Answer:
Y= 2e^(5t)
Step-by-step explanation:
Taking Laplace of the given differential equation:
s^2+3s-10=0
s^2+5s-2s-10=0
s(s+5)-2(s+5) =0
(s-2) (s+5) =0
s=2, s=-5
Hence, the general solution will be:
Y=Ae^(-2t)+ Be^(5t)………………………………(D)
Put t = 0 in equation (D)
Y (0) =A+B
2 =A+B……………………………………… (i)
Now take derivative of (D) with respect to "t", we get:
Y=-2Ae^(-2t)+5Be^(5t) ....................... (E)
Put t = 0 in equation (E) we get:
Y’ (0) = -2A+5B
10 = -2A+5B ……………………………………(ii)
2(i) + (ii) =>
2A+2B=4 .....................(iii)
-2A+5B=10 .................(iv)
Solving (iii) and (iv)
7B=14
B=2
Now put B=2 in (i)
A=2-2
A=0
By putting the values of A and B in equation (D)
Y= 2e^(5t)
Write the equation of the line that goes through the point
(5,8) and is parallel to the x-axis.
Answer:
Y=8
Step-by-step explanation:
If it's a line that is parallel to the x-axis, and you know the equation of a line is y=mx+b, the slope(m) is 0 because the line is not a positive or negative slope (since it's parallel to the x-axis).
So, we now have y=b, where b is the y-intercept. Now, since we know one of its coordinates are (5,8), we know that this line will always stay on y=8 since 8 is the y coordinate of (5,8)
An easy shortcut is if you see the question say parallel to the x-axis, the equation of the line will be y=___; if it says the line is parallel to the y-axis, the equation will be x=___
For 50 points x³+y³+z³=8
Answer:
x = 2
y = - z (for example 2)
Step-by-step explanation:
2³+2³+(-2)³= 8+8-8=8
Answer:
arrg
Step-by-step explanation:
Dr. Gordon has a scale drawing of a building site. The drawing uses the scale 2 in. on the drawing for every 100 ft on the building site. Dr. Gordon marks a 6 in. -by-3.2 in. section of the drawing to show the section she will search. What is the area of the section she will search? Show your work.
Answer:
48000
Step-by-step explanation:
6÷2= 3 in.
3×100= 300 in.
3.2÷2=1.6 in.
1.6×100= 160 in.
A= 160×300= 4800 in.
The required area of the section marked by Dr. Gordon is 48,000 feet².
Given that
Dr. Gordon has a scale drawing of a building site.
The drawing uses the scale 2 in. on the drawing for every 100 ft on the building site.
Dr. Gordon marks a 6 in. -by-3.2 in.
The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
Dr. Gordon marks a 6 in. -by-3.2 in
Length = 6 in
Length= 300 ft (since 2 in = 100 ft)
Width = 3.2 in
Width = 160 ft
Now the required area of the section is = length x width
= 300 * 160
= 48000 feet²
Thus, the required area of the section marked by Dr. Gordon is 48,000 feet².
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Is the relationship between the height of a staircase and the number of steps linear?
Answer:A stair rise is the vertical distance from the top of one tread to the top of the next tread. The total run is the overall horizontal distance traveled by the stringer.
Step-by-step explanation:
(Select all that Apply)
Which of the following is an equation?
O 11=11
6+5=11
6 +5 – 11
06-5=11
the seventh grade winner ran the mile in 5 minutes and 8 seconds. the eight grade winner ran the mile in 4 minutes and 55 seconds. how many more seconds did it take for the seventh grade winner to run a mile?
Answer:
13 seconds more
Step-by-step explanation:
There is a number such that four times the number plus 3 is equal to 19. Find the number.
An equation is formed of two equal expressions. The number is 4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that there is a number such that four times the number plus 3 is equal to 19.
Let the number be M.
Given that there is a number such that four times the number plus 3 is equal to 19. Therefore, We can write it as,
4M + 3 = 19
Now, we can write,
4M + 3 = 19
Subtract 3 on both sides
4M + 3 - 3 = 19 - 3
4M = 16
Divide both sides by 4,
4/4 M = 16/4
M = 4
Thus, the number is 4.
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What is 24.541 divided by 6
Which is not a way to solve 5 ÷ 1/2
Answer:
5 divided by 1/2 = 5/1 times 2/1 = 10
Step-by-step explanation:
Answer:la 2.5
Step-by-step explanation:
Which is the best estimate for the percent equivalent to 3/8?
A.) 26% B.) 27% C.) 37% D.) 38%
Answer:
C.) 37%
Explanation:
To find this out, turn 3/8 into decimal form, (0.375).
Now, turn each percent into standard form. (Also decimal form)
26% = 0.26, 27% = 0.27, 37% = 0.37, and 38% = 0.38.
The decimal closest to 0.375 is 37%.
Hope this helped! ♥♥
Mark Me as Brainliest Please! :3
Answer:
D.) 38%
Step-by-step explanation:
Convert the fraction into a decimal:
[tex]\frac{3}{8}=0.375[/tex]
Convert the decimal into a percent:
[tex]0.375*100=37.5[/tex]
0.375 = 37.5%
Round the percent:
37.5% ≈ 38%
Option D is the best answer.
Hope this helps.
(72- 12 / 3 of 2) + (18 - 6) ÷4
Answer:
I believe the answer is 72.
Gutina finds a limited edition shirt from her favorite singer. It was originally $52. Then, she got a discount, 30%. what is the price now?
Answer:
$36.40
Step-by-step explanation:
Purchase Price:
$52
Discount:
(52 x 30)/100 = $15.60
Final Price:
52 - 15.60 = $36.40
$36.40 is the answer. Hope this helps!
Answer:
$36.40
Step-by-step explanation:
Sorry if i'm wrong hope this helps
What are Three ways to name EF
When did the United States first establish its measuring system, and who was responsible for
picking the system?
Answer:
1975 Thomas Jefferson
Step-by-step explanation:
rational or irrational 0.135135135135
Answer: it is a rational
Step-by-step explanation:
solve for r
8(-3r-5)>104
Answer:
r<-6
Step-by-step explanation:
8(-3r-5)>104
-24r-40>104
-24r>144
r<144÷-24 (the sign switched because we divided by a negative number)
r<-6
A bag contain 6 tiles labeled B,C,D,E,F. And G. One tile will be randomly picked. What is the probability of picking a letter that is a vowel?
N(S)=6
P(vowel letter)= N(vowel letter)÷N(S)
= 1/6
Answer:1/6
Step-by-step explanation:f
A group of 23 friends gets together to play a sport. First, people must be divided into teams. Each teams has to have exaclty 4 players, and no one can be on more than one team. How many teams can they make?
Answer:
5
Step-by-step explanation:
Evaluate81−−√4 help ......................
Answer:
=81e^2lva^2ut-2
Step-by-step explanation:
what is the answer to d = -f + 2/3a
Answer:
For f = -d +2/3a
Step-by-step explanation:
12 + 4 - 8 / 2 * 3 workings pls
Answer:
4
Step-by-step explanation:
8/2=4
4*3=12
12+4=16
16-12=4
7/5 mile / 2/3 hour worked out please
Steps to solve:
7/5 ÷ 2/3
~Dot
7/5 * 2/3
~Flip
7/5 * 3/2
~Multiply
21/10
Best of Luck!
Answer:
21/10 = 2.1 mile/hour
Step-by-step explanation:
(a/b) ÷ (c/d) = (a*d) ÷ (b*c)
then:
(7/5) ÷ (2/3) = (7*3) ÷ (5*2) = 21/10 mile/hour
a triangle window has area 24 square feet and height six feet. what is its base? define variable, and set up and solve an equation to answer this.
Answer:
6*y/2=24
24*2=48
48/6=8
y=8
Step-by-step explanation:
The equation will be 24 = [tex]\frac{1}{2}[/tex] × b × 6 value of base will be b = 8 ft .
A triangle has area 24 square ft. and height 6 ft.
What will be its base. Find an equation also.
What is the formula of area of triangle ?
Area of triangle is ; Area = [tex]\frac{1}{2}[/tex] × b × h
∵ The equation of area of triangle will be ;
Area = A = [tex]\frac{1}{2}[/tex] × b × h ----- - --- --- --- Equation 1
A = 24 = [tex]\frac{1}{2}[/tex] × b × 6
⇒ b = [tex]\frac{24 * 2}{6}[/tex] = [tex]\frac{48}{6}[/tex] = 8
⇒ b = 8 ft.
Thus , the equation will be 24 = [tex]\frac{1}{2}[/tex] × b × 6 value of base will be b = 8 ft .
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Estimate then find the product of 4x979
Answer:
Around 4000[since 979 close to 1000]
Step-by-step explanation:
4x979
=>3916
Use the ogive to approximate (a) the number in the sample, (b) the location of the greatest increase in frequency.
Answer:
Step-by-step explanation:
A). Number of samples given in the ogive = Number of points given n the graph
Number of points plotted on the graph = 16
Therefore, number of samples given = 16
B). Frequency at a point where weight of the pumpkins is 23.5 = 10
Frequency at a point where weight of the pumpkin is 24.5 = 23
Increase in frequency = 23 - 10 = 13
None other points have the increase more than the given points.
Location of the greatest increase in the frequency is between the weights 23.5 - 24.5 pounds.
The number of samples is 16, and the location of greatest increase in frequency is 23.5 to 24.5.
We are provided with an ogive curve. In the x-axis, we have weight in pounds and y-axis represents frequency.
(a).
Now, the number of points on the ogive represents the number of sample.
So, the number of points on the curve is 16 which is also the number of samples.
(b).
The greatest increase in frequency is represented in the range 23.5 to 24.5.
The greatest hike in frequency is about 10.
Therefore, the number of samples is 16, and the location of greatest increase in frequency is 23.5 to 24.5.
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Question 3 (2 points)
Using the statement below, determine the hypothesis and conclusion,
If two integers are even, then their sum is even
Column A
Column B
1.
Hypothesis
a. If two integers are even
2.
Conclusion
b. then their sum is even
c. two integers are even
d. their sum is even
Answer:
Hypothesis
a. If two integers are even
Conclusion
b. then their sum is even
Step-by-step explanation:
We divide the statement into two parts . The first part is true only when the second is also true. The only way we can reject the hypothesis is that the conclusion is false.
In the statement "If two integers are even, then their sum is even" the part "If two integers are even" would be considered true or false on the basis of "then their sum is even" validity. So if the "then their sum is even" (conclusion ) Part is proved then the "If two integers are even" ( hypothesis) is also true.
Hence the hypothesis is
a. If two integers are even
and
Conclusion is
b. then their sum is even
Solve for x.
5x – 7 = 8x – 4
Answer:
x =-1
Step-by-step explanation:
[tex]5x- 7 = 8x - 4\\\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\5x-7+7=8x-4+7\\\\Simplify\\5x=8x+3\\\\\mathrm{Subtract\:}8x\mathrm{\:from\:both\:sides}\\5x-8x=8x+3-8x\\\\Simplify\\-3x =3\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{3}{-3}\\\\Simplify\\x=-1[/tex]
Answer:
x = -1
Step-by-step explanation:
[tex]5x - 7 = 8x - 4\\[/tex]
Collect like terms and simplify
[tex]5x-8x =-4+7\\-3x =3[/tex]
Divide both sides of the equation by -3
[tex]\frac{-3x}{-3} = \frac{3}{-3} \\\\x =-1[/tex]
The sum of three consecutive numbers is 600. What is the least of these three numbers?
Answer:
199
Step-by-step explanation:
So we have three consecutive numbers that totals 600 when added.
Let's let the first number be n.
This means that the next number is (n+1), and the subsequent number is (n+2).
This totals 600. In other words:
[tex](n)+(n+1)+(n+2)=600[/tex]
To solve for the integers, solve for n.
Combine like terms:
[tex]3n+3=600[/tex]
Subtract 3 from both sides:
[tex]3n=597[/tex]
Divide both sides by 3:
[tex]n=199[/tex]
So, the first integer is 199.
So our sequence is: 199, 200, 201.
So, the least of the three is 199.
And we're done!
Answer:
199 200 201
Step-by-step explanation:
199+200+201= 600
write an equation to represent the relationship, and find the amount of peanut butter used to make 25 cracker packages. the table is peanut butter (tbsp) 1/2,5/8,3/4,7/8, the bottom is cracker packages 2,2 1/2,3,3 1/2.
We are given 4 points.
[tex](\frac{1}{2},2)[/tex]
[tex](\frac{5}{8},\frac{5}{2})[/tex]
[tex](\frac{3}{4},3)[/tex]
[tex](\frac{7}{8},\frac{7}{2})[/tex]
Using this, we can make an equation.
[tex]y=4x[/tex]
I got [tex]m=4[/tex] by using the slope formula.
[tex]m=\frac{2.5-2}{0.625-0.5}[/tex]
[tex]m=\frac{0.5}{0.125}[/tex]
[tex]m=4[/tex]
So the equation we have is [tex]y=4x[/tex]
Now, we can solve for how much peanut butter is used to make 25 packages by plugging in 25 for [tex]y[/tex], which is the number of cracker packages.
[tex]25=4x[/tex]
[tex]x=\frac{25}{4}[/tex]
We need to use [tex]\frac{25}{4}[/tex] teaspoons of peanut butter to make 25 packages of crackers.
Hope this helps.
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Five people are tossing a coin in turn and agree that the first one to get a head wins. What's the probability that the first person who tosses the coin wins the game? a. 8/15 b. 16/31 c. 1/2 d. 1/5