Answer:
y = [tex]\frac{3}{2 + 3Ce^{-3t} }[/tex]
Step-by-step explanation:
As given , y' = 3y - 2y²
⇒y' - 3y = -2y²
Divide by y² in the above equation
⇒[tex]\frac{y'}{y^{2} } - \frac{3y}{y^{2} } = -\frac{2y^{2} }{y^{2} }[/tex]
⇒[tex]\frac{y'}{y^{2} } - \frac{3}{y } = -2[/tex] ........(1)
Now , let [tex]\frac{1}{y}[/tex] = u
⇒-[tex]\frac{1}{y^{2} } \frac{dy}{dt} = \frac{du}{dt}[/tex]
⇒-[tex]\frac{1}{y^{2} }y' = \frac{du}{dt}[/tex]
∴ equation (1) becomes
-[tex]\frac{du}{dt}[/tex] - 3u = -2
⇒[tex]\frac{du}{dt}[/tex] + 3u = 2
It is a linear differential equation
Now,
Integrating factor = I.F = [tex]e^{\int\limits {3} \, dt }[/tex] = [tex]e^{3t}[/tex]
∴ The solution becomes
u.(I.F) = [tex]\int\limits {2.(I.F)} \, dt[/tex] + C
⇒u.([tex]e^{3t}[/tex]) = [tex]\int\limits {2.(e^{3t} )} \, dt[/tex] + C
⇒u.([tex]e^{3t}[/tex]) = [tex]\frac{2e^{3t} }{3}[/tex] + C
⇒u = [tex]\frac{2}{3} + Ce^{-3t}[/tex]
As [tex]\frac{1}{y}[/tex] = u
⇒[tex]\frac{1}{y}[/tex] = [tex]\frac{2}{3} + Ce^{-3t}[/tex]
⇒ y = [tex]\frac{1}{\frac{2}{3} + Ce^{-3t} } = \frac{3}{2 + 3Ce^{-3t} }[/tex]
⇒ y = [tex]\frac{3}{2 + 3Ce^{-3t} }[/tex]
Dewayne is thinking of a number n, and he wants his sister to guess the number. His first clue is that seven less than five times his number is between thirteen and eighteen. Write a compound inequality that shows the range of numbers that Dewayne might be thinking of.
Answer:4<n<5
Step-by-step explanation: 13<5n-7<18
20<5n<25
4<n<5
Inequalities help us to compare two unequal expressions.The compound inequality that shows the range of numbers that Dewayne might be thinking of is 8<(5n-7)<13.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given clue by Dewayne can be written in the form of inequality as shown below. Therefore, we can write,
Five times the number → 5nSeven less than five times a number → 5n-7Seven less than five times his number is between thirteen and eighteen → 8 < (5n - 7) <13.Hence, the compound inequality that shows the range of numbers that Dewayne might be thinking of is 8<(5n-7)<13.
Learn more about Inequality here:
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PLEASE HELP! I'LL GIVE BRAINLIEST!
Write an equation for the line (y = mx + b)
Write a sentence explaining a real-life situation that this line could represent. (Make sure you use the word ascending in your sentence.)
How many meals would be packed in 20 hours?
Given :
A graph of Total Meals Packed vs Time( in hours ).
To Find :
How many meals would be packed in 20 hours.
Solution :
First we will find the equation of line.
Now, the line passes through ( 0, 0 ) and ( 4, 500 ).
So, equation of line passing through ( 0, 0 ) and ( 4, 500 ) is :
[tex]y - 0 = \dfrac{500-0}{4-0}( x - 0 )\\\\y = 125x[/tex]
Now, putting the value of x = 20 hours in above equation, we get :
y = 125 × 20 meals
y = 2500 meals
Therefore, number of meals packed in 20 hours is 2500 meals.
Dover City Printers needs to ship 419 graduation programs to a university. The printing company can fit 24 programs in each box. How many programs will be in the partially filled box?
Answer:
There will be 11 graduation programs in partially filled box.
Step-by-step explanation:
It is given that:
Number of graduation programs need to be shipped = 419
Number of programs in each box = 24
Number of boxes = [tex]\frac{419}{24}[/tex]
Number of boxes = [tex]17\frac{11}{24}[/tex]
Here,
17 is the number of full boxes and 11 is the remainder.
Therefore,
There will be 11 graduation programs in partially filled box.
Answer:
11
Step-by-step explanation:
hope this helps plz mark brainliest
You and three friends are going to the fair. The cost for
parking is $5 per car and admission to the fair is $19 per person. If you have
a total of $113, how much can each person spend on food?
Answer:
$17 on food per person
Step-by-step explanation:
The cost of parking a car is $5
Assuming that the friends used one car, then the parking cost=$5
Admission cost is 19
For three people, Admission cost =19*3=57
TOTAl COSTS=Parking cost+Admission cost
TOTAl COSTS=57+5=62
Remaining amount can be used for food
FOOD= 113-62=51
Therefore each person can spend 51/3=$17 on food
I hope this was helpful and clear to follow
Answer:
$8
Step-by-step explanation:
19 x 4 + 5 + c =113
81 + c =113
-81 -81
c =32
32 divided by 4 ppl = 8
100 POINTS!!!!!!! I WILL GIVE BRAINLIEST!
YOU MUST SHOW YOUR WORK OR I WILL NOT GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
In the morning, Jasmine biked to her grandma's house in 45 minutes. When she was biking back home in the evening it was foggy and she went 4 mph slower. The trip back took her 1 hour and 10 minutes. How far from her house does her grandmother live?
Answer:
8.4 milesStep-by-step explanation:
Let the speed in the morning be s, then in the evening it is s - 4
The distance is equal both directions:
45 min *s = 1 hr 10 min *(s - 4)Time in hours:
45*1/60*s = (1 + 10*1/60)(s - 4)3/4s = 7/6s - 7/6*4Multiply all terms by 12 to clear fraction:
9s = 14s - 565s = 56s = 56/5s= 11.2 mphThe distance is:
3/4*11.2 = 0.75*11.2 = 8.4 milesAnswer:
the answer is 8.4
Step-by-step explanation:
hope it helps. even I'm stuck so I went on brainly and the guy who helped you is a god ls mark the other person brainliest he deserves it with all the clean work and all
f(x)=x^4-5x^2-6x-10 is divided by x-3
Answer:
Step-by-step explanation:
STEP
1
:
10
Simplify ——
x
Equation at the end of step
1
:
10
((((x4)-(5•(x2)))-6x)-——)-3
x
STEP
2
:
Equation at the end of step
2
:
10
((((x4) - 5x2) - 6x) - ——) - 3
x
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using x as the denominator :
x4 - 5x2 - 6x (x4 - 5x2 - 6x) • x
x4 - 5x2 - 6x = ————————————— = ———————————————————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
x4 - 5x2 - 6x = x • (x3 - 5x - 6)
Polynomial Roots Calculator :
4.2 Find roots (zeroes) of : F(x) = x3 - 5x - 6
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -6.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,6
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -2.00
-2 1 -2.00 -4.00
-3 1 -3.00 -18.00
-6 1 -6.00 -192.00
1 1 1.00 -10.00
2 1 2.00 -8.00
3 1 3.00 6.00
6 1 6.00 180.00
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
x • (x3-5x-6) • x - (10) x5 - 5x3 - 6x2 - 10
———————————————————————— = ———————————————————
x x
Equation at the end of step
4
:
(x5 - 5x3 - 6x2 - 10)
————————————————————— - 3
x
STEP
5
:
Rewriting the whole as an Equivalent Fraction
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
3 3 • x
3 = — = —————
1 x
Checking for a perfect cube :
5.2 x5 - 5x3 - 6x2 - 10 is not a perfect cube
Trying to factor by pulling out :
5.3 Factoring: x5 - 5x3 - 6x2 - 10
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -6x2 - 10
Group 2: x5 - 5x3
Pull out from each group separately :
Group 1: (3x2 + 5) • (-2)
Group 2: (x2 - 5) • (x3)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
5.4 Find roots (zeroes) of : F(x) = x5 - 5x3 - 6x2 - 10
See theory in step 4.2
In this case, the Leading Coefficient is 1 and the Trailing Constant is -10.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,5 ,10
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -12.00
-2 1 -2.00 -26.00
-5 1 -5.00 -2660.00
-10 1 -10.00 -95610.00
1 1 1.00 -20.00
2 1 2.00 -42.00
5 1 5.00 2340.00
10 1 10.00 94390.00
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
5.5 Adding up the two equivalent fractions
(x5-5x3-6x2-10) - (3 • x) x5 - 5x3 - 6x2 - 3x - 10
————————————————————————— = ————————————————————————
x x
Polynomial Roots Calculator :
5.6 Find roots (zeroes) of : F(x) = x5 - 5x3 - 6x2 - 3x - 10
See theory in step 4.2
In this case, the Leading Coefficient is 1 and the Trailing Constant is -10.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,5 ,10
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -9.00
-2 1 -2.00 -20.00
-5 1 -5.00 -2645.00
-10 1 -10.00 -95580.00
1 1 1.00 -23.00
2 1 2.00 -48.00
5 1 5.00 2325.00
10 1 10.00 94360.00
Polynomial Roots Calculator found no rational roots
Final result :
x5 - 5x3 - 6x2 - 3x - 10
————————————————————————
x
WORTH: 40 POINTS ANSWER ALL OF THESE IN ITS SIMPLEST FORM (FRACTION)
A: 2/3 divided by 3
B: 6/7 divided by 3
C: 2/5 divided by 4
D: 5/6 divided by 5
E: 10/8 divided by 5
F: 4/7 divided by 4
G: 5/8 divided by 10
H: 20/6 divided by 2
(I WILL REPORT YOUR COMMENT IF YOU COMMENT RANDOM THINGS JUST TO GET POINTS LIKE DHSHRBABDB)
Answer:
2/9, 2/7, 1/10, 1/6, 1/4, 1/7, 1/16, 5/3Step-by-step explanation:
A: 2/3 divided by 3
2/3 : 3 = 2/3*1/3 = 2/9B: 6/7 divided by 3
6/7 : 3 = 6/7 *1/3 = 2/7C: 2/5 divided by 4
2/5 : 4 = 2/5*1/4 = 1/10D: 5/6 divided by 5
5/6 : 5 = 5/6*1/5 = 1/6E: 10/8 divided by 5
10/8 : 5 = 5/4 * 1/5 = 1/4F: 4/7 divided by 4
4/7 : 4 = 4/7*1/4 = 1/7G: 5/8 divided by 10
5/8 : 10 = 5/8*1/10 = 1/16H: 20/6 divided by 2
20/6 : 2 = 10/3 * 1/2 = 5/3Need help right now!!! Due soon!
Answer:
Step-by-step explanation:
HAHAHAHAHA! NOT IN THE MOOD!
How much milk is used for each slice of bread when recipe is 1 cup of milk and 8 slices of bread
Answer:
8 cups hope this helps have a nice day please give me brainliest:))
Step-by-step explanation:
Answer:
.125 cup
Step-by-step explanation:
when you divide 1 by 8 you get .125 (and in this case your answer).
Triangle A'B'C' is a dilation of AABC. What is AB?
B'
B
6
A4
10
C
A
15
С
o
A. 4
o
B. 5
C. 9
o
D. 16
Answer:
C. 9
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
I’ll give brainly The measure of ABC = 180°.
Find the value of y and type your result in the empty box.
Answer:
y=37
Step-by-step explanation:
the addition of the 3 angles is 180°
then 40 + y +29 +2y = 180
69 + 3y =180
3y = 180 -69
3y= 111
y =111 ÷ 3
y = 37
Subtract 1/2h -1 from 3/4 h -4
A.1/4h+3
B.-1/4+5
C.1/4h+5
D.-1/4h+5
Help plzzzz
Answer:
It would be option A.
Step-by-step explanation:
1/4h + 3
Solve 3,200 divided by 10 using a area model
the monthly rents for five apartments advertised in a newspaper were $700, $700, $770, $1750, and $860. use the mean, median, and mode of the rents to answer the question. which value gives the average rent?
Answer:
Step-by-step explanation:
Write the equation of an exponential function that has an initial
value of 150 and a growth rate of 4%, which occurs every 8
years.
Answer:
Step-by-step explanation:
Sheronda uses 1 cups of sugar in every batch of homemade muffins
she makes. One day, while making muffins for her son's bake sale, she
used 19 cups of sugar in all. How many batches of muffins did she make?
Answer:
19 batches of homemade muffins
Step-by-step explanation:
1 cup per 1 batch
You will get an amount of batches equal to the amount of cups of sugar, so if there are 19 cups there would be 1 batch of homemade muffins for each of the cups.
Answer:
19 batches of muffins
Step-by-step explanation:
She uses 1 cup for 1 batch which means
1 cup = 1 batches
So if you multiply 19 by 1 you should get 19 which means
19 cups = 19 batches
Theresa has a pile of sand grains and salt grains mixed together. She wants to separate the sand from the salt. What method can she use to separate these two substances?
Answer:
the answer is A
Step-by-step explanation:
Answer:
A. heat the pile to 100c so that half the pile boils
Step-by-step explanation: I just took the test :)
probability question!!!! help please!!!...Using a standard 52 card deck, what is the probability of pulling the king of hearts if you are
given two attempts (you will pull out one card and then another card)??
Answer:
4/103
Step-by-step explanation:
2/the average of 52 and 51
2/51.5 or 4/103
Express the sum of 1.202 x 10^3 and 3.45 x 10^2 in scientific notation.
Answer:
4.1469 x 10^5
Step-by-step explanation:
multiply the coefficients and add the exponents
1.202 x 3.45 = 4.1469
10³ x 10² = 10^5
What are the coordinates of point P?
(-2, -4.5)
Second answer down
A bag contains 5 red beads, 3 green beads and 2 blue beads (10 total). If beads are picked from the bag without
replacement, what is the probability that two red beads will be selected?
Оа
0.5
b
0.25
0.9444
ООО
Ο
d
0.2222
0.125
Answer:
2/9 or .22 repeating
Step-by-step explanation:
P(red,red) = [tex]\frac{5}{10}[/tex] · [tex]\frac{4}{9}[/tex] = 2/9 reduced form
Need help don’t know what to do I’m confused
Danielle wants to translate triangle XYZ so that vertex Y is moved from coordinates (-
4,2) to (0,-3). Which of the following mappings can be used to find the new
coordinates of X and Z?
A (x,y)-( * - 4, y + 5)
B (x,y)-(x+4, y - 5)
C(x,y)-(x - 4, y + 3)
D(x,y)-(x + 5, y - 4)
Answer:
We need to use the mapping [tex]U'(x,y) = (x+4,y-5)[/tex] to find the new coordinates of X and Y.
Step-by-step explanation:
Vectorially speaking, we must look for the defintion of the translation operation such that vertex Y becomes vertex Y', which is represented by:
[tex]T(x,y) = Y'(x,y) - Y(x,y)[/tex] (1)
Where [tex]T(x,y)[/tex] is the translation vector.
If we know that [tex]Y(x,y) = (-4,2)[/tex] and [tex]Y'(x,y) = (0,-3)[/tex], then the translation vector is:
[tex]T(x,y) = (0,-3)-(-4,2)[/tex]
[tex]T(x,y) = (4, -5)[/tex]
If [tex]U(x,y) = (x,y)[/tex], [tex]T(x,y) = (4, -5)[/tex] and [tex]U'(x,y)[/tex] is the translated vector, then we obtain the following definition:
[tex]U'(x,y) = U(x,y) +T(x,y)[/tex] (2)
[tex]U'(x,y) = (x,y) + (4,-5)[/tex]
[tex]U'(x,y) = (x+4,y-5)[/tex]
The correct answer is B.
Answer:
B is the answer
Step-by-step explanation:
The distance between two towns on a map is 9 centimeters. The actual distance between
two towns is 63 kilometers. What is the scale on the map?
OA) 1 cm: 6 km
OB) 1 cm: 7 km
O C) 1 cm: 8 km
OD 1 cm : 9 km
Answer: OB) 1cm: 7km
63/9=7
Step-by-step explanation:
Answer:
7KM
Step-by-step explanation:
Which sequence of transformation can be used to map parallelogram K l m n onto parallelogram k l m n
Answer:
I need to see it first please
How would you solve x^3=8
Answer:
2
Step-by-step explanation:
[tex]x^{3} =8\\x=\sqrt[3]{8} \\x=2[/tex]
use your calculator
4) Terry missed the sale on a $210 jacket. When he went to purchases it,
he jacket increased to a cost of $262.50 By what percent did the jacket
ncrease in price?
Answer:
The jacket increase by 25% in price.
Step-by-step explanation:
Given that:
Sale price of jacket = $210
New cost of jacket = $262.50
Change = New cost - Sale price
Change = 262.50 - 210 = $52.50
Percent increase = [tex]\frac{Change}{Sale\ price}*100[/tex]
Percent increase = [tex]\frac{52.50}{210}*100[/tex]
Percent increase = 0.25 * 100
Percent increase = 25%
Hence,
The jacket increase by 25% in price.
Riley has a loyalty card good for a 12% discount at her local pharmacy. What would
her total in dollars and cents be, after the discount and before tax, if the total cost of
all the items she wants to buy is $17.50? Round to the nearest cent.
Answer:
The cost after discount would be $15.40
Step-by-step explanation:
Given that:
Discount card = 12%
Cost of items bought = $17.50
Amount of discount = 12% of 17.50
Amount of discount = [tex]\frac{12}{100}*17.50[/tex]
Amount of discount = 0.12 * 17.50
Amount of discount = $2.10
Cost after discount = 17.50 - 2.10
Cost after discount = $15.40
Hence,
The cost after discount would be $15.40
Which functions graph is a translation of the graph of f(x)=x shifted 5 units to the right
a. g(x)=5x
b. g(x)=x-5
c.g(x)=x+5
d. g(x)=-5x
The function of the graph of a translation of the graph of f(x) = x shifted 5 units to the right is g(x) = x - 5, so option B is correct, the graph is also attached below.
What is function?When a function from one set to the other is utilized, every element of X receives precisely one element of Y. The function's domain and co-domain are collective terms used to refer to the sets X and Y, respectively.
Given:
f(x) = x, shifted 5 units to the right
A translation is a change in the graph's direction, either horizontally or vertically, parallel to the -axis.
Here, the translation is of 5 units,
Thus, the new function will be,
g(x) = x - 5
To know more about function:
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A class of 32 students earned
grades of A, B, C, or Don a test.
One-fourth of the students earned
an A Half of the remaining students
earned a B. Two students earned a
D. What fraction of the students
earned a C?
Answer:
5/16 Got a C
Step-by-step explanation:
A = 1/4 x 32
B = (32 - A)/2
D = 2
A = 8
B = (32 - 8)/2
B = 24/2
B = 12
D = 2
8 + 12 + 2 = 22
22/32 did not get a C
32/32 - 22/32 = 10/32
10/32 - > 5/16