Answer:
y = -2*x^3 - x + 2
Step-by-step explanation:
We want to solve the differential equation:
y'' + 12*x = 0
such that:
y(0) = 2
y'(0) = -1
We can rewrite our equation to:
y'' = -12x
if we integrate at both sides, we get:
[tex]\int {y''} \, dx = y'= \int {-12x} \, dx[/tex]
Solving that integral we can find the value of y', so we will get:
y' = -12* (1/2)*x^2 + C = -6*x^2 + C
where C is the constant of integration.
Evaluating y' in x = 0 we get:
y'(0) = -6*0^2 + C = C
and for the initial value problem, we know that:
y'(0) = -1
then:
y'(0) = -1 = C
C = -1
So we have the equation:
y' = -6*x^2 - 1
Now we can integrate again, to get:
y = -6*(1/3)*x^3 - 1*x + K
y = -2*x^3 - x + K
Where K is the constant of integration.
Evaluating or function in x = 0 we get:
y(0) = -2*0^3 - 0 + K
y(0) = K
And by the initial value, we know that: y(0) = 2
Then:
y(0) = 2 = K
K = 2
The function is:
y = -2*x^3 - x + 2
When a closed curve is parameterized by {x[t], y[t]}, then as you advance along the curve in the direction of the parameterization, which way do the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point; in the direction you are going, or in the direction opposite to the direction you are going?
Answer:
In the direction you are going,
Explanation:
We know that the tangent to {x[t], y[t]} are {x'[t], y'[t]}. Since {x'[t], y'[t]} are tangents at {x[t], y[t]}, we know that the tangent at a point is always parallel to the direction of the function at that point and in the direction of the function. So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in my direction of motion as I move along the curve.
So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in the direction you are going.
9 3/5 % as a decimal, rounded to 3 decimal places, is:
The graph of a quadratic function has x-intercepts of -7 and -1, and passes through the point (-4,36). Determine the equation of the quadratic function in the form
f(x) = a(x - m)(x − n).
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Answer:
f(x) = -4(x +7)(x +1)
Step-by-step explanation:
The x-intercepts tell us that m=-7 and n=-1. We can use the given point to find 'a'.
f(-4) = 36
a(-4+7)(-4+1) = 36
a = 36/-9 = -4 . . . . divide by the coefficient of 'a'
Filling in the known values, ...
f(x) = -4(x +7)(x +1)
What is the length of CD? In this diagram, AABC ~ AEDC. 20-% c * 7 21
Answer:
[tex]\frac{BC}{DC}=\frac{AC}{EC}[/tex]
[tex]\frac{20-x}{x} =\frac{21}{7}[/tex]
[tex]\frac{20-x}{x} =3[/tex]
[tex]20-x=3x[/tex]
[tex]4x=20[/tex]
[tex]x=5[/tex]
[tex]So, CD=5[/tex]
OAmalOHopeO
Which of the following statements are true? ONLY ANSWER IF YOU KNOW THE ANSWER
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Answer:
A, D, F
Step-by-step explanation:
A: true
B: false; it is positive
C: false; it may be positive: -1 -(-2) = +1
D: true, a variation of A
E: false; for c < 0, the inequality symbol reverses
F: true. This is the definition of an additive inverse.
G: false; multiplying anything by zero gives zero
H: false; -(-1) = +1, not a negative
I need this nowwww important
Answer:
7,7,12.5
Step-by-step explanation:
since we know that 2 sides are equal,
4x+1=5x-0.5
5x-4x=1+0.5
x = 1.5
sub x = 1.5 into the different eqns
4(1.5)+1 = 7
5(1.5)-0.5 = 7
9(1.5)-1 = 12.5
Question 4(Multiple Choice Worth 1 points) (08.01 LC) What are the x-intercepts of the parabola? graph of parabola falling from the left, passing through 2 comma 3 to about 4 comma negative 1, and rising to the right, passing through 6 comma 3 (0, 3) and (0, 5) (0, 4) and (0, 5) (3, 0) and (5, 0) (4, 0) and (5, 0)
Answer:
(4, 0) and (5, 0)
Step-by-step explanation:
Given
See attachment for graph
Required
The x intercepts
This is the point where [tex]y = 0[/tex]
From the graph, we have the following as the x-intercepts:
[tex](x_1,y_1) = (4,0)[/tex]
[tex](x_2,y_2) = (5,0)[/tex]
Because the curve crosses the x-axis at the above points
Answer:
(4, 0) and (5, 0)
Step-by-step explanation:
have a great day and please mark brainliest!
Which of the following is the solution of 2x + 14 = 22?
x = 4
O x=8
X = 11
OX= 14
Answer:
x=4
Step-by-step explanation:
2x + 14 = 22
Subtract 14 from each side
2x+14-14 = 22-14
2x = 8
Divide by 2
2x/2 = 8/2
x = 4
I don’t know the answer!!
I’m new to this app and I need help if you know the answer please tell me I don’t know English very good please help me.
Answer:
A. 2.04 seconds
B. 5.92
C: 1.48 - 0.4 = 1.08 seconds
Step-by-step explanation:
~~~~~~~~~~~~~~~~~~~~~
USE THIS TO GET "B"
the f(-b/2a) is the highest point,
the vertex of the parabola [-b/2a, f(-b/2a)] will give you the time
and height of the highest point
~~~~~~~~~~~~~~~~~~~
USE THIS TO GET "A"... you will get two answers one will be negative
ignore that one , the positive one is the time to hit the ground
if you factor the equation (use the quadratic formula) you will get
the "zeros" that is where the ball is on the ground...
~~~~~~~~~~~~~~~~~~~~~~~
THIS IS FOR PART "C"
if you set the equation equal to 4.5 meters and factor that for the "zeros" you will get the two times that the ball is at that height.. subtract the two times for the duration
Question 1 of 10
If f(x)= 2 -3 and g(x) = 4x2 + x - 4, find (f+ g)(x).
O A. 4x+x-7
O B. 4x2 +5x-1
O c. 6x2 - 7
OD 6+x-1
A
SUBMIT
Answer:
I believe it's A
Step-by-step explanation:
I'm not sure sorry if its wrong
Need help ASAP
In the figure, if the measure of ∠8 = 72o, what's the measure of ∠14?
Four Bisecting Lines
Question 3 options:
108°
72°
98°
62°
Answer:
72°
Step-by-step explanation:
[tex] m\angle \: 6 = m \angle \: 8 \\ (corresponding \: \angle s) \\ m\angle \: 8 = 72 \degree \\ \therefore \: m\angle \: 6 = 72 \degree \\ \\ m\angle \: 14 = m \angle \: 6 \\ (corresponding \: \angle s) \\\therefore \: m\angle \: 14 = 72 \degree [/tex]
Find x so that the distance between the points (1,2) and
(x, -10) is 13
Answer:
x = -4 or 6
Step-by-step explanation:
12^2 + (1-x)^2 = 13^2
(1-x)^2= 13^2 - 12^2
(1-x)^2= 25
1-x = 5
x = -4 or 6
A sample of 34 observations is selected from a normal population. The sample mean is 15, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 14 H1: μ > 14
Required:
a. Compute the value of the test statistic.
b. What is the p-value?
Answer:
1.944 ;
0.026
Step-by-step explanation:
Given :
Sample size, n = 34
Sample mean, xbar = 15
Population standard deviation, σ = 3
The hypothesis :
H0: μ ≤ 14
H1: μ > 14
The test statistic :
Test statistic = (xbar - μ) ÷ (σ/√(n))
Test statistic = (15 - 14) ÷ (3/√(34))
Test statistic = 1 / 0.5144957
Test statistic, Z = 1.944
The Pvalue :
Using the Pvalue from test statistic value :
Pvalue(1.944) = 0.026
Pvalue < α ; Reject H0
Let log base aU=X and log base aV=Y, then a to the x power =? and a to y power =?
Answer:
[tex]{ \bf{ log_{a}(U) = x}} \\ { \boxed{ \tt{ {a}^{x} = U}}} \\ \\ { \bf{ log_{a}(V) = y}} \\ { \boxed{ \tt{ {a}^{y} = V }}}[/tex]
Which expression is equivalent to (3x^2+4x-7)(x-2)
Answer:
Option C.
(3x² + 4x– 7)(x) + (3x² + 4x– 7)(–2)
Step-by-step explanation:
From the question given above, we obtained:
3x² + 4x– 7
x – 2
To know which option is correct, we shall obtained the product of the expression. The product of the expression can be obtained as follow:
(3x² + 4x– 7) (x – 2)
NOTE: (3x² + 4x– 7) will be multiplied by x and –2 as illustrated below:
x(3x² + 4x– 7) – 2(3x² + 4x– 7)
Rearrange
(3x² + 4x– 7)(x) + (3x² + 4x– 7)(–2)
Thus, Option C gives the correct answer to the question.
What are the domain and range of the function represented by the table?
X
-1
-0.5
0
0.5
1
y
3
4
5
6
7
A. Domain: -1 sxs 1
Range: y2 3
B. Domain: -1sxs1
Range: 3, 4, 5, 6, 7}
C. Domain:{-1, -0.5, 0, 0.5, 1}
Range: {3, 4, 5, 6, 7}
D. Domain:{-1,-0.5, 0, 0.5, 1}
Range: y23
PLEASE HELP!!
The probability that Barry Bonds hits a home run on any given at-bat is 0.16, and each at-bat is independent.
Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points)
Part B: What is the expected number of at-bats until the next home run? (5 points)
Answer:
i think 5 points home run will be on his fifth at bat . 10 point isthe expected number of at bats until the next home rum.
The numbers of home runs that Barry Bonds hit in the first 18 years of his major league baseball career are listed below. Find the mean and median number of home runs. Round the mean to the nearest whole number. Which measure of central tendency- the mean or the median- best represents the data? Explain your reasoning.
16 25 24 19 33 25 34 46 37
33 42 40 37 34 49 73 46 45
Answer:
Mean = 35.56
Median = 35.5
Step-by-step explanation:
Given the data:
16 25 24 19 33 25 34 46 37
33 42 40 37 34 49 73 46 45
Reordered data :
16, 19, 24, 25, 25, 33, 33, 34, 34, 37, 37, 40, 42, 45, 46, 46, 49, 73
The mean = ΣX / n
n = sample size ; ΣX = sum of values
The mean = 658 / 18
The mean = 36.56
The Median = 1/2(n+1)th term
1/2(18+1)th term = 1/2(19)th term = 9.5 term
Median = (9th + 10th) / 2 = (34 + 37) / 2 = 35.5
A machining center is in charge of producing 225 parts per day. The parts width. Any parts produced between 250mm and 260mm are considered gless than 250mm must be reworked at an additional cost of $8 per part. 260mm must be reworked at an additional cost of $2.50 per part. The varquantified as a standard deviation of 5.0mm. Measurements on these parhave the ability to set up the machine to achieve whatever mean width value you wish.
Required:
Setup a data table to determine the mean width setting that will minimize expected rework cost ($8 per small part and $2.50 per large part).
Couldn’t figure this out help please
(B)
Step-by-step explanation:
Rewrite the equations into their standard forms. The first one can be rewritten as
[tex]10x - 12y = -5[/tex]
and the 2nd can be rewritten as
[tex]3x + 5y = -1[/tex]
Solving this system either by substitution or elimination, we get
[tex]x = -\dfrac{37}{86}\:\:\text{and}\:\:y= \dfrac{25}{86}[/tex]
If you add x + y, you'll get a negative number.
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Answer:
B. x + y < 0
Step-by-step explanation:
The two equations can be cleared of fractions by multiplying by 15.
15(2/3(x +1) -4/5y) = 15(1/3)
10(x +1) -12y = 5
10x -12y = -5
and
15(2/5x +1/3(2y +1)) = 15(1/5)
6x +5(2y +1) = 3
6x +10y = -2
3x +5y = -1 . . . . . eliminate common factor of 2
__
You can find the solutions any way you like, but you can answer the question without doing that. The lines are not parallel, nor coincident, so there is exactly one solution. (choices C and D are incorrect)
If we can locate the solution relative to the line x + y = 0, we can tell if choice A or choice B is correct. A quick look at the intercepts of the equations tells us the solution cannot lie in quadrants 1 or 4. The negative y-intercept and shallow slope (-3/5) of the second equation tells us the solution must lie below the line x + y = 0. That means x+y < 0, choice B.
_____
In the attached graph, the line x+y=0 is dashed orange. Above that line, x+y>0; below that line, x+y<0. We see the intersection point of the red and blue lines is in the region where x+y < 0.
For standard form equation ax+by = c, the x- and y-intercepts are c/a and c/b, respectively, so are easy to find from that form. Knowing these makes it easy to make a sketch of the graph, locating the solution point relative to the line x+y = 0.
If a number is divisible by 6 and 8 then is it also divisible by 48?
Answer:
No
Step-by-step explanation:
Let's look at an example
24
24 is divisible by 6 24/6 = 4
24 is divisible by 8 24/8 = 3
24 is not divisible by 48 24/48 = 1/2 which is not an integer
If anyone can help me figure out the answer for this problem and show proper work I’ll give brainliest to them. Anyone who just tries to take points will be reported
Solve the system using substitution. x+y=-2 and x-y=-8
Answer:
1) x+y=-2
x=-2-y
2) x-y=-8
substitude value of x
(-2-y)-y=-8
-2-2y=-8
-2y=-6
y=3
Substitute value of y in 1
x=-2-3
x=-5
Brainliest please~
What is the solution to both systems A and B?
O(3, 4)
O (3,5).
O (4,3)
O (5,3)
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Answer:
(c) (4, 3)
Step-by-step explanation:
The next step in the solution of System B is to divide by 15 1/2. This will result in the equation ...
x = 4
The only answer choice that has x = 4 is the ordered pair (4, 3). That ordered pair is the solution to the system.
__
(15 1/2)x = 62 ⇒ (31/2)x = 124/2 ⇒ x = (124/2)/(31/2) = 124/31 = 4
Answer:
c
Step-by-step explanation:
got it right on the test
Donald has x twenty dollar bills and 1 yen dollar bill. How much money does Donald have?
Write your answer as an expression
what is the perimeter of a square garden
Answer:
Use this formula: length + length + width + width = perimeter
Step-by-step explanation:
An angle measures 19.4° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
37.8+52.2=90
Step-by-step explanation: x + (x + 14.4) = 90
2x + 14.4 = 90
2x = 75.6
x = 37.8 (one angle)
And (x + 14.4) = 52.2 (other angle).
A tumor is injected with 0.3 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?
Answer:
The time required is 60.3 days.
Step-by-step explanation:
initial amount, No = 0.3 g
rate, r = 1.15 % per day = 0.0115 per day
final amount, N = 0.15 g
Let the time is t.
[tex]N = No e^{-rt}\\\\0.15 = 0.3 e^{-0.0115 t}\\\\0.5 =e^{-0.0115 t}\\\\- 0.6931 = - 0.0115 t \\\\t = 60.3 days[/tex]
Graph the line with slope
3/4
passing through the point (-1, 4).
Answer:
y=3/4x+19/4
Step-by-step explanation:
y=mx+c
4=3/4*-(1)+c
4=-3/4+c
c=4+3/4
c=19/4
y=3/4x+19/4
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz. Her third quiz score is what percent higher than her first quiz score?
Answer:
30%
Step-by-step explanation:
you just add 10% and 20%
Hope it helps c:
Zelina scored 32% higher on the third quiz than on her first quiz.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.
Given that:-
Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz.From the given data we will see that:-
1 ) Zelina scored 10% higher on her second quiz than on her first quiz.
SQ = 1.10 FQ
2 ) On her third quiz, Zelina scored 20% higher than on her second quiz
TQ = 1.20SQ
From the above to expression solve for the first quiz:-
TQ = 1.20 x 1.10 FQ
TQ = 1.32FQ
Therefore Zelina scored 32% higher on the third quiz than on her first quiz.
To know more about percentages follow
https://brainly.com/question/24304697
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