Answer:
H = 49.56 m
Step-by-step explanation:
We have,
A kite is flying in the air has a 91 ft string attached to it.
The angle of elevation of the kite is 57 degrees.
It is required to find the height of the kite. If we consider a right angled triangle, 91 ft is the hypotenuse. Let H is the height of the kite.
[tex]\cos\theta=\dfrac{H}{91}\\\\H=91\times \cos(57)\\\\H=49.56\ m[/tex]
Hence, the height of the kite is 49.56 m.
Use the formula above to find the Celsius temperature equivalent to 185°F. A. 85°C B. 153°C C. 102°C D. 68°C
Answer: A. 85ᴼC
Step-by-step explanation:
0 degrees Celsius is at 32 degrees Fahrenheit.
100 degrees Celsius is at 212 degrees Fahrenheit.
212 - 32 = 180
180 / 100 = 1.8
So, every degree Celsius is 1.8 degrees Fahrenheit, starting at 32 of course.
1.8 * 85 = 153
153 + 32 = 185
Answer:
The correct answer is 85°C.
Step-by-step explanation:
I use the equation 9C = 5F - 160 to solve for temperatures.
Therefore, we just insert values for each variable except for the one that we want to solve for. In this case, we are doing Fahrenheit → Celsius, so we are solving for the unknown variable of C. We are given a value for F, 185°.
Therefore, just insert these into the equation and solve for C.
[tex]9C = 5(185)-160[/tex]
[tex]9C = 925 - 160[/tex]
[tex]9C = 765[/tex]
[tex]\frac{765}{9} = 85[/tex]
C = 85°C
The area of a hall is 806 sq. ft. Its length is 5 ft greater than its width. Find the dimensions of the hall. Enter the results in the answer box. Show work that leads to the final answer and clearly state the final answer.
Answer:
width is = 26ft
length is = 31ft
Step-by-step explanation:
The area of hall is 806 sq. ft.
length is 5 ft greater than its width.
L = 5+b
L*b = 806
(5+b)*b= 806
5b +b² = 806
B²+5B-806= 0
Solving quadratically
B² +31B -26B -806= 0
B(B+31)-26(B+31)= 0
(B-26)(B+31)= 0
B= 26 or -31
So the value of the width must be positive so the width is = 26ft
If width is 26, length is 26+5 = 31ft
Base of building 180 meters
Step-by-step explanation:
please give me full question
A road crew can pave 2/5 km in 1 1/2 hours.how many km of road can they pave in 10 hours?
Answer:
8/3 km
Step-by-step explanation:
we can represent the given information on a table:
Kilometers time (hours)
2/5 ⇔ 1 1/2
and since we want to know how many kilometers (x) will be paved on 10 hours:
Kilometers time (hours)
2/5 ⇔ 1 1/2
x ⇔ 10
The relationship these 3 numbers have can be described by using the rule of three, which is to multiply the cross quantities on the table (2/5 by 10) and then divide by the remaining amount (1 1/2):
x = [tex]\frac{2}{5}*10[/tex] ÷ [tex]1\frac{1}{2}[/tex]
x = [tex]\frac{20}{5}[/tex] ÷ [tex]1\frac{1}{2}[/tex]
we use [tex]1\frac{1}{2}=\frac{3}{2}[/tex]
x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex]
and we make the division:
x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{20*2}{5*3}=\frac{40}{15}[/tex]
we simplify the fraction by dividing the numerator and denominator both by 5, and we get the result:
x = [tex]\frac{8}{3}[/tex]
thus, in 10 hours the crew will pave 8/3 km. Which is about 2.66 km.
A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop's license if they find significant evidence that the shop is certifying vehicles that do not meet standards.
a. In this context, what is a Type I error?
b. In this context, what is a Type II error?
c. Which type of error would the shop's owner consider more serious? d. Which type of error might environmentalists consider more serious?
Answer:
Step-by-step explanation:
The null hypothesis in this case is: There is significant evidence that the shop is certifying vehicles that do not meet standards so their license gets revoked
a. A type I error in this context occurs if the null is rejected when in actuality, it is true. This means, the shop is certifying vehicles that do not meet standards but their license does not get revoked
b. A type II error in this context occurs if they fail to reject the null when in actuality, it is no true. This means, the shop is not certifying vehicles that do not meet standards but their license does get revoked.
c. Which type of error would the shop's owner consider more serious?
The type II error because it affects the shop owner despite their credibiity
d. Which type of error might environmentalists consider more serious?
The type I error.
A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of self-injurious behaviors (SIB’s) found in adolescents. They gave the anti-depressant to a group of 8 participants and counted the numbers of SIBs a person performed for a month after taking the drug for 6 months. Here are the number of SIB’S performed by the 8 people, 27, 25, 32, 40, 43, 37, 35, 38.
a. Find the mean variance, and standard deviation of this group.
b. Suppose the u=45, what is the z score?
c. What is the SEM for this particular group?
Answer:
a. The mean of the sample is M=35.
The variance of the sample is s^2=39.125.
The standard deviation of the sample is s=6.255.
b. z=-1.6
c. SEM = 2.212
Step-by-step explanation:
The mean of the sample is M=35.
The variance of the sample is s^2=39.125.
The standard deviation of the sample is s=6.255.
Sample mean
[tex]M=\dfrac{1}{8}\sum_{i=1}^{8}(27+25+32+40+43+37+35+38)\\\\\\ M=\dfrac{277}{8}=35[/tex]
Sample variance and standard deviation
[tex]s^2=\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2\\\\\\s^2=\dfrac{1}{7}\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\[/tex]
[tex]s^2=\dfrac{1}{7}\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\ s^2=\dfrac{273.875}{7}=39.125\\\\\\s=\sqrt{39.125}=6.255[/tex]
b. If the population mean is 45, the z-score for M=35 would be:
[tex]z=\dfrac{M-\mu}{\sigma}=\dfrac{35-45}{6.255}=\dfrac{-10}{6.255}=-1.6[/tex]
c. The standard error of the mean (SEM) of this group is calculated as:
[tex]SEM=\dfrac{s}{\sqrt{n}}=\dfrac{6.255}{\sqrt{8}}=\dfrac{6.255}{2.828}=2.212[/tex]
9. What is the scale factor of the dilation?
Answer:
D
Step-by-step explanation:
The scale factor is the ratio of the corresponding sides, image to original, that is
scale factor = [tex]\frac{P'S'}{PS}[/tex] = [tex]\frac{6}{3}[/tex] = 2 → D
1. Considere as funções f e g, ambas com domínio Z, dadas por f(x) = x²- 2x e g(x) = x³-1. Associe as colunas e assinale a alternativa que apresenta a sequência correta: *
1 ponto
a) f (-2) ( )29
b) g(-2) ( )15/7
c) f(-1) + g(3) ( )8
d) f(5) : g(2) ( )-9
a) C, D, A, B
b) A, B, D, C
c) D, C, A, B
d) A, C, D, B
ajuuuuuda
Answer:
(A)C,D,A,B
Step-by-step explanation:
[tex]f(x) = x^2- 2x\\g(x) = x^3-1[/tex]
a)
[tex]f(-2) = (-2)^2- 2(-2)\\=4-(-4)\\=4+4\\=8$ (C)[/tex]
b)
[tex]g(-2) = (-2)^3-1\\\=-8-1\\=-9 $(D)[/tex]
c)
[tex]f(-1) = (-1)^2- 2(-1)=1+2=3\\g(3) = (3)^3-1=27-1=26\\f(-1) + g(3)=3+26\\=29$ (A)[/tex]
d) f(5) : g(2)
[tex]f(5) = (5)^2- 2(5)=25-10=15\\g(2) = (2)^3-1=8-1=7\\f(5) :g(2)=15/7$ (B)[/tex]
The price of a dress is reduced by 50%. When the dress still does not sell, it is reduced by 50% of the reduced price. If the price of the dress after both reductions is $100, what was the original price?
Answer:
the answer is 400$
Step-by-step explanation:
The value of homes sold in Hampton VA are normally distributed with a mean of $200,000
and a standard deviation of $10,000. If 1216 houses were sold in 2012, how many houses would
have a value greater than one standard deviation above the mean?
Answer:
[tex]X \sim N(200000,100000)[/tex]
Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
[tex] Number = 1216*0.16 = 194.56[/tex]
And the answer woud be between 194 and 195 houses
Step-by-step explanation:
Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200000,100000)[/tex]
Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
[tex] Number = 1216*0.16 = 194.56[/tex]
And the answer woud be between 194 and 195 houses
Select the equivalent expression.
A, B or C?
Answer:
A
Step-by-step explanation:
The relevant rules of exponents are ...
(a^b)^c = a^(bc)
a^-b = 1/a^b
__
[tex]\left(\dfrac{2^{-10}}{4^2}\right)^7=\dfrac{2^{(-10)(7)}}{4^{(2)(7)}}=\dfrac{2^{-70}}{4^{14}}\\\\=\boxed{\dfrac{1}{2^{70}\cdot 4^{14}}}[/tex]
Use the GCF and the distributive property to find the expression that is
equivalent to 36 + 60.
18 (2+4)
3(12 + 20)
6(6+10)
12 (3+5)
Answer:
[tex]D[/tex]
Step-by-step explanation:
[tex]36 + 60[/tex]
[tex]12(3)+12(5)[/tex]
[tex]12(3+5)[/tex]
Answer:
12( 3+5)
Step-by-step explanation:
find the arc length of a partial circle
Answer:
23.55 or [tex]\frac{15}{2}[/tex]π
Step-by-step explanation:
The arc is 75% of the full circumference, as the cut away angle is 90º.
To find the arc length, you multiply the ratio of the whole circle that remains by the circumference: [tex]\frac{270}{360}[/tex]×π×2(5)=[tex]\frac{15}{2}[/tex]π, or 23.55 if you round pi to 3.14.
Answer:
7.85
Step-by-step explanation:
Solve this by using the formula for arc length with central angle in degrees.
Do this by identifying the formula and plugging in the given values. The formula for arc length is [tex]arc length = 2\pi r (\frac{theta}{360} )[/tex] , where the theta is represented by the central angle and r is the radius
The radius is shown on the circle is 5 and the theta (angle in degrees) is 90, represented by the tiny square in the middle.
Plug it all into the formula. Your equation should now look like this: arc length = 2 (3.14 or [tex]\pi[/tex]) (5) ([tex]\frac{90}{360}[/tex])
Solve for arc length and enter your answer as a decimal or in terms of pi
It is known that the highest weekly average price for gasoline in California during 2005 was $3.15 per gallon and the lowest weekly average price for gasoline in California during 2005 was $2.56. Use this information to estimate the standard deviation of the weekly average price for gasoline in California during 2005. The standard deviation is ($3.15-2.56) / 6. I was wondering why you divide by 6?
Answer:
$0.15
Step-by-step explanation:
To solve this problem, we apply the Range rule for estimating Standard deviation.
By the Range Rule:
Standard Deviation
Highest weekly average price for gasoline= $3.15 per gallon.
Lowest weekly average price for gasoline =$2.56 per gallon.
Therefore:
[tex]\text{Standard Deviation}\approx \dfrac{3.15-2.56}{4} \\=\dfrac{0.59}{4} \\\\=\$0.15 $(correct to the nearest cent).[/tex]
The standard deviation of the weekly average price for gasoline is approximately $0.15.
NOTE: You divide by 4 not 6.
For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two tailed, left tailed, or right tailed. The mean local monthly bill for cell phone users in this country was $47.79 in 2001. A hypothesis test is to be performed to determine whether last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.79.
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
This is a left tailed test.
Step-by-step explanation:
A hypothesis test is to be performed to determine whether last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.79.
Then, the claim that will be expressed in the alternative hypothesis is that the monthly bill is lower than $47.79.
The null hypothesis will state that the monthly bill does not differ significantly from $47.79.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
As we only want to test if its lower, we are interested only in the left tail of the distribution. We want to know if the test statistic is below the critical value to conclude if we have evidence for our claim. This is then a left tailed test.
Which of the x-values are solutions to both of the following inequalities? 60 > X and x > 57. Also, Please hurry I will give brainliest to whoever answers 1st.
Answer:
B
Step-by-step explanation:
x must be a number between 60 and 57 and those numbers are 58 or 59
60 is greater than 59, and 59 is greater than 57
Answer:
x = 59
Step-by-step explanation:
The number must be less than 60 from the first inequality and greater than 57 from the second inequality
so the integers allowed are 58,59
After shopping, it took Manuel 87 seconds to push a shopping cart directly to his car. In one-
third of that time, Manuel had moved 58 meters at a constant velocity. What was the cart's
velocity?
Answer:
The carts velocity= 2m/s
Step-by-step explanation:
It took Manuel 87 seconds to push a shopping cart directly to his car.
One third of 87 = 87/3 = 29
In 29 seconds the carts moved 58 meter's.
The carts velocity = distance/time
The carts velocity = 58/29
The carts velocity= 2m/s
Using π = 3.14, find the area of a circle with a radius of 9. Round your answer to the nearest hundredth.
Answer:
A =254.34 unit^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = 3.14 ( 9)^2
A =254.34
Answer:
254.34
Step-by-step explanation:
The formula for the area of a circle is πr² or in this case, 3.14r²
3.14×9²=
3.14×81=
254.34
Sorry if it looks like I'm copying Wegnerkolmp2741o but I didn't mean to make my answer like theirs.
The Grand canyon national park has a new parking lot.the perimeter is 84feet the shape of the parking lot is a square what is the length of each sides
Answer:
21 feet
Step-by-step Explanation:
Given that the new parking lot of the Grand Canyon National park has a square shape, which means all the lengths of the 4 sides of the parking lot are equal and the same, the perimeter of the parking lot = 4(L) = 84feet.
L = length of 1 side of the parking lot; perimeter = 84feet,
Therefore, solving for L (length of each side) would be:
84 = 4(L)
84/4 = L
L = 21ft
The length of each sides are all equal and each would be 21 feet long.
how much does 757 go into 68
Answer:
Divide 757 by 68 so:
Step-by-step explanation:
757 / 68 = 11.9 so 757 can go into 68 11.9 times.
Hope this helps, have a good day! :)
(Brainliest would be appreciated?)
The average of four numbers is 38, and the average of the first two numbers is 42, and the average of the last three numbers is 36. What is the second number?
Answer:
40
Step-by-step explanation:
let the numbers be a+b+c+d.
the average of 4 numbers is 38
; (a+b+c+d)/4 = 38
(a+b+c+d) = 152 ......equ1
the average of the first two numbers is 42
; (a+b)/2 = 42
(a+b) = 84 ...... equ2
the average of the last three numbers is 36
; (b+c+d)/3 = 36
(b+c+d) = 108 .....equ3
substitute equ3 into equ1
a + 108 = 152
a= 152 - 108
a = 44
input the value of a into equ2
44 + b = 84
b = 40
the second number is 40.
I hope this helps.
Which of the following are valid names for the given triangle? Check all that
apply
T
A
A. ATAY
B. AMAY
C. AMAX
D. AAXM
Ε. ΔΧΜΑ
F. AXMT
Answer:
I think it's just E.
Step-by-step explanation:
When you name triangles, you would often put a Δ and then the letters of the 3 angles. The only answer that fits that criteria is E.
The valid name for the given triangle is ΔΧΜΑ.
What is a triangle?
A triangle is a 3-sided polygon that consists of three edges and 3 vertices. The most vital asset of a triangle is that the sum of the inner angles of a triangle is identical to a hundred and eighty tiers. This belonging is called the attitude sum property of the triangle.
What are the types of triangles?
equilateral, isosceles, scalene, right triangles.
Learn more about triangle here https://brainly.com/question/2938476
#SPJ2
Types of bonds are divided into three categories: good risk, medium risk, and poor risk. Assume that of a total of 11, 332 bonds, 7,311 are good risk, 1,182 are medium risk, and the rest are poor risk. One bond is chosen at random. What is the probability that the bond is not a poor ? Write only a number as your answer. Round to two decimal places (for example : 0.43). Do not write as a percentage .
Answer:
Probabilty of not poor= 0.75
Step-by-step explanation:
total of 11332 bonds.
7311 are good risk.
1182 are medium risk.
Poor risk
= total risk-(good risk+ medium risk)
= 11332-(7311+1182)
= 11332-8493
= 2839.
Poor risk = 2839
Probabilty that the ball choosen at random is not poor= 1 - probability that the ball is poor
Probability of poor = 2839/11332
Probabilty of poor= 0.2505
Probabilty that the ball choosen at random is not poor= 1- 0.2505
= 0.7495
To two decimal place= 0.75
Out of 25 students taking a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one. Round your answer to the nearest percent. What percentage of students tried both questions? What percentage tried at least one question?
Answer:
Percentage of students who tried both questions = [tex]8\%[/tex]
Percentage of students who tried at least one question = [tex]96\%[/tex]
Step-by-step explanation:
Given: 25 students take a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one.
To find: percentage of students who tried both questions and percentage of students who tried at least one question
Solution:
Let A denotes students who answered the first of two bonus questions and B denotes students who answered the second bonus question.
Let U denotes the universal set denoting students who take a midterm psychology exam.
[tex]n(A)=15\,,\,n(B)=11\,,\,n(U)=25[/tex]
[tex]n\left ( A'\cap B' \right )=1[/tex]
[tex]n\left ( A'\cap B' \right )=n\left ( A\cup B \right )'\\=n(U)-n\left ( A\cup B \right )\\\Rightarrow 1=25-n\left ( A\cup B \right )\\n\left ( A\cup B \right )=25-1=24[/tex]
[tex]n\left ( A\cup B \right )=n(A)+n(B)-n\left ( A\cap B \right )\\24=15+11-n\left ( A\cap B \right )\\n\left ( A\cap B \right )=15+11-24=2[/tex]
Percentage of students who tried both questions = [tex]\frac{2}{25}\times 100=8\%[/tex]
Percentage of students who tried at least one question = [tex]\frac{24}{25}\times 100=96\%[/tex]
Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards. What is the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind)? (Round your answer to four decimal places.)
Answer:
The probability that he ends up with a full house is 0.0083.
Step-by-step explanation:
We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.
We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).
We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);
If he is given with two kings.If he is given one king and one ace.Only in these two situations, he will end up with a full house.
Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.
So, the ways in which we can draw two kings from available three kings is given by = [tex]\frac{^{3}C_2 }{^{47}C_2}[/tex] {∵ one king is already there}
= [tex]\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}[/tex] {∵ [tex]^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{3}{1081}[/tex] = 0.0028
Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = [tex]\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}[/tex]
= [tex]\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}[/tex]
= [tex]\frac{6}{1081}[/tex] = 0.0055
Now, probability that he ends up with a full house = [tex]\frac{3}{1081} + \frac{6}{1081}[/tex]
= [tex]\frac{9}{1081}[/tex] = 0.0083.
Answer:
0.0083
Step-by-step explanation:
The gambler will have full house if he is dealt two kings or ace and a king.Now, there are 47 cards left in the deck and two which are aces and three are king.
The probability of these event are [tex]\frac{3C_2}{47C_2}[/tex]
and [tex]\frac{3C_1\times 2C_1}{47C_2}[/tex] respectively. So, the probability of a full house is given as:
[tex]\frac{3C_2}{47C_2}+\frac{3C_1\times 2C_1}{47C_2}[/tex]
=0.0083
Write an algebraic expression for the phrase.
the sum of f and 6
Answer:
f+6
f+6 =(f+6)
What values of x and y satisfy the system of equations {10x+3y=−5−5x−4y=10? (0,−53) (25,−3) (−2,0) (12,−103)
Answer:
The solution of the equation
( 0.4 ,-3)
Step-by-step explanation:
Explanation:-
Step(i):-
Given system of equations
10 x+3 y = −5 ...(i)
- 5 x - 4 y = 10 ...(ii)
Multiply (i) with '5'
10 × 5 x + 3×5 y = - 25
50 x + 15 y = 25 ...(iii)
Multiply (ii) with '10'
-5 × 10 x - 4×1 0 y = 100
- 50 x - 40 y =100 ...(iv)
Step(ii):-
Solving (iii) and (iv)
50 x + 15 y =- 25
- 50 x - 40 y =100
- 25 y = 75
Dividing ' - 25' on both sides, we get
y = -3
substitute y = -3 in equation (i) , we get
10 x+3 y = −5
10 x - 9 = - 5
10 x = -5 + 9
[tex]x = \frac{4}{10}[/tex]
x = 0.4
Final answer:-
The solution of the equation ( 0.4 ,-3)
Any help would be greatly appreciated
Answer:
0.927
Step-by-step explanation:
Hope this helps.
Answer:
I think it would just be 0.927
Step-by-step explanation:
with 0.9267, 6 is in the thousandth spot. 2 is in the hundredth spot, and 9 is in the tenth spot. Since the number behind 6 is larger than five, you'd round your number 6 in the thousandth spot to a 7. Therefore, you should have 0.927.
The bottom of a deposit, of 300l of capacity, is cover by a layer of salt. Assuming that the velocity at which the salt is disolved is proportional to the difference between the concentration at this time and the concentration of the saturated solution ( 1 kg of salt for 3 liters of water), and also take into account that the amount of pure water disolve 1/3 de Kg of salt per minute. Find the ODE giving the amount of salt x(t), as a function of time, integrate it, and determine the amount of salt in the solution after one hour.Find the solutions of the ODE that satisfy the indicated conditions when x → ±[infinity]
Answer:
Step-by-step explanation:
Assuming x(t) to be the number of salt
The maximum bottom of deposits =300 Litre
Initial Concentration of the saturated salt solution = 1 kg of salt for 3 liters of water
[tex]x_ic_i= \dfrac{1}3[/tex]
⇒x = 0
The differential equation is :
[tex]\dfrac{dx(t)}{dt}[/tex] [tex]={x_ic_i}-{x_oc_o}[/tex]
[tex]= \dfrac{1}{3} - \dfrac{x(t)}{300}[/tex]
[tex]\dfrac{dx(t)}{dt} + \dfrac{x(t)}{300} = \dfrac{1}{3}[/tex]
Using the first order differential equation of the form :
x' + p(t) x = q(t)
where
[tex]p(t) = \dfrac{1}{300}[/tex] ; [tex]q(t) = \dfrac{1}{3}[/tex]
By integrating the factor:
[tex]\mu = e^{\int\limitsP(t)dt } \\ \\ =e^{\int\limits \dfrac{1}{300}dt } \\ \\ = e^{\frac{t}{300} }[/tex]
[tex]x(t) = \dfrac{1}{\mu(t) }\int\limits \mu (t) * q(t) dt \\ \\ = e ^{- t/300} \ \ [\int\limits e ^{+ t/300} * \dfrac{1}{3}dt ][/tex]
[tex]= e ^{- t/300} \ \ [\dfrac{1}{3} * \dfrac{e^{t/300}}{1/300} + C ][/tex]
[tex]x(t) = 100 + Ce ^{-t/300[/tex]
Thus the differential equation solution is : [tex]x(t) = 100 + Ce ^{-t/300[/tex]
However; we have initial concentration x(0) = 0
SO;
[tex]0 = 100 + Ce^{-0/300}[/tex]
C = -100
[tex]x(t) = 100 -100e ^{-t/300[/tex]
when x → ±[infinity]
[tex]\infty = 100 + Ce^{- \infty /300}[/tex]
[tex]x(t) = 100 -100e ^{-t/300[/tex]
Now; the amount of salt after an hour is as follows:
1 hour = 60 minutes
t = 60 min
[tex]x(60) = 100 -100e ^{-60/300[/tex]
= 100 -100 (0.818)
= 100 - 81.8
= 18.2
x(60) = 18.2 kg
This diagram to the right represents a small stage in the shape of a SEMIcircle (half of a circle). Find the area of the stage. ***Diameter of the semi circle is 10 yards
Answer:
above is the answer
Step-by-step explanation:
Area of a circle=
[tex]\pi {r}^{2} [/tex]
but this Is a semicircle so you divide it by 2 as in
[tex] a = \frac{\pi {r}^{2} }{2} [/tex]
so d=2r so r=5yd
A=5×5 pie/2
=25 pie/2=12.5 yards
