Answer:
AC = 2x-19yStep-by-step explanation:
Given vector the following vector equations OA = 13x+7y , OB = 5x+12y and CO = -15x+12y, the following expression is true about vector OA, OB and OC;
OA+OB = CO (CO is the resultant since its is moving in the opposite direction compare to OA and OB)
Also BO+OA = BA and AO+OC = AC
If OB = 5x+12y, then BO = -(5x+12y)
BO = -5x-12y (BO = -OB)
Since BO+OA = BA
BA = -5x-12y + 13x+7y
BA = -5x+13x-12y+7y
BA = 8x-5y
Similarly AO+OC = AC
Since AO = -OA and OC = -CO
-OA-CO = AC
AC = -(13x+7y)-(-15x+12y)
AC = -13x-7y+15x-12y
AC = -13x+15x-7y-12y
AC = 2x-19y
Write an equation that expresses the following relationship.
w varies directly with u and inversely with the square of d
In your equation, use k as the constant of proportionality.
Answer:
w = [tex]\frac{ku}{d^{2} }[/tex]
Step-by-step explanation:
An equation that expresses the given relationship is ud²=1.
Given that, w varies directly with u and inversely with the square of d.
We need to write an equation that expresses the following relationship.
What is directly and inversely varies?Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.
Now, w∝u⇒w=ku
and w∝1/d²⇒w=k/d²
⇒wd²=k
⇒w=wd²u
⇒ud²=1
Therefore, an equation that expresses the given relationship is ud²=1.
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Proceed as in Example 4 in Section 6.1 and find a power series solution y = [infinity] n = 0 cnxn of the given linear first-order differential equation. (Give your answer in terms of c0.) y' = xy
Let y be a solution to the given differential equation,
[tex]y' = xy[/tex]
where
[tex]\displaystyle y = \sum_{n=0}^\infty c_n x^n \\\\ y' = \sum_{n=0}^\infty nc_nx^{n-1} = \sum_{n=1}^\infty nc_nx^{n-1} = \sum_{n=0}^\infty (n+1)c_{n+1}x^n[/tex]
Substituting these series into the DE gives
[tex]\displaystyle \sum_{n=0}^\infty (n+1)c_{n+1}x^n = x\sum_{n=0}^\infty c_nx^n \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=0}^\infty c_nx^{n+1} \\\\ \sum_{n=0}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty (n+1)c_{n+1}x^n = \sum_{n=1}^\infty c_{n-1}x^n \\\\ c_1 + \sum_{n=1}^\infty \bigg((n+1)c_{n+1}-c_{n-1}\bigg)x^n = 0[/tex]
Then the coefficients [tex]c_n[/tex] in the series solution are governed by the recurrence,
[tex]\begin{cases}c_0 = c_0 \\ c_1 = 0 \\ (n+1)c_{n+1}-c_{n-1} = 0&\text{for }n\ge1\end{cases}[/tex]
We have
[tex](n+1)c_{n+1}-c_{n-1} = 0 \implies nc_n - c_{n-2} = 0 \implies c_n = \dfrac{c_{n-2}}n[/tex]
so it follows that [tex]c_1=c_3=c_5=\cdots = 0[/tex], while
[tex]c_0 = \dfrac{c_0}1 = \dfrac{c_0}{2^0\times0!} \\\\ c_2 = \dfrac{c_0}2 = \dfrac{c_0}{2^1\times1!}\\\\ c_4 = \dfrac{c_2}4 = \dfrac{c_0}{2\times4} = \dfrac{c_0}{2^2\times2!}\\\\ c_6 = \dfrac{c_4}6 = \dfrac{c_0}{2\times4\times6} = \dfrac{c_0}{2^3\times3!}[/tex]
and so on, with the general n-th coefficient being
[tex]c_n = \begin{cases}0&\text{if }n\text{ is odd} \\ \dfrac{c_0}{2^{n/2}\left(\frac n2\right)!} &\text{if }n\text{ is even}\end{cases}[/tex]
Then the power series solution is
[tex]\displaystyle y(x) = c_0 \sum_{n=0}^\infty \frac{x^n}{2^{n/2}\left(\frac n2\right)!} = c_0 \sum_{n=0}^\infty \frac1{\left(\frac n2\right)!} \left(\frac x{\sqrt2}\right)^n[/tex]
but this doesn't tell the whole story because it doesn't capture the odd-index-is-zero case.
More concisely: let n = 2k for integers k ≥ 0. Then
[tex]\displaystyle y(x) = c_0 \sum_{k=0}^\infty \frac{x^{2k}}{2^k k!} = c_0 \sum_{k=0}^\infty \frac1{k!} \left(\frac{x^2}2\right)^k[/tex]
and as a bonus, it's easier to get an exact solution for this DE,
[tex]y(x) = c_0e^{x^2/2}[/tex]
Identify the sample space in the following tree diagram
A.) H, T
B.) TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
C.) HHH, THH, TTH, TTT
D.) HT, TH, TT, HT
There are 2 sides per coin, and 3 flips, so 2^3 = 8 total items in the sample space
HHHHHTHTHTHHHTTTHTTTHTTTTracing each branch from left to right will help form the 8 different outcomes. For instance, if you go along the upper most path of the upper tree, then you'll get HHH meaning you got 3 heads in a row. The next branch down would be HHT, and so on.
Consider the following three expressions. To be the same what would P, Q, and R have to be
Step-by-step explanation:
Px^2+6x+1=x^2+x^2+Qx+1
P=2 and Q=6
Next, 3x^2-5-(x^2-6x+R/2)=2x^2+6x+1
2x^2-5-R/2+6x=x^2+6x+1
-5-R/2=6, R=-22
(15)(16)/a=(3)(4)(5)
Answer:
a = 4
Step-by-step explanation:
(15)(16)/ a = (3)(4)(5)
15 * 16 = 240
240/ a = (3)(4)(5)
240/a = 60
240/60 = a
a = 4
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can anyone show me this in verbal form?
Answer:
2 * (x + 2) = 50
Step-by-step explanation:
Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.
A representative for a soup company conducted a survey
to determine whether people in a city were aware of the
soup company's new advertising campaign. The
researcher set up a booth outside a local supermarket for
7 days and asked randomly selected patrons as they
entered the store whether they would be willing to
participate in a survey. Of the 530 selected patrons,
482 agreed to take the survey, and 48 refused. Which of
the following factors makes it least likely that a reliable
conclusion can be drawn about the awareness of the soup
company's advertising campaign by all people in the
city?
A) Sample size
B) Population size
C) The number of days the survey was given
D) Where the survey was given
Answer:
Step-by-step explanation:
hol sinaoteentnedbieinlrpeagntaaau
find lub and glb of the following set E={0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,.....}
The lub is 0.23[tex]\mathbf{\overline{43}}[/tex], while the glb is 0.2
The given set is presented as follows;
E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}
The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x ≤ B, while there all y ∈ E has a x ∈ E such that t < x
Therefore;
The supremum, lub of the given set is 0.23[tex]\overline{43}[/tex]
The greatest lower bound, glb, b, also known as the infimum, is defined as follows;
b is the greatest lower bound if for all x ∈ E then x ≥ b
Given that b < t, then where x ∈ E, there exist a x < t
The glb of the given set is 0.2
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Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
If 2^x=3^y=12^z then prove it 2/x = 1/z -1/y.
[tex] \begin{array}{l} 2^x = 3^y = 12^z \\ 2^x = 3^y = 2^{2z} \cdot 3^z \\ \Rightarrow 3 = 2^{\frac{x}{y}} \\ \Rightarrow 2^x = 2^{2z} \cdot 2^{\frac{xz}{y}} \\ \Rightarrow x = 2z + \frac{xz}{y} \\ \Rightarrow xy = 2zy + xz \\ \Rightarrow 2zy = xy - xz \\ \text{Dividing both sides by }xyz,\text{ we get:} \\ \dfrac{2}{x} = \dfrac{1}{z} - \dfrac{1}{y} \end{array} [/tex]
find the value and express it in standard form : 5×10^8×2×10^11 please answer
please mark this answer as brainlist
Which of the following is -32(5x-7)(x+8)/-4(x+8)(5x-7) simplified? A.8/(x+8) B.8 C.4 D.4/(5x-7)
Answer:
work is shown and pictured
Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the distribution of the population is normally distributed. 150 150 180 170
a. State the null and alternative hypotheses.
b. Using a critical value, test the hypothesis at the 10% level of significance.
c. Using a p-value, test the hypothesis at the 10% level of significance.
d. Using a confidence interval, test the hypothesis at the 10% level of significance.
e. Could a Type II error have been committed in this hypothesis test?
Answer:
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
Step-by-step explanation:
We formulate the null and alternative hypotheses as
a; H0: u= 140 Ha: u ≠ 140 two tailed test.
For a two tailed test the significance level ∝= 0.1 the critical region is given by
t ≤ t ( ∝/2) (n-1) and t > t ( ∝/2) (n-1)
So the critical region will be
t≤ t ( ∝/2) (n-1) =2.353
where
t= x` - u / s/ √n
Sr. No X X²
1 150 22500
2 150 22500
3 180 32400
4 170 28900
∑ 650 106,300
X`= ∑x/n = 650/4= 162.5
s²= 1/n-1 (x-x`)²= 1/n-1 [ ∑x² -(∑x)²/n ]
= 1/3[106,300 -650²/4] = 225
s= 15
Putting the values in the above equation
t= 162.5- 140/ 15/ √4
t= 3
So calculated value of t= 3
b. Therefore reject H0 as t= 3 ≠ t≤ t ( ∝/2) (n-1) =2.353 or
3 > t ( ∝/2) (n-1) =2.353
c. If we check from the table the p- value is 0.6 which lies between 0.1 and 0.05 therefore reject H0.
d. a 90% confidence interval based on the calculated values will be
x`± 1.645 (s)/ √n
Putting the values
162.5 ±1.645 ( 15/2)
162.5 ±12.3375
174.84 , 150.163
d. Again reject H0 as 140 < 150.163
e. A type II error has not been committed as H0 is rejected.
Identify the errors made in the finding the inverse of y= x^2 +12x
X= y^2+12x
Y^2= x- 12x
Y^2 = -11x
Y=√11x, for x greater than or equal to 0
9514 1404 393
Answer:
y was not substituted for every x
Step-by-step explanation:
To find the inverse of ...
y = f(x)
you need to solve ...
x = f(y)
Here, f(x) = x^2 +12x, so f(y) = y^2 +12y
This is not the expression we see on the right of ...
x = y^2 +12x
Apparently y was not properly substituted into f(x).
What is the 50th term of the arithmetic sequence having u(subscript)1 = -2 and d = 5
Answer:
243
Step-by-step explanation:
The general term for this arithmetic sequence is:
a(n) = -2 + 5(n - 1).
Then a(50) = -2 + 5(49) = 243
40pts and a brainliest to the person who answers this question with detailed explanations and steps to solve shown.
Find y. Give your answer in the simplest form.
Answer:
y = 7 sqrt(2)
Step-by-step explanation:
Since this is a triangle, we can use trig functions
sin theta = opp/ hyp
sin 45 = 7/y
y sin 45 = 7
y = 7/ sin 45
y = 7 / (1/sqrt(2) )
y = 7 sqrt(2)
Answer:
the answer is y = 7 sqrt (2)
Step-by-step explanation:
[tex]\sf{}[/tex]
♛┈⛧┈┈•༶♛┈⛧┈┈•༶
what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10
Answer:18.5
Step-by-step explanation:
10+8=18
18*5=90
90/4
22.5-4=18.5
The lengths of the sides of a triangle arc 3, 4, and 5. If Theta is the measure of the smallest angle of the triangle, what is the
value of tah theta?
(A)4/3
(B)5/4
(C)3/4
(D)3/5
Answer:
C
Step-by-step explanation:
Since they are pythagorian triplets, ABC is a right angled triangle at the angle between the arc 3 and arc 4. Theta is the angle opposite to 3 and hence tan(theta)=3/4
In a stable matching problem, if every man has a different highest-ranking woman on his preference list, and given that women propose, then it is possible that, for some set of women's preference lists, all men end up with their respective highest-ranking woman.a. Trueb. False
Answer:
True
Step-by-step explanation:
The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.
Why do interest rates on loans tend to be higher in a strong economy than in a weak one?
Integers are sometimes whole numbers
true or false
Answer:
True
Step-by-step explanation:
Integers are always whole numbers
negative, 0, positive:: whole numbers
find the surface area of the prism HURRY
Answer:
Does the answer help you?
Emily made a pot of cream of pumpkin soup for thanksgiving dinner. She put 5
cups of cream in the soup. She poured the soup into 24 small soup bowls. How
much cream (measured in oz.) is used for each small bowl of soup?
Answer:
1 2/3 ounces in each bowl
Step-by-step explanation:
We need to convert 5 cups to ounces
1 cup = 8 ounces
5 cups = 5*8 = 40 ounces
We divide the 40 ounces into 24 bowls
40 ounces / 24 bowl
5/3 ounces per bowl
1 2/3 ounces in each bowl
Answer:
each bowl can contain 5/3 oz. of soup.
Step-by-step explanation:
1 cup = 8 oz.
8 oz.
5 cups x -------------- = 40 oz.
1 cup
to get the measurement of each bowl,
40 oz. divided into 24 bowls.
therefore, each bowl can contain 5/3 oz. of soup.
solve the equation.
g - 16 = 8
g =
Answer:
24
Step-by-step explanation:
24-16=8
The solution to the equation is g = 24.
To solve the equation g - 16 = 8 and find the value of g.
we need to isolate the variable g on one side of the equation.
Starting with the given equation:
g - 16 = 8
To isolate g, we can add 16 to both sides of the equation:
g - 16 + 16 = 8 + 16
g = 24
Therefore, the solution to the equation is g = 24.
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logx-log(x-l)^2=2log(x-1)
Answer:
x = 1.00995066776
x = 2.52925492433
Step-by-step explanation:
This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...
[tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]
The attached graph shows zeros at
x = 1.00995066776 and 2.52925492433
_____
Comment on the equation
Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068
Comment on the answer refinement
We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.
Where r is the radius of the cone's base and h is the height of the cone. Find the approximate volume of a
cone when r is 4 inches and his 3 inches.
Use volume of cone formula
Answer:
The volume of this cone is V = 50 (~50.27)
(I'm assuming that 'his' is height?)
Answer: 50
Step-by-step explanation:
Graph the function f(x) = 1/2(2)^x
Answer; Down
Step-by-step explanation:The graph of the squaring function has the shape of a parabola that opens up. Its vertex is at (0,0). The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).
Draw the perpendicular bisector of the given line segment a.9.4 cm b. 8.6cm c. 10 cm
Answer:
Please do it by your shelf because if we measure it and send you may not be able to do by online .So, please do it by by yourself using your scale .
How many feet are in 26 miles, 1, 155 feet? Enter only the number. Do not include units
The solution is
Answer:
137, 280 feet
Step-by-step explanation:
There are 5,280 feet in a mile.
26 * 5,280 = 137,280
There are 137, 280 feet in 26 miles.
There are 137,280 feet in 26 miles.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We know that there are 5,280 feet in a mile.
So, the solution would be;
26 x 5,280 = 137,280
Thus, There are 137,280 feet in 26 miles.
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1km make how many cm
Answer:
100000
Step-by-step explanation: