be correct I will say ok if not I will give you the correct answer
Simplify -3(2w - 6) +4(w + 1)
Answer:
= -2w + 22
Step-by-step explanation:
-3(2w - 6) + 4(w+1)
= (-3*2w -3*-6) + (4*w + 4*1)
= -6w + 18 + 4w + 4
= -6w + 4w + 18 + 4
= -2w + 22
-40=-8(x+2) solve the equation
Answer:
x = 3
Step-by-step explanation:
-40 = -8 (x + 2)
-8 (x + 2) = -40 --- divide both sides by - 8
-8 (x + 2) -40
-------------- = ----------
-8 -8
x + 2 = 5 --- subtract 2 from both sides
x + 2 - 2 = 5 - 2 then simplify
x = 3
Answer:
x=3
Step-by-step explanation:
First, write out the equation as you have been given it:
[tex]-40=-8(x+2)[/tex]
Then distribute the -8 to the terms inside the parenthesis:
[tex]-40=-8x-16[/tex]
Next, add 16 to both sides:
[tex]-40+16=-8x-16+16\\-24=-8x[/tex]
Finally, divide both sides by -8:
[tex]\frac{-24}{-8}=\frac{-8x}{-8}\\3=x[/tex]
Therefore, x=3.
The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of −0.4. See the figure below. Suppose that the height of the candle after 11 hours is 16.6 centimeters. What was the height of the candle after 6 hours?
Answer:
height of the candle after 6 hours= 18.6 centimeters
Step-by-step explanation:
the function gives a line with a slope of −0.4.
the height of the candle after 11 hours is 16.6 centimeters.
after 6 hours, the height will be
But slope= y2-y1/x2-x1
Y2 is the unknown
Y1 = 16.6
X1= 11 hours
X2= 6 hours
y2-y1/x2-x1= -0.4
(Y2-16.6)/(6-11)= -0.4
(Y2-16.6)/(-5)= -0.4
(Y2-16.6)= -5( -0.4)
(Y2-16.6)= 2
Y2 = 2+16.6
Y2 = 18.6 centimeters
height of the candle after 6 hours= 18.6 centimeters
Test scores in a Test were normally distributed with a mean of 75 and a standard deviation of 10. Carl scored 90 in the Test . What is the z-score of Carl’s test score?
Answer:
Z-score = 1.5
Step-by-step explanation:
Z-score = (x-mean)/standard deviation
= (90-75)/10
= 1.5
What is the equation of the line?
The line cuts the X axis at [tex]x=3[/tex] and is parallel to the Y axis.
Thus the equation of the line is $\boxed{x=3}$
Answer:
The equation of the line is x = 3.
Step-by-step explanation:
When a line is parallel to the y-axis, its gradient will be undefined. There is no y-intercept and the line touches x-axis so the equation is x = 3.
Sherina wrote and solved the equation. x minus 56 = 230. x minus 56 minus 56 = 230 minus 56. x = 174. What was Sherina’s error?
Answer:
subtracting 56 instead of adding (or adding wrong)
Step-by-step explanation:
She wrote ...
x - 56 = 230
x - 56 - 56 = 230 -56 . . . . correct application of the addition property*
x = 230 -56 . . . . . . . . . . . . incorrect simplification
Correctly done, the third line would be ...
x -112 = 174
This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...
x - 56 + 56 = 230 + 56 . . . using the addition property of equality
x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides
__
There were two errors:
1) incorrect strategy --- subtracting 56 instead of adding
2) incorrect simplification --- simplifying -56 -56 to zero instead of -112
We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.
_____
* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.
Answer:
D: Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
I got a 100% on my test.
I hope this helps.
can anyone ans this question
Answer:
Question 1: the angle of y is the same as 49 degrees.
So, y = 49 degrees.
y + x = straight line
=> Straight line = 180 degrees
=> 49 + x = 180
=> 49 - 49 + x = 180 - 49
=> x = 131
Answer to Question 1:
x = 131 degrees
y = 49 degrees
Question 2: Angle x is the same as 119 degrees
x + y = straight line
=> Straight line = 180 degrees
=> 119 + y = 180
=> 119 - 119 + y = 180 - 119
=> y = 61
y + z = straight line
=> Straight line = 180 degrees
=> 61 + z = 180
=> 61 - 61 + z = 180 - 61
=> z = 119
Answer to Question 2:
x = 119 degrees
y = 61 degrees
z = 119 degrees
Which equation will solve the following word problem? Jared has 13 cases of soda. He has 468 cans of soda. How many cans of soda are in each case? 13(468) = c 468c = 13 468/13 = c 13 = c/468
Answer:
c = 468 / 13
Step-by-step explanation:
If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.
Answer:
468/13 = c
Step-by-step explanation: Further explanation :
[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]
Please help asap, will mark Brainliest xoxo
Answer/Step-by-step explanation:
Given, [tex] b(x) = (\frac{6}{7})^{x} [/tex]
The table for the function are:
When x = -2
[tex] b(-2) = (\frac{6}{7})^{-2} [/tex]
[tex] b(-2) = \frac{1}{(\frac{6}{7})^{2}} [/tex]
[tex] b(-2) = \frac{1}{(\frac{36}{49})} [/tex]
[tex] b(-2) = 1*\frac{49}{36} [/tex]
[tex] b(-2) = \frac{49}{36} [/tex]
When x = -1
[tex] b(-1) = (\frac{6}{7})^{-1} [/tex]
[tex] b(-1) = \frac{1}{(\frac{6}{7})} [/tex]
[tex] b(-1) = 1*\frac{7}{6} [/tex]
[tex] b(-2) = \frac{7}{6} [/tex]
When x = 0
[tex] b(0) = (\frac{6}{7})^{0} [/tex]
[tex] b(0) = \frac{6^0}{7^0} [/tex]
[tex] b(0) = \frac{1}{1} [/tex]
[tex] b(0) = 1 [/tex]
When x = 1
[tex] b(1) = (\frac{6}{7})^{1} [/tex]
[tex] b(1) = \frac{6}{7} [/tex]
When x = 2
[tex] b(2) = (\frac{6}{7})^{2} [/tex]
[tex] b(2) = \frac{6^2}{7^2} [/tex]
[tex] b(2) = \frac{36}{49} [/tex]
PLEASE HELP!! (3/5) - 50 POINTS -
Answer:
infinite number of solutions
Step-by-step explanation:
A dependent system is where the two equations are the same line has has an infinite number of solutions
Answer:
[tex]\boxed{\sf D) \ an\ infinite \ number \ of \ solutions}[/tex]
Step-by-step explanation:
A dependent system of equations has an infinite number of solutions.
When you graph the system of equations, both the equations represent the same line and have an infinite number of solutions.
determine whether the series is absolutely convergent, conditionally convergent, or divergent sin(n)/3^n convergent
Answer:
absolutely convergent
Step-by-step explanation:
given data
sin(n)/3^n
solution
we have given term [tex]\frac{sin(n)}{3^n}[/tex]
when n = 1
and we know that
value of sin(n) ≤ 1
so that we can say that
[tex]\frac{sin(n)}{3^n}[/tex] ≤ [tex]\frac{1}{3^n}[/tex] or [tex](\frac{1}{3})^n[/tex]
here [tex]\frac{1}{3^n}[/tex] is converges this is because common ratio in geometric series
here r is [tex]\frac{1}{3}[/tex] and here it satisfy that -1 < r < 1
so it is converges
and
[tex]\frac{sin(n)}{3^n}[/tex] is also similar
so it is converges
and here no [tex](-1)^n[/tex] term is
so we can say series is absolutely convergent
The chart shows a certain city's population by age. Assume that the selections are independent events. If 8 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 3 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old.
Answer:
0.000014
Step-by-step explanation:
The chart is not provided so i will use an example chart to explain the answer. Here is a sample chart:
City X's Population by Age
0-24 years old 33%
25-44 years old 22%
45-64 years old 21%
65 or older 24%
In order to find probability of independent events we find the probability of each event occurring separately and then multiply the calculated probabilities together in the following way:
P(A and B) = P(A) * P(B)
probability that the first 2 are 65 or older
Let A be the event that the first 2 are 65 or older
The probability of 65 or older 24% i.e. 0.24
So the probability that first 2 are 65 or older is:
0.24(select resident 1) * 0.24(select resident 2)
P(A) = 0.24 * 0.24
= 0.0576
P(A) = 0.0576
probability that the next 3 are 25-44 years old
Let B be the event that the next 3 are 25-44 years old
25-44 years old 22% i.e. 0.22
So the probability that the next 3 are 25-44 years old is:
0.22 * 0.22* 0.22
P(B) = 0.22 * 0.22 * 0.22
= 0.010648
P(B) = 0.010648
probability that next 2 are 24 or younger
Let C be the event that the next 2 are 24 or younger
0-24 years old 33% i.e. 0.33
So the probability that the next 2 are 24 or younger is:
0.33 * 0.33
P(C) = 0.33 * 0.33
= 0.1089
P(C) = 0.1089
probability that last is 45-64 years old
Let D be the event that last is 45-64 years old
45-64 years old 21% i.e. 0.21
So the probability that last is 45-64 years old is:
0.21
P(D) = 0.21
So probability of these independent events is computed as:
P(A and B and C and D) = P(A) * P(B) * P(C) * P(C)
= 0.0576 * 0.010648 * 0.1089 * 0.21
= 0.000014
A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answer:
F = 585844 N
Step-by-step explanation:
Given that:
A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface.
The objective of this question is to express the hydrostatic force against one side of the plate as an integral and evaluate it.
To start with the equation of a circle: a² + b² = r²
The equation of circle with radius r = 7 can be expressed as:
a² + b² = 7²
a² + b² = 49
b² = 49 - a²
b = [tex]\sqrt{49 -a}[/tex]
NOW;
The integral of the hydrostatic force with a semicircular plate with radius 7 m and the top is 3 m above the surface can be calculated as follows:
[tex]\mathtt{F = 2 \rho g \int \limits^7_3 (a -3) \sqrt{49 -y^2} \ \ da}[/tex]
[tex]\mathtt{F = 2 \rho g \begin {pmatrix}\dfrac{\sqrt{49 -a^2} \ (2a^2-9a - 98)-(441 \times sin^{-1} (\dfrac{a}{3})) }{6} \end{pmatrix}}[/tex]
where;
density of water is 1000 kg/m3
and acceleration due to gravity is 9.8 m/s
Solving the integral; we have:
F = 2 × 1000 kg/m³ × 9.8 m/s × (29.89)
F = 585844 N
