Answer:
12 and 5
Step-by-step explanation:
Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration) dy/dt = 27t^8 y = Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integration.) dy/dx =8x^7/9 y =
Answer: [tex]y=Ce^(^3^t^{^9}^)[/tex]
Step-by-step explanation:
Beginning with the first differential equation:
[tex]\frac{dy}{dt} =27t^8y[/tex]
This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:
[tex]\frac{1}{y} \frac{dy}{dt} =27t^8[/tex]
Multiply both sides by 'dt' to get:
[tex]\frac{1}{y}dy =27t^8dt[/tex]
Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:
[tex]\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt[/tex]
[tex]ln(y)=27(\frac{1}{9} t^9)+C[/tex]
[tex]ln(y)=3t^9+C[/tex]
We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:
[tex]e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)[/tex]
[tex]y=e^(^3^t^{^9} ^+^C^)[/tex]
We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:
[tex]y=e^(^3^t^{^9}^)e^C[/tex]
The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:
[tex]y=Ce^(^3^t^{^9}^)[/tex]
To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:
[tex]\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))[/tex]
[tex]\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)[/tex]
[tex]\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8[/tex]
Now check if the derivative equals the right side of the original differential equation:
[tex](Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)[/tex]
[tex]Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)[/tex]
QED
I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.
Integral of (sin(2x) + cos(2x)) dx=
[tex]\displaystyle \int (\sin 2x + \cos 2x)~ dx\\\\=\displaystyle \int \sin 2x ~dx + \displaystyle \int \cos 2x ~ dx\\\\=-\dfrac{\cos 2x}2 + \dfrac{\sin 2x}2 +C\\\\=\dfrac{\sin 2x - \cos 2x}2+C[/tex]
Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel and petrodiesel. Random samples of 38 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9350 with a standard deviation of 0.0090, within what interval will 90 percent of yhe sample means fall? Round your answers to 4 decimal places.
Answer:
10 men can complete work l in 120 doy . In how many days does 30 me can complete it.
-
Write the set in set-builder notation.
{1, 3, 5, 7, 9, 11, ... , 47}
{1, 3, 5, 7, 9, 11, ... , 47}
To Write The Following in Set-builder notation
Solution[tex] \text{A} = [/tex] {x : x ∈ N;x is an odd number, x ≤ 47}
Hope This Helps!!Jane drinks 85ml of juice out of half a litre carton. How much juice left?
Answer:
415ml
Step-by-step explanation:
there is 1000 ml in 1litre so the question says half which means 500 ml so if he drank 85ml then
500ml-85ml= 415 ml
Find the angle measures.
Answer:
∠ 1 = 155° , ∠ 2 = 25°
Step-by-step explanation:
the 2 angles are adjacent angles and sum to 180° , that is
5x + x - 6 = 180
6x - 6 = 180 ( add 6 to both sides )
6x = 186 ( divide both sides by 6 )
x = 31
then
∠ 1 = 5x = 5(31) = 155°
∠ 2 = x - 6 = 31 - 6 = 25°
A cookie recipe for 60 cookies calls for 4 cups of flours how much flour or s needed to make 90 cookies
Answer:
6 Cups of Flower
Step-by-step explanation:
First form a ratio
Cookies:Flour
60:4
Simplify
15:1
Since we now need to find the amount of cups for 90 cookies we must finds the amount of flower.
90:X
Using our old ratio of 15:1 we must divide 90/15 in order to get a factor to multiply 1 to make 15:1 equivalent to 90:X.
90/15 = 6 | 6 is the factor
15(6):1(6)
90:6
If the perimeter of a rectangle is 75 meters, and the length is 1.5 times the width, find the area of the rectangle in square meters. Round your answer to two decimal places.
Answer:
263.86cm²
Step-by-step explanation:
75/4 = 18.75
to find width = 18.75×1.5=28.13
to find length = 18.75×0.5=9.38
28.13×9.38=263.86cm²
Sally is planning on painting her room. A gallon of paint covers 120 square feet and costs $38.95 per gallon. If Sally’s room is 9 feet by 17 feet and has an 12.5 foot ceiling, how much does Sally need to budget? (Round your answer to the nearest dollar.)
Answer:
$272
Step-by-step explanation:
9x7x12.5=787.5 120x7=840 38.95x7= 272.65 and she said to round to the nearest dollar so $272 dollars
three subtracted from the product of six and a number is greater than 17
Use the variable b for the unknown answer.
I have down 3-6(b>17)
Do you think you could help me?
Answer:
b is equal to 14 or higher
Step-by-step explanation:
NEED HELP WITH THIS MATH PROBLEM!!
Answer:
278°
Step-by-step explanation:
You want the measure of arc RSQ given inscribed angle RSQ has a measure of 41°.
Inscribed angleAn inscribed angle has half the measure of the arc it subtends. This means short arc RQ will have double the measure of angle RSQ:
arc RQ = 2 × 41° = 82°
Long arcThe measure of long arc RSQ will complete the 360° circle:
arc RSQ = 360° -arc RQ
arc RSQ = 360° -82°
arc RSQ = 278°
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The data set below represents the number of televisions repaired in a service shop over an 11-week period.
1, 48, 50, 25, 21, 19, 26, 30, 18, 17, 3
The outlier of the data set is____
Answer:
50
Step-by-step explanation:
It is on edge
Answer:
it is counting 48 than going down
Step-by-step explanation:1,48
A laptop computer is purchased for $2600. Each year, its value is 80% of its value the year before. After how many years will the laptop computer be worth
$500 or less?
the will he worth less because 80% a year is a 10% so 2600-500=2100 so 2100÷10=210
PLEASE HELP WITH GEOMETRY
Step-by-step explanation:
If 76° gives 7.5 meters, we must find out how many meters it is for 360°.
Find how much for 1°: [tex]\frac{7.5}{76}[/tex]
For 360°: [tex]\frac{7.5}{76} \times 360[/tex] = 35.53 meters
HHHHHEEEELLLLLPPPPPP
PLS
Answer:
m∠F = 100
Step-by-step explanation:
Sum of interior angles in a hexagon is 720.
( x - 60 ) + ( x - 40 ) + 130 + 120 + 110 + ( x - 20 ) = 720
x + x + x - 60 - 40 - 20 + 130 + 120 + 110 = 720
3x - 120 + 120 + 130 + 110 = 720
3x + 130 + 110 = 720
3x + 240 = 720
3x = 720 - 240
3x = 480
x = 480 / 3
x = 120
m∠F = x - 20
Substitute the value of x,
m∠F = 120 - 20
m∠F = 100
Three times a number plus three times a second number is negative twelve. Five times the first number plus twice the second is four
Consider the numbers as, if we assume our first number to be x and second number being y, then from the given information we will be having the following equations :
[tex]{:\implies \quad \begin{cases}\sf 3x+3y=-12\\ \\ \sf 5x+2y=4\end{cases}}[/tex]
Now, rewrite the second equation as ;
[tex]{:\implies \quad \sf 3(x+y)=-12}[/tex]
Divide both sides by 3 ;
[tex]{:\implies \quad \sf x+y=-4\quad ---(i)}[/tex]
Now, consider the second equation of the above cases
[tex]{:\implies \quad \sf 5x+2y=4\quad ---(ii)}[/tex]
Now, multiply (i) by 2 on both sides :
[tex]{:\implies \quad \sf 2x+2y=-8\quad ---(iii)}[/tex]
Now, subtracting (ii) from (iii) will give us :
[tex]{:\implies \quad \sf 2x+2y-(5x+2y)=-8-4}[/tex]
[tex]{:\implies \quad \sf 2x+2y-5x-2y=-12}[/tex]
[tex]{:\implies \quad \sf -3x=-12}[/tex]
[tex]{:\implies \quad \boxed{\bf{x=4}}}[/tex]
Now, putting x = 4 in (i), will give y + 4 = -4, then solving for y will yield [tex]{\boxed{\bf{y=-8}}}[/tex]
Hence, we can conclude that :
[tex]{\quad \qquad \longrightarrow \begin{cases}\bf x=4\\ \\ \bf y=-8\end{cases}}[/tex]
B. It is a reflec
C. They are 6
D. They are 2
3. 6.RP.1.3
A dairy farmer uses two trucks to deliver
milk. The two trucks use different kinds of
fuel. Truck A uses gasoline and Truck B uses
diesel. The table below shows the distance,
in miles, that each truck can travel per
gallon of fuel. Based on the table, what is
the total number of gallons of diesel Truck B
will use to travel 132 miles?
Miles Traveled per Gallon of Fuel
5. 6.NS.3.7
A fish swims at an
A bird flies at an al
Which of the follo
Select all that apply
Gallons
of Fuel
1
2
Truck A Truck B
(Gasoline) (Diesel)
8 miles 12 miles
16 miles 24 miles
24 miles 36 miles
miles
A. The bird's a
fish's altitude.
OB. The bird's al
fish's altitude.
C. The fish is cl
bird.
D. The fish is fa
3
18 maila
The total number of gallons of diesel Truck B used to travel 132 miles is 11.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A dairy farmer uses two trucks to deliver milk. The two trucks use different kinds of fuel. Truck A uses gasoline and Truck B uses diesel.
From the given table we can see that
The total number of gallons of diesel Truck B used to travel 12 miles = 1
Number of gallons of diesel Truck B used to travel 1 mile = 1 /12
The total number of gallons of diesel Truck B used to travel 132 miles
= 1 /12 x 132
= 132 / 12
= 11
Thus, The total number of gallons of diesel Truck B used to travel 132 miles is 11.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ1
meaning of complement in set theory
solve for x ~
[tex]x {}^{2} - 36 = 0[/tex]
thankyou ~
Answer:
[tex]x {}^{2} - 36 = 0 \\ \\ x {}^{2} = 36 \\ \\ x = \sqrt{36} \\ \\ x = + 36 \: \: or \: \: - 36[/tex]
hope helpful -,-
It takes 7 hours for Will to paint a house. Judy can paint the same house in 3 hours. How long will it take them to paint the house if they work together?
Answer:
2 hours
Step-by-step explanation:
1/7 + 1/3 = 10/21
21/10= 2.1
Hey Rachael is removed from a rectangle to create the shaded region chandelier find the area of the shaded region be sure to include the correct unit in youranswer
Answer:
34.5 cm²
Step-by-step explanation:
The area of the shaded region is the area of the rectangle minus the area of the right triangle.
The area of the rectangle is simply the length 7 cm multiplied by the width 6 cm.
To find the area of the right triangle, you must first find the base and height of the triangle.
The two lengths can be found this way:
7 cm - 2 cm = 5 cm
6 cm - 3 cm = 3 cm
area of shaded region = LW - bh/2
area of shaded region = 7 cm × 6 cm - 5 cm × 3 cm / 2
area of shaded region = 42 cm² - 7.5 cm²
area of shaded region = 34.5 cm²
can some one solve this for me
Answer:
x = 2
Step-by-step explanation:
24 - 7x = 10
Rearrange terms,
-7x + 24 = 10
Subtract 24 from both sides,
-7x + 24 - 24 = 10 - 24
-7x = 10 - 24
-7x = -14
Divide by sides by -7,
[tex]\frac{-7x}{-7}=\frac{-14}{-7}[/tex]
[tex]x=\frac{-14}{-7}[/tex]
x = 2
Graph the function. f(x)=3/5x-5
If y=x+4 then what is (x-y)^3
Answer:
64
Step-by-step explanation:
y = x + 4
y - x = 4
4^3 = 64
The net of the figure shown is made of which set of
shapes?
O 3 triangles and 1 square
O 3 triangles and 1 rectangle that is not a square
О 4 triangles and 1 square
O4 triangles and 1 rectangle that is not a square
Step-by-step explanation:
It's not 3 triangles and 1 square because you need four triangles to make the siding and the square wont go anywhere because of how it's going to look.
It's not 3 triangles and 1 rectangle because still you need four to make the sides and a rectangle is too long.
4 triangles and 1 rectangle is still not correct because the rectangle on the bottom of the net is going to mess it up fir the whole shape.
So in conclusion, 4 triangles and 1 squares is the correct answer.
I need a explanation
Answer:
convert the mixed fractions into decimals. do this by converting them into improper fractions and dividing the numerator by the denominator
If it takes one man three days to dig a hole, how long does it take two men to dig half a hole?
Answer: This is wrong. It takes 4 men to dig a hole and you cannot dig half a hole.
Step-by-step explanation:
Answer:
u have to be kidding me 2 Men can not dig a hole it takes like 4 or 5 men
You bought a laptop computer for $525 on the 12 months is the same as cast plan. The terms of the plan on the contract stated that
not paid within 12 months, you would be assessed 155 percent APR for the amount on the first day of the pian
If you pay the laptop in 11 months, how much will you have paid?
O $525
O $540.50
O $595 50
O $606 38
6×1(4+7)÷8×19(7-13)
solve and the correct answer wins the Brainlist
Answer:
-940.5
Step-by-step explanation:
Answer:
-940.5
Step-by-step explanation:
use pemdas
1.parenthesis
2.exponets
3.multiply
4.divide
5.add
6.subtract
MULTIPLE CHOICE
What is the distance from A to B in the diagram below?
Answer:
if not 24.5, it should be 31 yds
Step-by-step explanation:
ok so, I don't know how you want me to solve this but, if you're asking the distance diagonally, then it will be 24.5 yds. If you want the distance in straight lines, it will be 31 yds
lol there wasn't much information, sorry