Answer:
The answer is -4.
Step-by-step explanation:
Whenever you're adding a positive number to a negative number you are basically subtracting. So 3+-7 will be -4.
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' y'-4x-4y=e^-t x' y' 2x y=e^4t
It looks like the system of ODEs is
[tex]\begin{cases} 2x' + y' - 4x - 4y = e^{-t} \\ x' + y' + 2x + y = e^{4t} \end{cases}[/tex]
Differentiate both sides of both equations with respect to [tex]t[/tex].
[tex]\begin{cases} 2x'' + y'' - 4x' - 4y' = -e^{-t} \\ x'' + y'' + 2x' + y' = 4e^{4t} \end{cases}[/tex]
Eliminating the exponential terms, we have
[tex](2x' + y' - 4x - 4y) + (2x'' + y'' - 4x' - 4y') = e^{-t} + (-e^{-t}) \\\\ \implies (2x'' - 2x' - 4x) + (y'' - 3y' - 4y) = 0[/tex]
[tex](x'' + y'' + 2x' + y') - 4 (x' + y' + 2x + y) = 4e^{4t} - 4\cdot e^{4t} \\\\ \implies (x'' - 2x' - 8x) + (y'' - 3y' - 4y) = 0[/tex]
Now we can eliminate [tex]y[/tex] and it derivatives.
[tex]\bigg((2x'' - 2x' - 4x) + (y'' - 3y' - 4y)\bigg) - \bigg((x'' - 2x' - 8x) + (y'' - 3y' - 4y)\bigg) = 0 - 0 \\\\ \implies x'' + 4x = 0[/tex]
Solve for [tex]x[/tex]. The characteristic equation is [tex]r^2 + 4 = 0[/tex] with roots at [tex]r=\pm2i[/tex], hence the characteristic solution is
[tex]\boxed{x(t) = C_1 \cos(2t) + C_2 \sin(2t)}[/tex]
Solve for [tex]y[/tex]. Substituting [tex]x[/tex] into the second ODE gives
[tex]x' + y' + 2x + y = e^{4t} \\\\ \implies y' + y = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t)[/tex]
The characteristic equation this time is [tex]r + 1 = 0[/tex] with a root at [tex]r=-1[/tex], hence the characteristic solution is
[tex]y(t) = C_3 e^{-t}[/tex]
Assume a particular solution with unknown coefficients [tex]a,b,c[/tex] of the form
[tex]y_p = ae^{4t} + b \cos(2t) + c \sin(2t) \\\\ \implies {y_p}' = 4ae^{4t} - 2b\sin(2t) + 2c\cos(2t)[/tex]
Substituting into the ODE gives
[tex]5ae^{4t} + (b+2c) \cos(2t) + (-2b+c) \sin(2t) = e^{4t} + C_1 \cos(2t) + C_2 \sin(2t) \\\\ \implies \begin{cases}5a = 1 \\ b+2c = C_1 \\ -2b+c = C_2\end{cases} \\\\ \implies a=\dfrac15, b=\dfrac{C_1-2C_2}5, c=\dfrac{2C_1+C_2}5[/tex]
so that the general solution is
[tex]\boxed{y(t) = \dfrac15 e^{4t} + \dfrac{C_1-2C_2}5 \cos(2t) + \dfrac{2C_1+C_2}5 \sin(2t) + C_3 e^{-t}}[/tex]
Grandma has one cup of sugar. How many dozen cookies will she be able to make?
.chris p. bacon worked 44 hours last week and gets double time pay for overtime. his regular pay is $14 per hour. how much was his paycheck for the week?
The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week, regular pay $14 per hour and double time pay for overtime.
As given,
Regular pay per hour = $14
Overtime work payment= 2 × ($14)
Total hours work done last week = 44hours
Let regular timing be 8 hours per day 5 days a week
Total regular working hours = 8 × 5
= 40 hours
Over time = 44-40
= 4 hours
Payment check = (40 × 14)+ (4 × 28)
= $672
Therefore, The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week.
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In which triangle is the value of x equal to tan−1(StartFraction 3.1 Over 5.2 EndFraction)?
(Images may not be drawn to scale.)
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 5.2 and the length of the side adjacent to the right angle is 3.1. The angle opposite to side with length 3.1 is x.
A right triangle is shown. The length of 2 sides are 5.2 and 3.1. The angle opposite to side with length 5.2 is x.
The right triangle that shows the length of the two sides is 5.2 and 3.1.
It is required to find the triangle.
What is trigonometry?The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.
Given:
In trigonometry function, in a right triangle, a tangent of an angle x is equal to the ratio of the opposite side to angle x to the adjacent side to angle x.
According to given question we have:
Given that angle x will be:
[tex]x=tan^{-} \frac{3.1}{5.2}[/tex]
The opposite to angle x or perpendicular = 3.1 units
The adjacent side to angle x or base angle = 5.2 units
Therefore, the right triangle that shows the length of the two sides is 5.2 and 3.1.
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Answer:
b
Step-by-step explanation:
Select the correct answer.
Jonathan has 30 chocolates. He gives some chocolates to his friend David. He then gives Sarah half the number of chocolates that he gave David and gives Lily two-thirds of what he gave David. After giving away the chocolates, Jonathan has 4 chocolates left. If the number of chocolates Jonathan gives David is x, which equation represents the situation? How many solutions does this equation have?
A. x + 1/2x + 2/3x = 30 - 4, which has no solution
B. x + 1/2x + 2/3x = 30, which has infinitely many solutions
C. x + 1/3x + 2/3x - 4 = 30, which has one solution
D. x + 1/2x + 2/3x +4 = 30, which has one solution
E. 1/2x + 2/3x = x - 4, which has no solution
Answer: C, I think is correct
What is the least common multiple of 10 and 11 ?
Answer:
Step-by-step explanation:
The answer is 110
hope this helps :)
Which number contains digits where the hundreds digit is 1/10 the value of the thousands digit?
The number that contains digits where the hundreds digit is 1/10 the value of the thousand's digit is: 748917.
What is number system?A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.Firstly, refer to the image attached for the complete question.
Now,
Given: The value of the digit in the hundreds place in 653,841 is: 800
Now, the following cases arise for the given options:
748,917Value of digit in the thousands place = 8000
=> 1/10 the value of the digit = [tex]\frac{1}{10}(8000) = 800[/tex]
749,817Value of digit in the thousands place = 9000
=> 1/10 the value of the digit = [tex]\frac{1}{10}(9000) = 900[/tex]
784,817Value of digit in the thousands place = 4000
=> 1/10 the value of the digit = [tex]\frac{1}{10}(4000) = 400[/tex]
797,481Value of digit in the thousands place = 7000
=> 1/10 the value of the digit = [tex]\frac{1}{10}(7000) = 700[/tex]
Out of all the options, as shown above, only Option A satisfies the given condition.
Hence, the correct Option is A, i.e., The number that contains digits where the hundreds digit is 1/10 the value of the thousand's digit is: 748917.
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Drag the numbers below to put them in order from least to greatest:
0.1 2.4 -7.9 -3.3 -7.7 -13
Submit Answer
Answer:
-13, -7.9, -7.7, -3.3, 0.1, 2.4
Step-by-step explanation:
Evaluate the expression [8(2)-4^2]+7(4)
The value of expression using PEMDAS rule is 28 .
Given : expression [ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )
To find : value of expression
Calculation : Using V-BODMAS
[ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )
= [ ( 8 * 2 ) - ( 4 * 4 ) ] + ( 7 * 4 )
= [ 16 - ( 4 * 4 ) ] + ( 7 * 4 )
= [ 16 - 16 ] + ( 28 )
= [ 0 ] + ( 28 )
= 28
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please help i’m literally so stressed out
Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $209.67.
•He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.
•He plans to spend some or all of the money he has left to buy new biking outfits
for $37.16 each.
Which inequality can be used to determine x, the maximum number of outfits Luis
can purchase while staying within his budget?
The inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
How to solve inequality?Luis has $420 to spend at a bicycle store for some new gear and biking outfits.
He buys a new bicycle for $209.67.He buys 2 bicycle reflectors for $6.04 each and a pair of bike gloves for $25.77.He plans to spend some or all of the money he has left to buy new biking outfits for $37.16 each.Therefore,
x = maximum number of outfits Luis can purchase while staying within his budget.
Hence, the inequality that can be used to represent the situation is as follows;
209.67 + 6.04(2) + 25.77 + 37.16x ≤ 420
235.44 + 12.08 + 37.16x ≤ 420
247.52 + 37.16x ≤ 420
37.16x ≤ 420 - 247.52
37.16x ≤ 172.48
divide both sides by 37.16
x ≤ 4.64155005382
x ≤ 4
Therefore, the inequality that can be used to determine x, the maximum number of outfits Luis can purchase while staying within his budget is x ≤ 4
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HELP EASY LOOKING FOR ANSWERS TO NUMBER FOUR
Answer:
Step-by-step explanation:
it should be Venus
hmmm. im thinking its venus
If tanθ= 3/4, find sin θ
P= 3
b=4
By using pythagorus therom,
h^2=p^2+b^2
=3^2+4^2
=9+16
=25
h =5
now,
sin(theta)= p÷h
=3÷5
How do you add and subtract radicals? If you could please give me the instructions step by step and with examples, that would be helpful too.
It is for a homework assignment in school, but I wasn't there the day they did it.
p.s I need an explanation right away.
You can add and subtract radicals by ensuring that they have same radical parts.
What's radical?It should be noted that a radical expression is an expression that contains the radical symbol which is ✓.
The necessary steps to add or subtract radicals include:
Identify the radical parts.
Add them together.
If there's unlike radical parts, one will manipulate the parts involved before solving.
Example: Add ✓63 + 5✓7
It should be noted that ✓63 = ✓9 × ✓7 = 3✓7
Therefore, ✓63 + 5✓7 will be:
= 3✓7 + 5✓7
= 8✓7.
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PLEASE HELP... Students are making necklaces of six beads for their mothers. There are
six colours available. There is no clasp, so the necklace can be rotated.
The necklace can also be turned over.
In how many different ways can the students place the beads around the
necklace if exactly two colours are used?
Answer:
Step-by-step explanation:
#1 Number of ways picking 2 from 6 = 6C2 = 15
#2 Arranging them in a circle (consider 1 pair AB)
can be done
1,5 (ABBBBB) or (5,1)
2,4 ( AABBBB) or (4,2)
3,3
1,1 (ABABAB)
all up = 7 ways
#3 = product of #1 and #2 = 15x7 = 105
There are 60 different ways the students can place the beads on the necklace using exactly two colors.
To find the number of different ways the students can place the beads on the necklace using exactly two colors, we need to consider the different arrangements that can be made.
We can first choose the two colors to be used, which can be done in C(6, 2) = 15 ways (where C(n, r) represents the combination of n items taken r at a time).
Once the colors are chosen, we can arrange the beads on the necklace in two ways: either clockwise or counterclockwise.
We can also flip the necklace to get a different arrangement.
Therefore, for each combination of colors, there are 2 x 2 = 4 different arrangements possible.
Thus, the total number of different ways the students can place the beads on the necklace is 15 x 4 = 60.
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find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continuesm8, 0, 8, 0,
The formula for the general term and of the sequence is ±8.
What do we mean by sequence?A sequence in mathematics is an enumerated collection of objects in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the sequence is defined as the number of elements (which could be infinite). Unlike a set, the same elements can appear multiple times in a sequence at different positions, and the order does matter. Formally, a sequence can be defined as a function from natural numbers (the sequence's positions) to the elements at each position. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not is numbered to another set of elements.To find the formula for the given sequence:
Given sequence: 8, 0, 8, 0, So, the formula cen be ±8.+8 to get the terms of odd numbers and -8 to get the terms of even numbers.Therefore, the formula for the general term and of the sequence is ±8.
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help please
15 points
1) d - c is calculated as; -4
2) Simplifying ³/₄ - ²/₅ gives; 7/20
What is the solution to basic arithmetic?
1) We are given;
c = 12 and d = 8. Thus;
d - c is calculated as;
8 - 12 = -4
2) We want to simplify ³/₄ - ²/₅
Factoring out 1/20 gives;
1/20(15 - 8) = 7/20
3) Number of pencils purchased = 888 pencils
Number of pencils in a box = 12
Thus;
Number of boxes purchased = 888/12 = 74 boxes
4) An integer is a whole number (not a fractional number) that can be positive, negative, or zero. The only one that is not an integer here is; 20/6
5) √64 = 8
6) (30 - 4 * 2)/(2 * 2²)
= (30 - 8)/8
= 22/8 = 11/4
7) 11 = x + 19
x = 11 - 19
x = -8
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Which of the following are solutions to the equation below?
Check all that apply.
(4x-1)² = 11
A. x = -√12/4
B. x=-√11+1/4
C. x=√11+1/4
D. x=-√11+1/4
E. x=√12/4
F. x=√11+1/4
Answer:
A.
B.✅
C.✅
D.✅
E.
F.✅
Step-by-step explanation:
[tex](4x-1)² = 11 \\ 4x-1 = \sqrt{11 } \\ 4x = \sqrt{11} + 1 \\ x = \frac{ \sqrt{11} + 1 }{4} [/tex]
*PLS HELP*
Suppose a and b give the populations of two states where a > b. Compare the expressions and tell
which of the given pair is greater or if the expressions are equal.
a-b
5
(select)
b
5
lauren and three of her friends are going to magic springs. the total trip: gas, tickets, and food cost $125.76. how much will each person pay for their fun trip
Answer:
$31.44
Step-by-step explanation:
$125.76 ÷ 4 = $31.44
Lauren $31.44
Friend 1 $31.44
Friend 2 $31.44
Friend 3 $31.44
+ ________
$125.76
3. The graph below shows the number of points that Lebron scored in each of his first
four games of a season.
On average, how many more points per game did Lebron score in the last two games than the
first two games?
Using the mean concept, it is found that LeBron scored 10 more points per game on his last two games than on his first two.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
For his first two games, he scored 20 + 15 = 35 points, hence the mean is:
35/2 = 17.5 points per game.
For his last two games, he scored 25 + 30 = 55 points, hence the mean is:
55/2 = 27.5 points per game.
The difference is:
27.5 - 17.5 = 10.
On average, LeBron scored 10 more points per game on his last two games than on his first two.
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witch equation is true when x=4? A 3X+4=8 B 5X-2=18 C 2X+8=40 D 4X+4=12
Answer:
5X - 2 = 18
Step-by-step explanation:
5 x 4 = 20
20 - 2 = 18
The width of a rectangle is 3 less than its length find the width of the rectangle if its perimeter is 26ft
The width of rectangle is 5 feet.
Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).
Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -
Perimeter = 2 × (length + width)
Keep the values in formula to find the value of width
26 = 2 × (x + x - 3)
Performing addition of variables inside the bracket
26 = 2 × (2x - 3)
Shifting 2 to other side of equation to find the value of x
2x - 3 = [tex]\frac{26}{2}[/tex]
Performing division to find the value of x
2x - 3 = 13
Shifting 3 to other side of equation to find the value of x
2x = 13 + 3
Performing addition to find the value of x
2x = 16
Shifting 2 as denominator to other side of equation to find the value of x
x = [tex]\frac{16}{2}[/tex]
Performing division to find the value of x
x = 8
So, length of rectangle is 8 feet
Width of rectangle = x - 3
Width of rectangle = 8 - 3
Width of rectangle = 5 feet
Hence, the width of rectangle is 5 feet.
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5 less than 2/3 of a number is 19. Find the number
Answer:
the anser in 60
Step-by-step explanation:
Let the original number be x.
According to the question we can write as (2/3)x+20x
On rearranging x−(2/3)x=20
Now taking the L.C.M od 1 and 3 is 3
(3x−2x)/3=20
x/3=20
Again by transposing x=60
So the original number is 60
Grayson bought snacks for his team's practice. He bought a bag of popcorn for $3. 50
and a 5-pack of juice bottles. The total cost before tax was $11. 5. Write and solve an
equation which can be used to determine j, how much each bottle of juice cost.
Please include equation and answer(j= )
If the total cost before tax was $11.5, then the cost of each bottle of juice j= $1.6 which can be found by the equation 5j + $3.50 = $11.50.
The cost of each bottle can be determined by using an algebraic expression.
An algebraic expression can be defined as the use of both numerals and letters in a mathematical equation.
To find the cost of each bottle, an algebraic expression can be given as,
Cost of a 5-pack of juice bottles + Cost of popcorn = Total cost before tax
5j + $3.50 = $11.50
Solving for j,
5j = 11.50 - 3.50
5j = 8
j = 8/5
j = $1.6
Hence, the cost of each bottle from a 5-pack of juice bottles is calculated to be $1.6
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Tyrone makes a scale drawing of his backyard. The scale from the backyard to the drawing is 2 ft to 1 in. The width of the patio on the drawing is 8 in. What is the width of Tyrone's actual patio? Show your work
Answer:
The width of Tyrone's actual patio is 16 feet
Step-by-step explanation:
[tex]\frac{2ft}{1in}[/tex] = [tex]\frac{x}{8}[/tex] If we look at what we know, we see that the scale tells us that 1 inch is proportional to 2 ft. What do we need to multiple 1 inch by to get 8 inches? 8. So, we multiply 2 feet by 8 to get the actual size of the patio which is 16 feet.
Eight families live on abbie's street. she asks each family how many pets they have. abbie's data set is: 0, 0, 1, 1, 2, 2, 2, 5. the modal number of family pets on abbie's street is:__________
Answer:
Step-by-step explanation:
It is asking for the "mode" which is the data element you see the most, therefore it is 2.
PLEASE HELP ME
TEMPERATURE The hottest temperature recorded in Key West, Florida, was 98°F. This was 25°F colder than 3 times the coldest temperature
recorded in Key West. Which equation can be used to find the coldest temperature recorded in Key West? What is the coldest temperature
recorded in Key West?
A) 3T + 2598; 24.3°
O B) T+25=98; 73°
O C) 3T98; 32.7"
OD) 3T-25= 98; 41°
The equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.
What is an equation?The equation represents the relationship of two expressions on either side of the sign.
We have,
The hottest temperature = 98°F.
And that this was 25°F colder than 3 times the coldest temperature.
If we let the coldest temperature be denoted by T
We can write an equation as:
98°F + 25°F = 3T
Subtracting 25° on both sides.
98°F = 3T - 25°F
3T - 25°F = 98°F
The coldest temperature recorded in key west:
3°T - 25°T = 98°F
3°T = 123°F
T = 103°F / 3
T = 41°F
Thus the equation that can be used to find the coldest temperature recorded in Key west is 3T - 25°F = 98°F and the coldest temperature recorded is 41°F.
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I need answer please. I don’t know how to divide and what to divide by.. could someone give me answers to these questions?
Answer:
1) 60 miles per hour (60.00, if rounded)
2) 152 customers per day (150, if rounded)
3) 3.5 meters per second (3.50, if rounded)
4) 1.48 dollars per pound (1.48, if rounded)
5) 0.4825 dollars per pair (0.48, if rounded)
( shown work in screenshots, 1-5; magnify it to see better :D )
The difference of a number p and 1 is greater than 6
Answer: p - 1 > 6, or p > 7
Step-by-step explanation:
We will write an expression from the sentence given.
difference of a number (p) and 1 ➜ p - 1
is greater than ➜ >
The difference of a number p and 1 is greater than 6 ➜ p - 1 > 6
To solve for the possible values of p, we will add 1 to both sides of the equation;
p > 7
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What will be the value of f(k)?
4x² - 6x +7
Answer: f(k)=4k² - 6k +7
Step-by-step explanation:
f(x)=4x² - 6x +7
f(k)=4k² - 6k +7
