Answer:
[A] 1406
Step-by-step explanation:
To see which is NOT divisible by 8 all we have to do is divide each answer choice by 8.
Not divisible means that the answer is a whole number (Not a decimal).
[A] 1406/8 = 175.75
[B] 1488/8 = 186
[C] 3608/8 = 451
[D] 5016/8 = 627
As we can see, the only one that is not divisible by 8 is [A] 1406.
RevyBreeze
What is the value of the expression below when w = 6?
Answer:
7w+6
Submit Answer
the value of expression is 48 at w = 6.
What is an expression?Expression in math's is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given, an expression 7w + 6,
Since the value of w is given 6
Thus,
The value of Expression = 7 * 6 + 6
The value of Expression = 48
Therefore, the value of expression is 48 at w = 6.
Learn more about expression here:
https://brainly.com/question/23246712
#SPJ1
estimate the following sum: 2 1/3 + 5 5/16 + 2/7=
The of sum of the fraction 2 1/3 + 5 5/16 + 2/7 is 7 313/336
How to estimate the sum of fractions?
Fractions are represented as numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing
We want the of sum 2 1/3 + 5 5/16 + 2/7 =
For convenience sake, we can convert the mixed fractions to improper fractions. That is:
2 1/3 = 7/3
5 5/16 = 85/16
2 1/3 + 5 5/16 + 2/7 = 7/3 + 85/16 + 2/7
The LCM of 3, 16 and 7 is 336
= (7*112 + 85*21 + 2*48)/336
= (784 + 1785 + 96)/336
= 2665/336
= 7 313/336
Learn more about fractions on:
brainly.com/question/11562149
#SPJ1
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 3 comma 7
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The y-intercept is at (27/2 ,9) in the Slope Intercept Form .
What is a line's Slope Intercept Form?
A line with m as its slope, m as its y-intercept, and c as its coefficient makes up the graph of the linear equation y = mx + c. The values of m and c in this version of the linear equation known as the slope-intercept form are real numbers.
The graph of the line passes through (0,9) and (3,7) .
Slope of the line = (7 - 9)÷(3 - 0) = -2/3
Hence the line will have the equation:
y - 9 = -2/3 ( x - 0 )
or, y - 9 = -2x/3
or, 3y - 27 = -2x
2x + 3y = 27
Now from the real world situation at y = 0, x = 27/2
and at x = 0, y = 9
Hence the y-intercept is at (27/2 ,9)
Learn more about the Slope Intercept Form
brainly.com/question/29146348
#SPJ1
What is the name of the segment inside the large triangle?
Answer:
Altitude: Segment from a vertex of a triangle that is perpendicular to the opposite side. This segment may be inside the triangle, on the triangle, or outside the triangle. Pictured below are the altitudes (represented as black segments) of acute, right, and obtuse triangles.
Step-by-step explanation:
Draw a rough sketch of the function (x-1)(x+2)(x+5)
Answer:
Step-by-step explanation:
Zeroes of a Function:The main idea you need to understand here is multiplicity, zeroes, and end behavior.
If a function has an odd degree that means that the end behaviors will be opposite so if on the right side the polynomial is going up, then on then on the left side it's going down and vice versa.
As for multiplicity, if the multiplicity or exponent of a zero is odd then it crosses the x-axis otherwise it has a turning point meaning it touches the x-axis and just turns around.
The last thing to understand is if the polynomial has a positive leading coefficient then the graph will be going up on the right side otherwise it will be going down.
We're given the function: f(x) = (x-1)(x+2)(x+5) and if you set each factor equal to zero, you can solve for the zeroes getting: x = 1, --2, and -5 as zeroes. Since the coefficients inside the factors are all positive when we multiply this out, we would get a positive leading coefficient and since the exponent of them is all one, the degree would be 3 when multiplying out the 3 binomials.
So on the right side it's going up, the left side it's going down (since odd degree) and at each zero it crosses the x-axis since they all have an odd multiplicity. This allows us to draw a rough sketch which I have provided using paint.,
You are a marketing manager and need to summarize recent spending on advertisements. You have placed 2 small advertisements that cost $325 each, 5 WILL FAST!! MARK BRAINLYIST IF RIGHT ANSWER
medium-sized advertisements that cost $750 each, and 12 large advertisements that cost $1,300 each. Which expression shows how to calculate the mean cost per advertisement?
A: 325 + 750 + 1,300 / 3
B: 325 + 750 + 1,300 / 19
C: 2 X 325 + 5 X 750 + 12 X 1,300 / 3
D: 2 X 325 + 5 X 750 + 12 X 1.300 / 120
The required expression used to calculate the mean cost per advertisement is 325 + 750 + 1,300 / 3. Option A is correct.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
Here,
Mean cost of each type of advertisement
= the sum of the cost of small. medium and large advertisement / 3
= 325 + 750 + 1,300 / 3
Thus, the required expression used to calculate the mean cost per advertisement is 325 + 750 + 1,300 / 3. Option A is correct.
Learn more about mean here:
https://brainly.com/question/15397049
#SPJ1
7. A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Can such a system have a unique solution? Explain. Choices: a. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If there is a free variable, the solution set contains a unique solution. b. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains infinitely many solutions. If the linear system is inconsistent, there is no solution. c. Yes, it can have a unique solution. Because there are more equations than variables, there are no free variables. If the system is consistent and there are no free variables, the solution set contains a unique solution. If the system is inconsistent, there is no solution. d. Yes, it can have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains either a unique solution or infinitely many solutions. If the linear system is inconsistent, there is no solution.
The correct answer is b. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains infinitely many solutions. If the linear system is inconsistent, there is no solution.
A linear system is a set of linear equations that can be expressed in the form Ax = b, where A is a matrix of coefficients, x is a vector of unknowns, and b is a vector of constants. Linear systems can be solved using a variety of methods, such as matrix inversion, Gaussian elimination, or the LU decomposition. In addition, linear systems can be used to model a variety of real-world problems, such as linear programming, optimization problems, and electrical networks.
Learn more about linear systems:
https://brainly.com/question/2030026
#SPJ4
Determine whether the solution of each equation is positive or negative. Select Positive or Negative for each solution. -9x=36 -36 - 12 = -7b -8.2d 28.1 = 3.6d 2 (4t-5) = 6t - 18 Positive Positive Positive Positive O Negative ONegative O Negative O Negative
The solutions of the given equations are grouped into negative or positive as follows:
-9x=36= negative
-3b-12=-7b = positive
-8.2d+28.1=3.6d = positive
How to calculate the positive and negative equations?For -9x=36;The final result is a negative result because of the following;
-9x= 36
X= -36/9
X= -4
For -3b-12=-7b;The final result is a positive result because of the following;
-3b-12=-7b
-3b+7b =12
4b=12
b= 12/4= 3
-8.2d+28.1=3.6d;The final result is a positive result because of the following;
-8.2d+28.1=3.6d
28.1= 3.6d+8.2d
28.1 = 11.8d
28.1/11.8 = d
d= 2.4
Learn more about division here:
https://brainly.com/question/25289437
#SPJ1
A video game system and several games are sold for $668. The cost of the games is 3 times as much as the cost of the system. Find the cost of the
system and the cost of the games.
Cost of the video game system:
URGENT
the cost of the system and the cost of the games is: $501. This can be solved using the concept of equation.
What is an equation?The connection between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
The total cost of the video game system and the several game = $668
Let, the cost of several game = x and
The cost of video game system = 3x
To find the cost of the system and the games
According to the problem,
or, x + 3x = 668
or, 4x = 668
or, x = $167
Hence, the cost of several game = $167 and
The cost of video game system = $3 × 167 = $501
To know more about equation refer to:
brainly.com/question/22688504
#SPJ1
The perimeter of a rectangle window is 352 cm. If the length of the window is 95 cm, what is its width? ADD WORK/STEPS!!
The width of the rectangle is 81 cm.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Perimeter = 352 cm
Length = 95 cm
Width = W
Now,
Perimeter = 2 (Length + Width)
352 = 2 (95 + W)
176 = 95 + W
W = 176 - 95
W = 81 cm
Thus,
The width is 81 cm.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
{100 points} Shown is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work W is done by the force in moving an object a distance of 8 m?
W = _______ J
The work done by the force in moving an object a distance of 8 m is; 144 J
How to solve a Force Distance Graph?A force-displacement graph will have force (in N) on the vertical axis and displacement (in m) on the horizontal axis. The area of the graph is = Fs. This quantity represents the work done on the object.
The area of the given graph is gotten by using the area of a trapezium which is;
Area = ¹/₂(sum of parallel sides) * height
Plugging in the relevant values gives;
Area = ¹/₂(8 + 4) * 24
Area = 144 J
This area represents the work done
Read more about Force Distance Graph at; https://brainly.com/question/13743674
#SPJ1
Simple Question what is 100 plus 100
Answer: 200 because 100 plus 100 equal 200
PLEASE ANSWER
The perimeter of the rectangle below is 120 units. Find the length of side VY .
Write your answer without variables.
The length of side VY is 25.
What is a regular figure and its perimeter?A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).
Suppose that length of each side of that figure be of u units, then we have the perimeter as:
P=u+u+...+u (n times) = n xu
units.
Given;
The perimeter of the rectangle below is 120 units
The two sides of rectangle are 2y+3 and3y+2
Now,
2l+2b=120
2(2y+3)+2(3y+2)=120
4y+6+6y+4=120
10y+10=120
y+1=12
y=11
VY=2y+3
VY=2*11+3
VY=25
Therefore, the length according to given perimeter will be 25units.
Learn more about perimeter here:
https://brainly.com/question/10466285
#SPJ1
Blake flips a fair coin and stops flipping once he gets a head. He gets the minimum of $16 and $2 n, where n is the total number of Blake's flips. For example, if Blake flips a head on the first try, then n=1. What is the fair value of this game?
If Blake flips a fair coin , and stops flipping once he get head , then the fair value of the game is 7 .
The Fair Value /Expected value is a mathematical definition that refers to the average outcome of a random process, such as a game or an investment. It is calculated by taking into account all the possible outcomes of the process, weighting each outcome by its probability of occurrence, and summing up the results.
We know that every coin flip has a equal chance of being heads or tails.
So, the probability of getting a head on each flip = 0.5 ;
The expected value is calculated as :
⇒ P(n=1)×(2¹) + P(n=2)×(2²) + P(n=3)×(2³) + P(n=4)×(2⁴) + P(n=5)×(2⁵) + P(n≥6)×(2⁶) ;
⇒ (0.5¹)×2 + (0.5²)×4 + (0.5³)×8 + (0.5⁴)×16 + (0.5⁵)×32 + (1-0.5-0.25-0.125-0.0625 - 0.03125)×64 ;
⇒ 5 + 0.03125 × 64 ;
⇒ 5 + 2
⇒ 7
Therefore , The Fair Value of this game is 7 .
The given question is incomplete , the complete question is
Blake flips a fair coin and stops flipping once he gets a head. He gets the minimum of $16 and $2ⁿ , where n is the total number of Blake's flips. For example, if Blake flips a head on the first try, then n=1. What is the fair value of this game?
Learn more about Coin Flip here
https://brainly.com/question/30044725
#SPJ4
In radiation protection, which of the following is a measure of the probabilistic health effect on an individual as a result of an intake of radioactive material into the body?
A. TEDE
B. Gyt
C. Gya
D. CEDE
The correct answer is A. TEDE, which stands for Total Effective Dose Equivalent.
This is a measure of the effective dose equivalent to an individual resulting from an intake of radioactive material. It takes into account the type of material ingested and the radiation dose received.
It takes into account the type of material ingested and the radiation dose received. TEDE is generally used in radiation protection to estimate the probabilistic health effect on an individual as a result of an intake of radioactive material.
Learn more about TEDE:
https://brainly.com/question/30261101
#SPJ4
Question 3 Mutiple Choice Worth 4 points)
(05.02 MC)
Two families went to a baseball game. The first family bought 3 pretzels and 5 sodas, which totaled $23. The second family bought 4 pretzels and 6 sodas, which totaled $28. How much did one soda cost?
O $3
O$4
O $5
O $6
Answer:
B) $4--------------------------------
Let the cost of a pretzel be p and cost of a soda be s.
The first family bought 3 pretzels and 5 sodas, which totaled $23:
3p + 5s = 23The second family bought 4 pretzels and 6 sodas, which totaled $28:
4p + 6s = 28Divide the second equation by 4 to get:
p + 1.5s = 7p = 7 - 1.5sSubstitute this into first equation and solve for s:
3(7 - 1.5s) + 5s = 2321 - 4.5s + 5s = 230.5s = 23 - 210.5s = 2s = 2/0.5s = 4Cost of a soda is $4, this is option B.
Answer:
B is the answer
Step-by-step explanation:
I took the test and I got 100 percent.
please answer quickly, question from ixl.
Answer:
5x>20 and 4
Step-by-step explanation:
x is how many packs Dave bought
5x>20 because he went over the 20 dollar budget
5(4) = 20
Buying 4 packs of cards wouldn't go above the budget, so he must've bought more than 4 packs of cards.
Which of the following is a factor of 9x^2+21+10
Answer: 3x+5
Step-by-step explanation:
trust me i had that question for home work
Calculate the average speed of a cyclist who travels 30 km in 3 hr
Given:-
[tex] \rm{Distance= \bold{ 30km}}[/tex][tex] \: [/tex]
[tex] \rm{Time = \bold{3hr}}[/tex][tex] \: [/tex]
To Find:-
[tex] \rm{Speed \: of \: a \: cyclist = ?}[/tex][tex] \: [/tex]
By using formula:-
[tex] \boxed{ \bold{ \rm{ \color{skyblue}Speed = \frac{Distance}{Time} }}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{Speed = \frac{Distance}{time} }\\ = \rm{\cancel\frac{30}{3}} \\ \: \:\: \: \: \: \: \: \: \underline {\boxed{\rm \red{= 10km/hr}}}[/tex]
[tex] \: [/tex]
hope it helps!:)
The average speed of the cyclist is 10 km/hr.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
As per the question,
Given that the distance is 30 km and the time is 3 hours.
To calculate the average speed of a cyclist, we can use the formula:
average speed = distance/time
Substitute the given values in the above formula,
average speed = 30 km / 3 hr
average speed = 10 km/hr
Therefore, the average speed of the cyclist is 10 km/hr.
Learn more about the average speed here :
brainly.com/question/12322912
#SPJ2
Can someone help me please
I have to do this maze for Geometry and it’s due tomorrow.
X has to equal 11 and all I have to work with is “the measure of angle 2 = 3x+5” and a random 64.
These are isosceles triangles. I don’t understand.
Help :’)
The measure of angle 2 is 38° and the value of x is 11
How to find the measure of angle 2?Geometry is a branch of mathematics concerned with the study of space, shapes, sizes, and positions of objects. It covers topics such as points, lines, angles, surfaces, and solids.
Check the attached image for labelling. From the figure:
u = 64° (base angles of an isosceles triangle are equal)
t = 180 - 64 - 64 = 52° (Sum of angles in a triangle)
y = 90 - t
y = 90 -52 = 38°
y = m∠2 (base angles of an isosceles triangle are equal)
m∠2 = 38°
m∠2 = 3x + 5
3x + 5 = 38°
3x = 38 - 5
3x = 33
x = 33/3
x = 11
Therefore, the value of x is 11
Learn more about geometry on:
brainly.com/question/11435541
#SPJ1
qualitive or quantitive .tHE NUMBER OF CARS SOLD by a car dealer last month
Help Please I have 7 of these to do within 30 minutes and i dont get them
Answer:
angle JKL is 22°
Step-by-step explanation:
You want the measure of exterior angle JKL represented by (5x-3)°, given that the remote interior angles of ∆IJK are I = (2x +8)° and J = (x -1)°.
Exterior angleThe exterior angle is equal to the sum of the remote interior angles:
angle JKL = angle I + angle J
5x -3 = (2x +8) +(x -1)
5x -3 = 3x +7 . . . . . . . . . simplify
2x = 10 . . . . . . . . . . . add 3-3x
x = 5 . . . . . . . divide by 2
5x -3 = 5(5) -3 = 22 . . . . . degrees
Angle JKL is 22 degrees.
__
Additional comment
It is helpful to draw a figure. The attached figure is not to scale, but the angle measures are appropriately labeled.
The unlabeled interior angle at K is supplementary to the labeled exterior angle there. That same interior angle is also supplementary to the sum of the other two interior angles, since the sum of all the angles is 180°. Two angles supplementary to the same angle are congruent. This means the exterior angle JKL is congruent to the sum of the two marked interior angles. It's a simple relation, easy to derive, and useful to remember.
<95141404393>
Question content area top
Part 1
A car moving at a constant speed passed a timing device at tequals
0.
After 9
seconds, the car has traveled 828
ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
Then the linear function rule to model the distance the car has traveled in any number of seconds will be d = 92t.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Times
s = d/t
d = st
The value of 's' is given as,
s = 828 / 9
s = 92 feet per second
Then the linear function rule to model the distance the car has traveled in any number of seconds will be d = 92t.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ1
Graham volunteers each Saturday at a veterinarian's office.
He spends 3 hours cleaning.
He walks dogs for 15 minutes (0.25 hours) each.
• He walks 1 dog at a time.
He volunteers no more than a total of 5 hours each Saturday.
The inequality 3+0.25x ≤5 describes the situation, where x represents the number of dogs he walks. Which of the following is a
reasonable solution to this inequality?
A. 7
B. 11
C. 9
D. -5
Cleatus owns a large number of goats and relies on them to make his living. He
wakes up one morning to find half of his flock dead in the field. Cleatus cannot see
any evidence of a predator and is at a loss as to what happened to his goats Local
scientist Alcmaeon asks if he can take a few of the dead goats with him to attempt to
figure it out. How will Alcmaeon MOST likely attempt to solve this mystery of sudden
goat death that decimated Cleatus's flock?
The most likely way Alcmaeon will try to solve this mystery about the sudden death of the goats would be by taking blood samples to analyze a possible disease or epidemic in the goat herd.
What would be the best option to decipher the cause of death of the Cleatus goats?The best option to decipher the cause of death of the Cleatus goats is to take a sample from one of the goats to do an autopsy and identify the possible cause of death. Additionally, you can take blood samples to analyze a possible disease or infection that has caused the death of the sheep.
This would be the most effective way of detecting a possible cause of death as it allows Cleatus to know if the goats left alive are sick or at risk of dying from a disease.
Learn more about goats in: https://brainly.com/question/29409151
#SPJ1
In Exercises 1-4, determine if the system has a nontrivial solution. Try to use as few row operations as possible. (1). 2 x1 - 5 x2 + 8 x3 = 0 -2 x1 - 7 x2 + x3 = 0 4 x1 - 2 x2 + 7 x3 = 0 (2). x1- 3 x2 + 7 x3 = 0 -2 x1 - x2 + 4 x3 = 0 x1 - 2 x2 + 9 x3 = 0 (3). -3 x1 - 5 x2 + 7 x3 = 0 -6 x1 - 7 x2 + x3 = 0 (4). -5 x1 - 7 x2 + 9 x3 = 0 x1 - 2 x2 + 6 x3 = 0
(1). 2 x1 - 5 x2 + 8 x3 = 0
-2 x1 - 7 x2 + x3 = 0
4 x1 - 2 x2 + 7 x3 = 0
Add the first and second equation:
0 x1 - 12 x2 + 9 x3 = 0
Add the third equation:
4 x1 - 2 x2 + 7 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(2). x1- 3 x2 + 7 x3 = 0
-2 x1 - x2 + 4 x3 = 0
x1 - 2 x2 + 9 x3 = 0
Add the first and second equation:
-x1 - 4 x2 + 11 x3 = 0
Add the third equation:
0 x1 - 6 x2 + 16 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(3). -3 x1 - 5 x2 + 7 x3 = 0
-6 x1 - 7 x2 + x3 = 0
Add the first and second equation:
-9 x1 - 12 x2 + 8 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(4). -5 x1 - 7 x2 + 9 x3 = 0
x1 - 2 x2 + 6 x3 = 0
Add the two equations:
-4 x1 - 5 x2 + 15 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
To learn more about nontrivial solution:
https://brainly.com/question/26574408
#SPJ4
What is the solution to the square root equation?
x+3 = √2x−1 +5
Answer: x - √2x = 1
Step-by-step explanation:
jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. if m represents the number of ounces of mango juice in the blend and p represents the number of ounces of papaya juice in the blend, which of the following inequalities represents this scenario? A m - p< 32 m - p2 32 C m+p<32 D m+p2 32
jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. So, m + p ≤ 32 inequalities represents this scenario.
What is an inequality?A relationship that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. Less than, larger than, less than or equal to, and more than or equal to are the four fundamental inequalities. A mathematical connection between two expressions is known as an inequality, and it is shown using one of the following: "≤" , "≥" , "<" and ">".
Given that,
Number of mango = m
Number of papaya = p
The limit of juices should be less than or equal to 32 ounces
Thus, the sum of mass of mangoes and papaya should be less than or equal to 32 ounces.
So, m + p ≤ 32
To know more about inequalities refer to:
https://brainly.com/question/28230245
#SPJ1
The complete question is as follows:
Solve the given initial-value problem. dy + 2(t + 1)y2 = 0, y(0) dt 1 15 1 y(t) = 2 + 2t + 15 x Give the largest interval I on which the solution is defined. (Enter your answer using interval notation.)
The Largest interval in which the solution of the differential equation is defined is (-5, 3).
dy/dt + 2(t + 1)y² = 0 and y(0) = -1/15
Now, dy/dt + 2(t + 1)y² = 0
dy/dt = -2(t + 1)y²
By separating variables
dy/y² = -2(t + 1) dt
Integrating both sides
∫dy/y² = -∫(t + 1) dt
-1/y = -(t²+2t) + c
y(t) = /(t²+2t - c)
We know, y(0) = -1/15
So, -1/15 = 1/(0+0-c)
c = 15
∴ y(t) = 1/(t² + 2t - 15)
Now, y(t) is defined if t² + 2t - 15 ≠ 0
Let t² + 5t - 3t - 15 = 0
(t + 5)(t - 3) = 0
t = -5, 3
So, the intervals are (-∞ , -5), (-5, 3) and (3, ∞)
As t = 0 lies in between (-5, 3) hence the interval in which the solution is defined is (-5, 3)
To learn more about differential equations here:
brainly.com/question/25731911
#SPJ4
Describe at least two similarities between constructing a perpendicular line through a point on a line and constructing a perpendicular through a point off a line
Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.
What is the equation of a perpendicular line?Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The following are the two similarities between drawing a perpendicular line through a point on a line and drawing one through a point of a line:
Both of these procedures start by drawing two arcs to the sides of the point. They both have six angles.Both of these procedures start by drawing two arcs to the sides of the point and they both have six angles.
More about the equation of a perpendicular line link is given below.
https://brainly.com/question/14200719
#SPJ1
