Answers
The correct option is the root of auxiliary equation are 0 and6
What is differential equation?A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.General Differential Equations. Consider the equation y′=3x2, which is an example of a differential equation because it includes a derivative. There is a relationship between the variables x and y:y is an unknown function of x. Furthermore, the left-hand side of the equation is the derivative of y.Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. Also, in medical terms, they are used to check the growth of diseases in graphical representationTo learn more about differential equation refers to:
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Related Questions
A diver begins at 90 feet below sea level. She descends at a steady rate of 6 feet per minute for 6 minutes. Then, she ascends 20 feet. This expression shows her current depth in feet.
Negative 90 minus 6 (6) + 20
What is her current depth?
Negative 596 feet
Negative 556 feet
Negative 146 feet
Negative 106 feet
Answers
Step by step
Diver is at -90
She descends at -6’ per minute x 6 minutes
So -90 and -36 = -126 ft below sea level
Now she ascends up + 20 feet
So -126 + 20 = -106 current depth
Problem solved
The graph below represents which of the following functions?
-12
-10
OA.
OB.
O C.
D.
4
F(x) =
[[|-*|× <1}
(x+4×21}
F(x) =
F(x) =
F(x) =
{/4-x²|x<2}
x2 2f
X
14-x²|x> 21
x x≤ 2}
2}
XS
{|-*² |× > 3)
(x+4× ≤3)
10
12
C
Answers
Answer: B
Step-by-step explanation:
The parabola has an open hole at x=2, and the line has a closed hole at x=2.
This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].
This eliminates everything except for B.
Simplify the following fractions.
Please Slove this 2 question
Answers
Answer:
b)14/3 or 4 2/3 C) 256/15 or 14 1/15
Step-by-step explanation:
In the second fraction, the "of" means to multiply
Answer:
#b
[tex] \displaystyle{ \pmb{ \pink{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }}}[/tex]
[tex]\frak{SOLUTION:}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex]\displaystyle{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }[/tex]
Convert mixed fractions into improper fractions:[tex] = \displaystyle{ \frac{16}{5} \times \frac{7}{2} \div \frac{12}{5} }[/tex]
[tex]=\displaystyle{ \frac{16}{5} \times \frac{7}{2} \times \frac{5}{12} \frak{(Performing division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel{16} \: {}^{2} \times 7 \times \cancel5}{ \cancel5 \times \cancel 2 \times 12} }[/tex]
[tex]\displaystyle{ = \frac{8 \times 7}{12} }[/tex]
[tex] =\displaystyle{} \frac{56}{12} [/tex]
[tex]\displaystyle{ = \frac{ \cancel2 \times \cancel2 \times 2 \times 7}{ \cancel2 \times \cancel 2 \times 3} }[/tex]
[tex]\displaystyle{ = \frac{14}{3} \frak {\: or} \: 4 \frac{2}{3} } [/tex]
#c
[tex]\displaystyle{\pmb{ \pink{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }}}[/tex]
[tex]\displaystyle{ \frak{SOLUTION:}}[/tex]
[tex]\displaystyle \frak{Here,}[/tex]
[tex] \displaystyle{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \left( \frac{1}{2} \times \frac{16}{5} \right)\frak{(Performing "of")}}[/tex]
[tex] = \displaystyle{ \frac{8}{3} \div \left( \frac{1 \times \cancel{16} \: {}^{8} }{ \cancel2 \times 5} \right) }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \div \frac{8}{5} }[/tex]
[tex]\displaystyle{ = \frac{8}{3} \times \frac{5}{8} \frak{(Performing \: division)} }[/tex]
[tex]\displaystyle{ = \frac{ \cancel8}{3} \times \frac{5}{ \cancel8} }[/tex]
[tex] = \displaystyle{ \frac{5}{3} \frak{ \: or \: }1 \frac{2}{3} }[/tex]
Answered by :
[tex]\frak{\pink{seolleaphrodite}}[/tex]
Which is the only state that uses to calculate its area
Answers
Answer:
The answer is circle.
Step-by-step explanation:
For all the rest of the shapes, we use certain base x height formulas. Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula [tex]\pi r^{2}[/tex] where r= radius.
Select the correct locations on the graph.
Select the lines that represent functions.
Answers
Answer:
(I've marked the lines considered functions with a check mark)
Step-by-step explanation:
Give the opposite of each number. a. 3 b. –9 c. –5 d. 12 Solve each of the following problems. a. 9 + (–6) = ? b. (–5) + 8 = ? c. (–12) + (–6) = ? d. 10 – (–8) = ? e. (–4) – (+2) = ? f. –9 – (–5) = ? Solve each problem. Be sure to include the correct sign in your answer. a. 8 × 3 = ? b. –7 × 5 = ? c. –6 × (–9) = ? d. 8 ÷ (–2) = ? e. –24 ÷ (–3) = ? f. –36 ÷ 6 = ?
Answers
Answer:
Give the opposite of each number : a. -3; b. 9; c. 5; d. -12
Solve each of the following problems : a. 3; b. 3; c. -18; d. 18; e. -6; f. -4
Solve each problem. Be sure to include the correct sign in your answer :
a. 24; b. -35; c. 54; d. -4; e. 8; f. -6
Answer:
Step-by-step explanation:
1.a. –3
b. 9
c. 5
d. –12
2. a. 9 + (–6) = 3
b. (–5) + 8 = 3
c. (–12) + (–6) = –18
d. 10 – (–8) = 18
e. (–4) – (+2) = –6
f. –9 – (–5) = –4
3. a. 8 × 3 = 24
b. –7 × 5 = –35
c. –6 × (–9) = 54
d. 8 ÷ (–2) = –4
e. –24 ÷ (–3) = 8
f. –36 ÷ 6 = –6
5. Multiply the service charge by the number of months in a year.
12 × 7 = $84
Answer: $84 is deducted per year.
6. Add the balance of each year to determine the closing balance.
–$1500 + (–$1200) = –$2700
penn foster
A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
11.65 seconds
50.00 seconds
171.65 seconds
210.00 seconds
Answers
The time it will take the roller coaster to reach the ground is 171.65 seconds
Function and valuesGiven the roller coaster’s height given by the following parameters
h = –0.025t² + 4t + 50
On the ground level, the height will be zero. Substitute h = 0 and determine the value of t
–0.025t² + 4t + 50 = 0
0.025t² - 4t - 50 = 0
Factorize
On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds
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A ball is thrown downward from the top of a 120-foot building with an initial velocity of 20 feet per second. The
height of the ball h in feet after t seconds is given by the equation h= - 16t²-20t+120. How long after the
ball is thrown will it strike the ground?
Answers
Answer:
[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]
Step-by-step explanation:
The ball strikes the ground when h = 0.
[tex]-16t^2 - 20t + 120 = 0 \\ \\ 4t^2 + 5t - 30=0 \\ \\ t=\frac{-5 \pm \sqrt{5^{2}-4(4)(-30)}}{4(2)} \\ \\ t=\frac{-5 \pm \sqrt{505}}{8}[/tex]
However, as time most be positive, we only consider the positive case.
So,
[tex]t=\frac{-5+\sqrt{505}}{8}[/tex]
In the diagram the origin is at the center of a cube that has edges 6 units long. The x-,y-, and z-axes are perpendicular to the faces of the cube give the coordinates of the corner at point A.
Answers
Answer:
the third answer (-3, -3, 3)
Step-by-step explanation:
the dotted lines indicate that these lines (or part of lines) are invisible due to being inside or behind the cube.
so, we know that A is the left-back-upper corner of the cube.
the x-axis goes front-back. front is positive.
the y-axis goes left-right. right is positive.
the z-axis goes up-down. up is positive.
since the origin (0, 0, 0) is the center of the cube, and the sides are all 6 units long, the corners can have only -3 or +3 coordinates (half of a side length on either side of the origin) in each direction.
as we said : left-back-upper corner.
left means negative y.
back means negative x.
upper means positive z.
so, the coordinates of A are
(-3, -3, 3)
Find the root of the function f(x)=−4x+1.
Answers
Answer: A
Step-by-step explanation:
[tex]-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4[/tex]
What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?
domain is x is all real numbers where x does not equal 4 comma range is y is all real numbers where y does not equal 11
domain is x is all real numbers where x does not equal 7 comma range is y is all real numbers where y does not equal negative 4
domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11
domain is x is all real numbers where x does not equal negative 7 comma range is y is all real numbers where y does not equal 4
Answers
The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C
What is the domain of a function?The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.
Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.
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Answer:
The answer is C.
which statement describes the function below
f(x)=x^3-x^2-9x+9
Answers
2x3 i think maybe yes
Please please Help!
Need Answer to Multiple Choice! Brainliest!
The scores on the ACT exam are normally distributed with a mean of 21 and a standard
deviation of 5. If we selected a random sample of 37 test takers, what is the probability that the
sample mean of those test takers who would be less than a 19.8?
a) .0721
b) .5000
c) .0808
d) .0582
Answers
Answer:
a) 0.0721
Step-by-step explanation:
Let the random variable X be the score on the ACT exam.
Given:
mean (μ) = 21standard deviation (σ) = 5Therefore, the random variable X is normally distributed:
[tex]X \sim\textsf{N}(21,5^2)[/tex]
Z-score for a sample mean
[tex]\textsf{If }\: X \sim\textsf{N}(\mu,\sigma^2)\:\textsf{ then }\: \overline{X} \sim \left(\mu,\dfrac{\sigma^2}{n}\right) \implies Z=\dfrac{\overline{X}-\mu}{\sigma / \sqrt{n}} \sim \textsf{N}(0,1)[/tex]
[tex]\textsf{then the test statistic is}: \quad z=\dfrac{\overline{x}-\mu}{\sigma / \sqrt{n}}[/tex]
Given:
[tex]\overline{x}[/tex] = 19.8μ = 21σ = 5n = 37Therefore, the test statistic is:
[tex]\implies z=\dfrac{19.8-21}{5/ \sqrt{37}}=-\dfrac{6\sqrt{37}}{25}=-1.459863007=-1.46\:\: \sf (3\:s.f.)[/tex]
Using the Z-tables to find the probability:
[tex]\implies \text{P}(Z \leq -1.46)=0.0721[/tex]
90% of the flights that left a certain airport yesterday departed on time. If there were 150 flights from the airport yesterday, how many flights DID depart on time
Answers
Three brothers, Jarek, Jerzy and Justyn, share a block of chocolate in the ratio of their ages. Jarek gets half of the bar. Jerzy gets 3\5 of the rest. Work out the ratio, in the form Jarek: Jerzy: Justyn, of how the brothers share the bar of chocolate.
Answers
Answer:
5:3:2
Step-by-step explanation:
see image
Jarek gets half. Then from the other half, Jerzy gets 3 pieces of 5 and Justyn gets the leftover 2 pieces. But Jarek's piece is all 5 pieces of the first half.
Jarek 5 parts:
Jerzy 3 parts:
Justyn 2 parts
5:3:2
see image
Maria has 26 cars available to rent. Let C be the number of cars she would have left after renting R of them. Write an equation relating C to R. Then use this equation to find the number of cars she would have left after renting 23 of them.
Answers
Answer:
26 - R = C
3 cars
Step-by-step explanation:
26-R = C
26-23 = 3
cual es el valor de 10=z-6
Answers
Answer:
z=16
Step-by-step explanation:
10=z-6
10+6=z-6+6
16=z
Answer:
10=z-6
or, z= 10+6
or, z = 16
the vale of y is 16
Which rules define the function graphed below?
65
4
3
32
(0.2)
-2
-3-
(3,5)
--3--2--11 1 2 3 4
O y=x; y = 5
O y = x + 2; y = 5
O y=x; x = 5
O y=x+2; x = 5
Answers
The rules that define the piecewise function graphed are as follows:
y = x + 2, y = 5.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
In this problem, for x between 0 and 3, a linear function is given, with slope given as follows:
m = (5 - 2)/(3 - 0) = 1.
The y-intercept is of 2, as y = 2 when x = 0, hence the definition is:
[tex]y = x + 2, 0 \leq x \leq 3[/tex]
For x greater than 3, the function is constant at y = 5, hence the definition is:
y = 5, x > 3.
Hence, the rules that are used to define the piecewise function graphed are as follows:
y = x + 2, y = 5.
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The function g(x) is a transformation of the quadratic parent function, fx):
What function is g(x)?
90x)
15(x)
A. g(x) = 4x²
OB. g(x) = ² ->
O c. g(z) = -1¹
D. g(x)=-4x²
Answers
Answer: D
Step-by-step explanation:
The graph is narrower, so the coefficient of [tex]x^2[/tex] has an absolute value more than 1.
Eliminate B and C.Also, because g(x) opens down, the coefficient of [tex]x^2[/tex] is negative.
Eliminate A.This leaves D as the answer.
Pizza prices by city (Data in Pizza prices) The company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in each market:
Answers
The answers to the questions are
a. No they are not the same
b. The presence of outliers are known to affect the market.
How to solve the box plot
For these areas we have
Q1 = 2.7 Q3 = 3 median = 2.8 out;ier 2.
Q1 = 2.5 Q3 = 2.7 median = 2.6 out;ier 3.1.
Q1 = 2.5 Q3 = 2.75 median = 2.65 out;ier 1.6
Q1 = 2.4 Q3 = 2.6 median = 2.5
We can see that the median prices in the markets are nearly similar except for the one that is conatined in the first market.
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Assume that the average healthy body temperature is 98.249 degrees and the standard deviation is 0.733 degrees. How many standard deviations below the mean would I be if my body temp is 97.2 degrees,
Answers
The standard deviation is 1.43 below the mean
How to determine the number of standard deviation?The given parameters are:
Mean = 98.249
Standard deviation = 0.733
x = 97.2
To calculate the number of standard deviation below the mean, we use
[tex]x = \bar x - n\sigma[/tex]
So, we have:
[tex]97.2 = 98.249 - n * 0.7333[/tex]
Evaluate the like terms
[tex]-1.049 =- n * 0.7333[/tex]
Divide both sides by -0.733
n =1.43
Hence, the standard deviation is 1.43 below the mean
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Solve for x if AB = 5x and BC = 3x + 24.
Answers
The value of x according to the given task is; 12.
What is the value of x?It follows from the task content that the value of x is to be determined.
Since, lines AB and BC are both tangent to the circle and they both share a point of intersection; it follows that;
5x = 3x +24
collect like terms2x = 24
divide both sides by 2x = 24/2
x = 12.
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Answer to the question on the image attached to this thread. Thank you!
Answers
The solution of the system of equation of the matrix is as follows:
x = - 8
y = 3
How to find the solution of matrix?3x + 10y = 6
x + 3y = 1
multiply equation(ii) by 3
3x + 10y = 6
3x + 9y = 3
Therefore,
y = 3
Hence,
x + 3y = 1
x + 3(3) = 1
x + 9 = 1
x = 1 - 9
x = -8
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Find the unit rate for each brand. Round to the nearest cent (hundredth).
Answers
The unit rate of each of the brands are:
Brand A's unit rate = 37 cents per ounce.
Brand B's unit rate = 31 cents per ounce.
How to Find the Unit Rate?The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.
To find the unit rate of each brand, do the following:
Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.
Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.
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On a piece of graph paper, plot the following points: A (0, 0), B (5, 0), and C (2, 4). These coordinates will be the vertices of a triangle. How would you use the distance formula to determine what kind of triangle this is? Is the triangle equilateral, right, or scalene? Now use the midpoint formula to determine the midpoints of the triangle's sides: segments AB, BC, and CA. Connect the midpoints to make four triangles within the first triangle. Are these four triangles similar?
Answers
The triangle is an isosceles triangle and the four triangles are similar
How to determine the triangle type?
The coordinates are given as:
A (0, 0), B (5, 0), and C (2, 4).
Calculate the distance between the coordinates using:
[tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2[/tex]
So, we have:
[tex]AB = \sqrt{(0 -5)^2 +(0-0)^2} =5[/tex]
[tex]AC = \sqrt{(0 -2)^2 +(0-4)^2} =4.5[/tex]
[tex]BC = \sqrt{(5 -2)^2 +(0-4)^2} =5[/tex]
The above shows that two sides are congruent.
Hence, the triangle is an isosceles triangle
The midpoints of the sidesThis is calculated using:
(x, y) = 0.5 * (x1 + x2, y1 + y2)
So, we have:
AB = 0.5 * (0 + 5, 0 + 0) = (2.5, 0)
AC = 0.5 * (0 + 2, 0 + 4) = (1, 2)
BC = 0.5 * (5 + 2, 0 + 4) = (3.5, 2)
From the attached graph, we can see that the triangles are similar
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Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3). Create an equation for a line passing through point A and perpendicular to BC.
Answers
The required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.
How to estimate the slope of the line?First, we must obtain the slope of the line perpendicular to BC
Given the coordinates B(7,5), and C(2,3)
Get the slope BC, exists
[tex]$m_{BC} = \frac{3-5}{2-7}[/tex]
= -2/-5 = 2/5
The slope of the line perpendicular to BC will be -5/2.
The slope of the required line in point-slope form exists expressed as;
[tex]$y - y_0 = m(x - x_0)[/tex]
m = -5/2
[tex](x_0, y_0) = (3, 8)[/tex]
Substitute the values into the formula we get
y - 8 = (-5/2)(x - 3)
2(y - 8) = (-5)(x - 3)
2y - 16 = (-5x + 15)
2y + 5x = 15 + 16
2y + 5x = 31
Therefore the required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.
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Educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines.
A- True
B- False
Answers
The statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A
Ways to improve mathematics education
They include;
Using hands-on learning methodsUsing visualsIntegration of mathematics gameConnecting math concepts to everyday lifeAllow students to explain their reasoningRewarding students progressThus, the statement ' educators should ensure math instruction is only taught through structured activities rather than through everyday situations and routines is True. Option A
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Answer:
Step-by-step explanation:
false
Write out the sum. Do not evaluate.
∑∑k=1 (k^2-5k-3)[tex]4\\E(K^2-5k-3)\\k=1[/tex]
Answers
Series are sum of a given sequence.. The sum of the given expression is -33
Sequence and seriesSeries are sum of a given sequence. According to the given expression
∑∑k=1 (k^2-5k-3)
Taking the sum from k = 1 to k = 4
Sum = (1-5-3) + (4-10-3) +(9-15-3)+(15-20-3)
Sum = (-7) + (-9) + (-9) + (-8)
Sum = -33
Hence the sum of the given expression is -33
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explain me the formula for a point that forms a partiton of a ratio on a segment in the 2nd grade real numbers.
Let’s say the ratio a:b, our formula those becomes
{(bx1 + ax2)/(a + b) ,( by1+ay2)/a+b}
From the question, we can identify that
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
Answers
The partition point is (-7/2, 23/4)
How to determine the partition point?The given parameters are:
(x1,y1) = (-6,-1)
(x2,y2) = (4,8)
a = 1 and b = 3
The partition point is calculated as:
(x, y) = ((bx1 + ax2)/(a + b) ,( by1+ay2)/a+b)
So, we have:
(x, y) = ((3 * -6 + 1 * 4)/(1 + 3) ,(3 * 8 + 1 * -1)/1+3)
Evaluate
(x, y) = (-14/4, 23/4)
Simplify
(x, y) = (-7/2, 23/4)
Hence, the partition point is (-7/2, 23/4)
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. Which of the following is parallel to
5x + 2y = 1?
Answers
Answer:
when the question is rearranged so that y is by itself, any of the options that say - 2.5x will be parallel.
Step-by-step explanation:
5x + 2y = 1
to get y by itself, simple algebra rules must be applied.
1. subtract 5x from both sides.
5x - 5x + 2y = 1 - 5x
2y = 1 - 5x
divide both sides by 2
2y / 2 = 1 / 2 - 5x / 2
twos cancel out on the left1/2 = 0.5- 5x /2 = - 2.5xtherefore the new equation is:
y = 0.5 - 2.5x
this is very close to standard form for a line which is y = mx + b
rearrange the right side of the equals sign:
y = -2.5x + 0.5
in a standard linear equation, the x value determines the gradient of the line. therefore, anything with the same gradient (in this case -2.5x) will be parallel to the given equation.
Hope this makes sense :)