The integrating factor of the given differential equation is I(t) = e^(sin(t)).
To find the integrating factor of the given differential equation, dy/dx = -cos(t)y t^2, follow these steps:
Rewrite the differential equation in the standard form:
(dy/dx) + P(t)y = Q(t), where P(t) and Q(t) are functions of t.
In our case, P(t) = cos(t) and Q(t) = -t^2.
Calculate the integrating factor, I(t), using the formula:
I(t) = e^(∫P(t) dt)
Here, P(t) = cos(t), so we need to integrate cos(t) with respect to t.
3. Integrate cos(t) with respect to t:
∫cos(t) dt = sin(t) + C, where C is the constant of integration. However, since we only need the function part for the integrating factor, we can ignore the constant C.
4. Substitute the integration result into the integrating factor formula:
I(t) = e^(sin(t))
So, the integrating factor of the given differential equation is I(t) = e^(sin(t)).
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five litres of paint costs R575 .Work out the cost of fifteen litres of paint
Answer:
first of all learn how to spell liters
1725
Step-by-step explanation:
15 liters of pain will cost Rs.225
What is multiplication?Multiplication is a process of adding a number repetitively. Mathematically, we can write -
m = a x b
Given is that the 5 liters of paint costs Rs. 75.
5 liters of paint costs Rs. 75.
1 liter of paint will cost Rs. (75/5)
15 liters of pain will cost Rs. (75/5 x 15) = 75 x 3 = Rs. 225
Therefore, 15 liters of pain will cost Rs.225
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how many solutions does the equation 5x+13=13 have
Answer:
It only has one solution
Step-by-step explanation:
Which value is the solution for this equation
2/3(6h-9)=6
A) -1
B) 1
C) 3
D) 5
Answer:
h = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
2/3(6h - 9) = 6
Step 2: Solve for h
[Division Property of Equality] Divide 2/3 on both sides: 6h - 9 = 9[Addition Property of Equality] Add 9 on both sides: 6h = 18[Division Property of Equality] Divide 6 on both sides: h = 3Set up a system of equations for the following situation: The girls basketball team spent a total of $1,590 on new basketballs and sweat suits for the players. If each new basketball cost $30 and each sweat suit cost $90, how many of each did the team purchase? *
Answer:
there are 13 players in a team
-12 + 2t = - 14
Solve for t
Answer:
-1
Step-by-step explanation:
-12 + 2t = -14
12 + -12 + 2t = -14 + 12
2t = -2
2t/2 = -2/2
t = -1
OOPS my submitted answer was wrong.
Submitting this is so you can give other person points! :]
please help! how do you do this question?
9514 1404 393
Answer:
(0.75, -1)
Step-by-step explanation:
The center of the circle is at the midpoint of any diameter segment. The midpoint formula can be used.
C = (A +B)/2
C = ((-1, 1) +(2.5, -3))/2 . . . . fill in A and B
C = (-1+2.5, 1-3)/2 . . . . . . . add the coordinates
C = (1.5, -2)/2 . . . . . . finish the addition; next, divide by 2
C = (0.75, -1) . . . . . . the center of the circle
What is the name for a savings account in which money must stay deposited for a specific amount of time? A. Traditional savings account B. Certificate of deposit C. Money market account D. Retirement account
Answer:
B. Certificate of deposit
Step-by-step explanation:
in traditional savings account you can take the money out anytime (usually up to 5 times a month)
in retirement account (well this could include 401k ,etc..)
Answer: B
Step-by-step explanation:
Solve this system of equations.Write your answer as an ordered pair.3x+4y=36 y=-1/2x+8
Answer:
x = 4
y = 6
Step-by-step explanation:
[tex]\left \{ {{3x+4y=36} \atop {\frac{1}{2}x+4y=8 }} \right.[/tex] rewrite the equations and multiply bottom equations by -4
[tex]\left \{ {{3x+4y=36} \atop {-2x-4y=-32}} \right.[/tex] add both equations together
x = 4
then, input x=4 into equation 3x+4y=36:
3(4)+4y=36 (simplify)
12+4y=36 (subtract 12 from both sides)
4y=24 (divide both sides by 4)
y=6
At a real estate agency, an agent sold a house for $389,000. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 30% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answer:
I fr don’t know
Step-by-step explanation:
Round 13,649 to the nearest thousand
Answer:
14,000
Step-by-step explanation:
13,649
the 6 in the hundredths place rounds up therefore the 3 in the thousands place turns into a 4
A flower vase bought for Rs. 72 and sold for Rs. 63. Find the loss percent.
Answer:
12.5% is loss....
hope it helps.
Answer:
the lost percentage is 14.28%
Step-by-step explanation:
1 - (72÷63) = -0.1428 x 100% = -14.28 %
(Please heart the answer if you find it helpful, it's a motivation for me to help more people)
Y=-x-2
2x-3y=-9
Solve for x and y
Answer:
y = - x - 2
2x - 3y = - 9
put value of y
2x - 3(-x - 2)= -9
2x +3x +6 = - 9
5x = - 9 - 6
5x = - 15
x = - 3
now put x in y = - x - 2
y = - (-3)-2
= 3-2
y = 1
Angle ABC is a straight angle. The measure of angle ABD is x. What is the value of x?
Answer:
45 degrees
Step-by-step explanation:
A straight angle is equal to 180, so subtract 135 from 180
Answer:
45
Step-by-step explanation:
1/8 = 2/5 times X . What is X
Answer: 5/16
Step-by-step explanation:
Answer:
0.0125
Step-by-step explanation:
1/8=2/5x
Divide by 2/5 on each side of the equation. X=0.0125. 0.0125=1/80. The last option.
The fisherman pays a contractor to repair his dock. The charges are $1200 for lumber, $60 for sales tax, and $750 for labor. The fisherman pays $260 down and finances the remainder. There is a finance charge of $41.06.
Answer:
Im guessing we have to add these, considering you did not put the rest of the question. In that case, the answer would be 2311.06
Step-by-step explanation:
Can someone please help me with this I will give brainliest
Answer:
Step-by-step explanation:
2(2x +4) - 2x = x + 18
4x +8 -2x = x +18
2x -x = 18-8
X = 10
Put the value of x in both side
Left side *+*+*+*+*+
2 ( 2*10+4)-2*10
48-20 = 28
Right side +*+*+*+*+*
X + 18
10+ 18 = 28
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Halppppppppppppppppppp
Answer:
Yes
Step-by-step explanation:
[tex]y\leq 3x+9\\\\8\leq 3(7)+9\\\\8\leq 21+9\\\\8\leq 30[/tex]
Yes, the given point makes the inequality true. We end up with a true statement.
Hope this helps.
Plz help with all 3 questions i will give Brainliest
Answer:
Step-by-step explanation:
8) entire cost of meal = m
m = 14.68 + 14.68
= 29.36
Solution $29.36
9) Let Elijah's height = h
h + 6 = 48
h = 48 - 6
Solution 42 inches
10) x - 15 = 20
x = 20 + 15
Solution 35 ounces
Simplify the expression -1x-5(2x-y)-3y
Answer:
-11x + 2y
Step-by-step explanation:
Evaluate the expression when y=6 and x=9.
x+7y
Answer:
9+(7)(6)
9+42=51
Step-by-step explanation: hope this help
Determine which points are a solution to the system of inequalities.
the answer choices are:
a. (0,0)
b. (4,1)
c. (3,-2)
d. (2,0)
e (4,-4)
f (1,3)
Answer:
I think it's e 4 -4
Step-by-step explanation:
hope this helps
Determine the intercepts of the line:
y = -9x - 14
Answer: (-14/9, -14) or (-1.5, -14)
Step-by-step explanation:
y = -9x - 14
the coefficient without a variable in a slope-intercept equation is the y-intercept -- in this case, it is -14
to find the x intercept you use the equation given, set y to equal zero and Solve for x
- Your new equation should be: 0 = -9x - 14
Our new goal is to isolate the x
Start by doing the inverse of the coefficient, so add 14 to both sides
- Your new equation should be: 14 = -9x
Theres still a -9 attached to the x and the -9 is attached by multiplication -- so now you do the inverse function and divide both sides by -9
Your final answer: -14/9 = x or -1.5 with a repeating decimal
Find the midpoint of the segment with the following endpoints.
(8,2) and (1,10)
Answer:
I am not sure but i think the midpoint is 4.5 and 6
cual numero es mayor q 9/5
Answer:
9/5 es mayor que 4/5 Realmente espero que esto te ayude
Sam bought 6 pens for an unknown price plus a
backpack. If he spent a total of $28.50, write an
equation to find the cost of each pen.
write a quadratic equation with the roots 1/2 and -5
x = 1/2 or x = -5
2x - 1 = 0 or x + 5 = 0
(2x-1)(x+5) = 0
2x² + 10x - x - 5 = 0
2x² + 9x - 5 = 0
Hope it helps!
Answer:
2[tex]x^{2}[/tex] + 9x - 5 = 0
Step-by-step explanation:
// Use the Vijet's theorem,
// note that the kofficient before [tex]x^{2}[/tex] = 1
Sum of the roots is:
1/2 + (-5) = - 4,5
Product of the roots is:
0,5 * (-5) = - 2,5
Formation of quadratic equation:
[tex]x^{2}[/tex] - (sum of the roots) x + product of the roots = 0
[tex]x^{2}[/tex] - (-4,5) * x + (-2,5) = 0
[tex]x^{2}[/tex] + 4,5x -2,5 = 0
// multiply both sides by 2
2[tex]x^{2}[/tex] + 9x - 5 = 0
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the sum of the number and 5 is 12
Answer:7
Step-by-step explanation: x+5=12 solve for x = 7
Answer:
"a number" = 7
Step-by-step explanation:
let "a number" = x.
x + 5 = 12
Isolate the variable x. Note the equal sign, what you do to one side, you do to the other. Subtract 5 from both sides.
x + 5 (-5) = 12 (-5)
x = 12 - 5
x = 7
7 is your answer.
~
If a rectangle measures 21 centimeters by 28 centimeters what is the length in centimeters of the diagonal of the rectangle
Answer:
35cm
Step-by-step explanation:
Given data
Length= 21cm
Width= 28cm
Diagonal= ???
Applying Pythagoras theorem
D^2= L^2+W^2
D^2= 21^2+28^2
D^2= 441+784
D^2= 1225
D= √1225
D= 35cm
Hence the diagonal is 35cm
A meal costs $30 before tax and tip.
There is a 7% sales tax. After the tax, a 20% tip is
added.
What is the total after tax and tip?
Answer:
$38.1
Step-by-step explanation:
Tax: 30*0.07 = 2.1
Tip: 30*0.2 = 6
Total: 30 + 2.1 + 6 = 38.1
Suppose $ 1,250 is placed in a savings account over 2 years. Find the interest earned if the rate is 4.5%
Answer: $112.50
Step-by-step explanation:
The Simple interest will be calculated using:
= Principal × Rate × Time
= 1250 × 4.5% × 2
= 1250 × 0.045 × 2
= $112.50
Therefore, the interest earned will be $112.50
Answer:$112.50
Step-by-step explanation: