Answer:
1. 110°Step-by-step explanation:
Given angle - 610°
Coterminal angle is an angle in the interval 0°- 360° added or subtracted to multiples of 360°:
-610° + 2*360° = -610° + 720° = 110°Correct option is 1.
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+3y=8te^−t+6e^−t−(9t+6)
with initial values y(0)=2andy′(0)=2.
We're given the ODE,
y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) - (9t + 6)
(where I denote exp(x) = eˣ )
First determine the characteristic solution:
y'' + 4y' + 3y = 0
has characteristic equation
r ² + 4r + 3 = (r + 1) (r + 3) = 0
with roots at r = -1 and r = -3, so the characteristic solution is
y = C₁ exp(-t ) + C₂ exp(-3t )
For the non-homogeneous equation, assume two ansatz solutions
y₁ = (at ² + bt + c) exp(-t )
and
y₂ = at + b
• y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) … … … [1]
Compute the derivatives of y₁ :
y₁ = (at ² + bt + c) exp(-t )
y₁' = (2at + b) exp(-t ) - (at ² + bt + c) exp(-t )
… = (-at ² + (2a - b) t + b - c) exp(-t )
y₁'' = (-2at + 2a - b) exp(-t ) - (-at ² + (2a - b) t + b - c) exp(-t )
… = (at ² + (b - 4a) t + 2a - 2b + c) exp(-t )
Substitute them into the ODE [1] to get
→ [(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c)] exp(-t ) = 8t exp(-t ) + 6 exp(-t )
(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c) = 8t + 6
4at + 2a + 2b = 8t + 6
→ 4a = 8 and 2a + 2b = 6
→ a = 2 and b = 1
→ y₁ = (2t ² + t ) exp(-t )
(Note that we don't find out anything about c, but that's okay since it would have gotten absorbed into the first characteristic solution exp(-t ) anyway.)
• y'' + 4y' + 3y = -(9t + 6) … … … [2]
Compute the derivatives of y₂ :
y₂ = at + b
y₂' = a
y₂'' = 0
Substitute these into [2] :
4a + 3 (at + b) = -9t - 6
3at + 4a + 3b = -9t - 6
→ 3a = -9 and 4a + 3b = -6
→ a = -3 and b = 2
→ y₂ = -3t + 2
Then the general solution to the original ODE is
y(t) = C₁ exp(-t ) + C₂ exp(-3t ) + (2t ² + t ) exp(-t ) - 3t + 2
Use the initial conditions y (0) = 2 and y' (0) = 2 to solve for C₁ and C₂ :
y (0) = C₁ + C₂ + 2 = 2
→ C₁ + C₂ = 0 … … … [3]
y'(t) = -C₁ exp(-t ) - 3C₂ exp(-3t ) + (-2t ² + 3t + 1) exp(-t ) - 3
y' (0) = -C₁ - 3C₂ + 1 - 3 = 2
→ C₁ + 3C₂ = -4 … … … [4]
Solve equations [3] and [4] to get C₁ = 2 and C₂ = -2. Then the particular solution to the initial value problem is
y(t) = -2 exp(-3t ) + (2t ² + t + 2) exp(-t ) - 3t + 2
Find the area of the trapezoid below by decomposing the shape into
rectangles and triangles.
6
5
8
3
Answer:
72 square units
Step-by-step explanation:
The area of the rectangle in the middle: 6x8 = 48 square units
The area of the triangle on the left: (5x6)/2 = 30/2 = 15 square units
The area of the triangle on the right: (3x6)/2 = 18/2 =9
(The 6 for the height of the triangle on the right is from the left side of the rectangle in the middle, they have to be the same length)
48+15+9 = 72 square units
can you help me please
Answer:
Please check the explanation.
Step-by-step explanation:
Given that
|v|=38
Ф = 120°
Finding the horizontal component
The horizontal component can be obtained using the formula
Vx = |v| cos Ф
= 38 cos 120°
= 38 (-0.5)
= -19
Thus, the horizontal component is:
Vx = -19
Finding the vertical component
The vertical component can be obtained using the formula
Vy = |v| sin Ф
= 38 sin 120°
= 38 (0.86)
= 32.68
Thus, the vertical component is:
Vy = -19
A vector 'v' with magnitude |v| and direction Ф can be written as:v = |v| cos Ф i + |v| sin Ф j
As
|v|=38
Ф = 120°
Thus, the vector is
v = 38 cos 120° i + 38 sin 120° j
or
v = -19 i + 32.68 j
Graph the line that passes through the point (0,-7) and (-3,-9) and determine the equation of the line
Answer:
The equation is y=2/3x-7
Step-by-step explanation:
-9-(-7) /-3-0
-2/-3
that's your answer
Carle is cutting pieces of string that are exactly inches long. How many pieces can she cut from a ball of string that has 100 feet?
Answer:
Carle is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that has 100 feet? 1 foot= 12 inches. A) 49 pieces.Oct 14, 2016
Step-by-step explanation:
A string is 5.8 meters long. What is it's length in centimeters
Answer:
a
Step-by-step explanation:
because I said it was jejwjwjeiejehxueh ed uejrhcu
Answer:
580
Step-by-step explanation:
If 100 centimeters are in a meter, then we have to multiply 5.8 by 100 to find out the length of the string in centimeters.
(hope this helped)
1)A student earned a grade of 80% on a math test that had 60 problems. How many
problems on this test did the student answer correctly?
Answer:
48
Step-by-step explanation:
80% = .8
60 x .8 = 48
Answer: 48
Step-by-step explanation:
80% of 60 or 80/100 x 60 = 48
Can some one help me plz
Answer:
4h
2d
Step-by-step explanation:
can commas be used to separate the ones, tens and hundreds
Answer: no? because the comma goes after every three numbers.
Find the measurement of
an interior angle of a regular
decagon (10-sided figure).
Answer:
144°
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Sum of Angles: 180(n - 2)Step-by-step explanation:
Step 1: Define
Number of sides n = 10
Step 2: Find
Substitute: 180(10 - 2)Subtract: 180(8)Multiply: 1440°Step 3: Find 1 angle
We have 10 sides.
Divide: 1440/10 = 144A person saving for retirement makes an initial deposit of $1,000 to a bank account earning interest at a rate of 3% per year compounded monthly, and each month she adds an additional $200 to the account For each nonnegative integer n, let An be the amount in the account at the end of n months. Find a recurrence relation relating Ak to Ak-1. Use iteration to find an explicit formula for An.
Answer:
Step-by-step explanation:
(a)
From the given information:
Let An denote the amount in the account at the end of n month
Thus,
[tex]A_o[/tex] =1000
After the first month ends, interest = [tex]=A_o \times \dfrac{3}{100} \times \dfrac{1}{12}[/tex]
= [tex]0.0025A_o[/tex]
Additional deposit = $200
Now,
[tex]A_1 = A_o + 0.0025A_o + 200[/tex]
[tex]=1.0025A_o + 200 --- eqn(1)[/tex]
Interest after 2nd month, = [tex]A_1 \times \dfrac{3}{100} \times \dfrac{1}{2}[/tex]
Additional deposit = $200
[tex]A_2 = A_1 + 0.0025A_1 + 200[/tex]
[tex]=1.0025A_1 + 200 --- eqn(2)[/tex]
Thus:
[tex]A_n = 1.0025A_{n-1} +200[/tex]
(b)
From above;
[tex]A_1 = 1.0025A_ 0+ 200[/tex]
Thus;
[tex]A _2 = 1.0025A_ 1+ 200[/tex]
[tex]A_2 = 1.0025( 1.0025A_ 0+ 200)+ 200[/tex]
[tex]A_2 = 1.0025^2A_o +200 ( 1+1.0025)[/tex]
[tex]A _3 = 1.0025A_ 2+ 200[/tex]
[tex]A _3 = 1.0025( 1.0025^2A_o +200 ( 1+1.0025))+ 200[/tex]
[tex]A _3 = 11.0025^3A_o +200 ( 1+1.0025 + 1.0025^2)[/tex]
To continuity...
[tex]A_n = 1.0025^n A_o + 200 (1+1.0025 +1.0025^2 +...+ 1.0025^{n-1} ) ---- (3)[/tex]
Thus, we have a geometric term [tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1}[/tex]
where:
a = 1 (first term)
r = 1.0025>1 (common ratio)
Thus;
[tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1} = \dfrac{a(r^n -1)}{r-1}[/tex]
[tex]= \dfrac{1(1.0025^n -1)}{1.0025-1}[/tex]
[tex]= 400(1.0025^n -1)[/tex]
From equation(3)
[tex]A_n = (1.0025^n \times 1000) + 80000(1.0025^n -1)[/tex]
[tex]A_n = 1.0025^n \times 81000-80000[/tex]
7 1/2÷3/4 Please help this mom out!!
Answer:
10
Step-by-step explanation:
give me brainly
am i correct? let me know
One batch of cookies requires the following ingredients:
2 1/3 cups of flour
3/4 of a cup of chocolate chips
2/5 of a cup of chopped almonds
1 1/2cups of brown sugar
3/8of a cup of white sugar
1/2 of a teaspoon of salt
Eric wishes to triple the recipe.
How much of each ingredient should he use? Select all that apply.
A) 9/12 cup of chocolate chips
B) 6/5 cups of chopped almonds
C) 1/6 of a teaspoon of salt
D) 1 1/8 cups of white sugar
E) 6 1/3 cups of flour
F) 2 1/2 cups of brown sugar
Answer ASAP will give brainliest, thanks.
Answer:
B
Step-by-step explanation:
4x+2y=6
6x-4y=-12
2y=6-4x
y=3-2x
6x-4(3-2x)=-12
6x-12+8x=-12
2x-12=-12
2x=0
x=0
4(0)+2y=6
2y=6
y=3
(0,3)
Complete the table so that the cost per banana remains the same.
number of
bananas
cost in
dollars
unit price
(dollars per banana)
4
0.50
6
0.50
7
0.50
10
0.50
10.00
0.50
16.50
0.50
Step-by-step explanation:
No. of banana Cost Unit price
4 2 0.50
6 3 0.50
7 3.5 0.50
20 10 0.50
20 10 0.50
33 16.50 0.50
Cost = No of banana x unit price
Cost = 4 x 0.50 = 2
Cost = 6 x 0.50 = 3
Cost = 7 x 0.50 = 3.50
Cost = 20 x 0.50 = 10
No of banana = Cost / Unit price
No of banana = 10 / 0.50 = 20
No of banana = 16.50 / 0.50 = 33
Help me please I’m dying
Answer:
[tex]\boxed{x = 2+2\sqrt{6} ~~or~~x = 2 - 2 \sqrt{6} }[/tex]
.
Step-by-step explanation:
To find x, use pythagoras form
[tex]c^2 = a^2 + b^2[/tex]
[tex](x + 4)^2 = x^2 + (x + 1)^2[/tex]
[tex]x^2 + 8x + 16 = x^2 + x^2 + 2x + 1[/tex]
[tex]2x^2 + 2x + 1 - x^2 - 8x - 16 = 0[/tex]
[tex]x^2 - 6x - 15 = 0[/tex]
[tex]x^2 - 6x = 15[/tex]
[tex](x - 3)^2 - 9 = 15[/tex]
[tex](x - 3)^2 = 15 + 9[/tex]
[tex](x - 3)^2 = 24[/tex]
[tex]x - 2 = \pm \sqrt{24}[/tex]
[tex]x = 2 \pm 2\sqrt{6}[/tex]
.
[tex]x_1 = 2 + 2\sqrt{6}[/tex]
[tex]x_2 = 2 - 2\sqrt{6}[/tex]
.
Happy to help :)
6) A climber is on a hike. After 2 hours she is at an altitude of 400 feet. After 6 hours, she is at an
altitude of 700 feet. What is her rate of change?
Answer:
Her rate of change is 75 ft/h
Step-by-step explanation:
Rate of Change
It measures how one quantity varies with respect to another. The second variable usually is the time.
The climber is hiking. We are given two points of her progress: At 2 hours, she is at 400 ft. This corresponds to the point (2,400).
At 6 hours, she is at 700 ft. This is the point (6,700)
The rate of change is the slope between these two points or the quotient of the variations of each variable:
[tex]\displaystyle m=\frac{700\ ft-400\ ft}{6\ h-2\ h}[/tex]
[tex]\displaystyle m=\frac{300\ ft}{4\ h}[/tex]
[tex]m=75\ ft/h[/tex]
Her rate of change is 75 ft/h
The elves are loading all of the toys from Santa's workshop to the sleighs. They filled 2 small sleighs and 9 big sleighs with 241 toys. Later, they filled 14 small sleighs and 13 big sleighs with 437 toys. How many toys can fit on each type of sleigh?
Answer:
2*9=18 14*13=182 18+182=200
Step-by-step explanation:
well you multiply 2 times 9 and you get 18 and then you multiply 14 times 13 and you get 182 and then you 18+182 and that will give you 382.
Help Me please
Veronica wants to check her work after evaluating 108 ÷(-6) what steps can she follow to verify her answer?
Divide her answer by -6 and see if the result is -108.
Divide her answer by -108 and see if the result is -6.
Multiply her answer by -6 and see if the result is -108.
Multiply her answer by -108 and see if the result is -6.
Answer:
Its C
Step-by-step explanation:
I need the answer to this test question. We were assigned to correct our test for homework. I cannot think of another solution to this problem, please help.
Answer:
angle 1 = 70 degree and angle 2=95 degree
Step-by-step explanation:
for the first angle
180 -70 = 110
and 180-110 = 70 ( opposite angles )
for the second angle
180-85 =95
and again 180-95 =85(opposite angles)
180-85=95 (the straight line property)
Dawn purchased 6 quarts of motor oil for $14.12. What is the Unit Price per quart rounded to
the nearest cent?
Answer:
$2.35 per quart (rounded to nearest cent)
Step-by-step explanation:
6 quarts --- $14.12
1 quart --- [tex]\frac{1}{6}[/tex] × $14.12 = $2.35 (rounded to nearest cent)
URGENT !!
A popular television show recently released a video
preview for the upcoming season on íts website As
fans of the show discover the video, the number of
views of the preview video has grown each day
during the last 2 vweeks. The number of days since
the release of the video and the natural log of the
number of video views ís shown in the scatterplot.
Answer:C
Step-by-step explanation:
Solve the system of equations using the elimination method.
(8x +11y = 37
8x+y=7
You increase your walking speed from 1 m/s to 3 m/s in a period of 1 s.
What is your acceleration?
Answer:
2 m/s
Step-by-step explanation:
Answer:
2m/s²
Step-by-step explanation:
acceleration= v-u/t
=3-1/1
=2m/s²
winston earns $140.00 by selling 56 hotdogs at a concession stand at school. by using the same rate for the cost of one hotdog , how many more would Winston need to sell to earn $175.00?
18 ≤ -2x = what?? please answer im in class
Answer:
-9
Step-by-step explanation:
Wrote a linear function f with the values f(-4)=0 and f(4)=2
Answer:
y = (1/4)x + 1
Step-by-step explanation:
The points mentioned are (-4,0) and (4,2).
We can find the slope m:
(2-0)/(4-(-4)) = 2/8 = 1/4
We now have the equation y = (1/4)x + b
Now we must find the y-intercept.
Plugging in the first point:
0 = (1/4)*(-4) + b
0 = -1 + b
1 = b
y = (1/4)x + 1
the sum of three consecutive multiples of 24 is 288 find these multiples
plzz solve these question now
click on the picture attached to get the answer
hope it helps!
..........
triangle ABC has veritices A(-2,3), B(0,3), and C (-1,-1). Find the coordinates of the image after a reflection over the x-axis.
Answer:
A' = (-2, -3)
B' = (0, -3)
C' = (-1, 1)
I did this on edg
Step-by-step explanation:
Since it's a reflection over the x axis, the x coordinates will stay the same while the y coordinates will be opposite of what they are.
After reflected: A'(-2,-3), B'(0,-3), C'(-1,1)
Jared a beekeeper placed 120 hives in a apple orchard
Answer: 20
Step-by-step explanation: