I'm not sure if the last two apostrophes are part of the quote - "Solve ... " - or if you mean the second derivative [tex]x''[/tex]. I think you mean the first interpretation, but I'll include both cases since they are both solvable.
If the former is correct, separate variables to solve.
[tex]x' = -9tx \implies \dfrac{dx}{dt} = -9tx \implies \dfrac{dx}x = -9t\,dt[/tex]
Integrate both sides to get
[tex]\ln|x| = -\dfrac92 t^2 + C[/tex]
Solve for [tex]x[/tex].
[tex]e^{\ln|x|} = e^{-9/2\,t^2 + C} \implies \boxed{x = Ce^{-9/2\,t^2}}[/tex]
If you meant the latter, then the ODE can be rewritten as
[tex]9t x'' + x' = 0[/tex]
Reduce the order of the equation by substituting [tex]y(t) = x'(t)[/tex] and [tex]y'(t) = x''(t)[/tex].
[tex]9t y' + y = 0[/tex]
Solve for [tex]y'[/tex] and separate variables.
[tex]y' = -\dfrac y{9t} \implies \dfrac{dy}{dt} = -\dfrac y{9t} \implies \dfrac{dy}y = -\dfrac{dt}{9t}[/tex]
Integrate.
[tex]\ln|y| = -\dfrac19 \ln|t| + C[/tex]
Solve for [tex]y[/tex].
[tex]e^{\ln|y|} = e^{-1/9 \,\ln|t| + C} \implies y = Ct^{-1/9}[/tex]
Solve for [tex]x[/tex] by integrating.
[tex]x' = Ct^{-1/9} \implies x = C_1 t^{8/9} + C_2[/tex]
Claire buys a condo for $350,000. The value of the condo appreciates on average 5% per year where she
bought the condo
If you know the rest of the problems on the page then that would help;)
1. The best way that we can represent the condo that Claire bought is by option B. [tex]350000(1.05)^{t}[/tex]
How to determine the functionTo determine the function, we would have to do so by making use of the given equation that we have here.
This is given as
Ct = [tex]A(1+r)^t[/tex]
Where a is the principal
r is the rate of interest and
t is the time
2. we have 70 = 30(1.03)^t
70/30 = (1.03)^t
We have to take the log of the function above in order to find the value of t
t = 28.665
This is approximated to 29
Hence the answer here is option A after 29 weeks.
Read more on interest rate here: https://brainly.com/question/2294792
#SPJ1
Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 . Assume the leading coefficient is 1.
f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x) are − 3 , 4 , − 3 assuming that the leading coefficient is 1. This can be obtained by formula of polynomial function.
Find the required equation:The zeroes or roots of a polynomial function are x values for which f(x) = 0If the zeroes or roots are r₁, r₂, r₃,... then possible polynomial function is⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
where a is the leading coefficient
Here in the question it is given that,
Polynomial should be with degree 3zeros of f(x) are − 3 , 4 , − 3By using the formula of polynomial function we get,
⇒ f(x) = a(x - r₁)(x - r₂)(x - r₃)
⇒ f(x) = 1(x - (-3))(x - (4))(x - (-3))
⇒ f(x) = 1(x + 3)(x - 4)(x + 3)
⇒ f(x) = (x + 3)(x² - x - 12)
⇒ f(x) = x³ - x² - 12x + 3x² - 3x - 36
⇒ f(x) = x³ + 2x² - 15x - 36
Hence f(x) = x³ + 2x² - 15x - 36 is the equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): − 3 , 4 , − 3 assuming that the leading coefficient is 1.
Learn more about polynomial function here:
brainly.com/question/12976257
#SPJ1
Research suggests that students could benefit from later school starting times. A school administrative team is considering a proposal to move the starting time of the local schools one hour later than the current start time. To measure interest in the proposal, members of the team randomly select subjects attending a large high school soccer tournament played on the high school grounds on a Saturday morning. The team finds that 58% of those surveyed support a later high school start time. Which type of bias is most likely to be present in the survey results?
This is undercoverage bias because adults with older children are more likely to be included in the sample.
This is question wording bias because the phrasing of the later start times question may be confusing to some subjects.
This is nonresponse bias because some of those selected may choose to not provide their opinion on later start times.
This is voluntary response bias because vocal supporters of later start times will be more likely to offer their opinion.
The type of bias which is most likely to be present in the survey results is undercoverage bias because adults with older children are more likely to be included in the sample.
ResearchThis is a diligent inquiry or examination to seek or revise facts, principles, theories,or applications. It is used to make an extensive investigation or search for truth in an experiment.
Bias
In statistics, bias is the difference between the expectation of the sample estimator and the true population value, which reduces the representativeness of the estimator by systematically distorting it
Learn more about research:
https://brainly.com/question/968894
#SPJ1
A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the standard normal table to estimate the proportion.
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.140 = 110 + 2 x 15.These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
More can be learned about the Empirical Rule at brainly.com/question/24537145
#SPJ1
Triangular prism advertising boards are being placed along the edge of the arena’s stage with the following dimensions: Select which of the nets below are labelled with the correct dimensions. What should the dimensions be of any advertisement that wants to fill the longest side of the shape?
The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m
According to the statement
we have given that the Triangular prism of size 0.75 m, 1m and length of 2m.
And we have to find the by which size of advertisement board need to fill the longest side of the shape.
A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
So, for this purpose,
we know that the longest side of triangular prism is 2m and we have to cover it with the advertising board.
Obviously the length of the advertising board is of 2m to cover the longest side of the shape.
So, The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m
Learn more about triangular prism here https://brainly.com/question/16595877
#SPJ1
Evaluate each expression given the variable. 3x+7, when x=2
Answer:
13
Step-by-step explanation:
3x + 7
x = 2
3 × 2 + 7 = 6 + 7 = 13
Hi there.
3x+7
x=2 :
3(2)+7
6+7
13
That's it.
Find the area between the following curves.
y=x^3-x^2+x+8 ; y=5x^2-7x+8
Find where the two curves meet.
[tex]x^3 - x^2 + x + 8 = 5x^2 - 7x + 8 \\\\ \implies x^3 - 6x^2 + 8x = 0 \\\\ \implies x (x-2) (x - 4)= 0 \implies x=0, x=2, x=4[/tex]
The area between the curves is
[tex]\displaystyle \int_0^4 \left|\left(x^3-x^2+x+8\right) - \left(5x^2 - 7x + 8\right)\right| \, dx = \int_0^4 \left|x(x-2)(x-4)\right| \, dx[/tex]
When [tex]x[/tex] is between 0 and 2, [tex]x(x-2)(x-4)[/tex] is positive; when [tex]x[/tex] is between 2 and 4, [tex]x(x-2)(x-4)[/tex] is negative. So we split the integral at [tex]x=2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_2^4 x(x-2)(x-4)\,dx[/tex]
In the second integral, substitute [tex]y=x-2[/tex] to get
[tex]\displaystyle \int_0^2 x(x-2)(x-4) \, dx - \int_0^2 (y+2)y(y-2)\,dy[/tex]
[tex]\displaystyle \int_0^2 x(x-2) \bigg((x-4) - (x+2)\bigg) \, dx[/tex]
[tex]\displaystyle -6 \int_0^2 x(x-2) \, dx[/tex]
[tex]\displaystyle 6 \int_0^2 \left(2x - x^2\right) \, dx[/tex]
[tex]\displaystyle 6 \left(x^2 - \frac13x^3\right)\bigg|_0^2 = \boxed{8}[/tex]
QUESTION 29
Two variables x and y, assume the values x₁= 2, X2 = -8, X3= 4 X4=1 and y₁
=-3 y2 =-8 y3 = 10 y4=6 Calculate x
OA. -1
OB. -4
OC.-7
OD. -9
The sum of the set of x - values given to us is calculated as; ∑X = -1
How to find the the sum of a set of data?We are given;
X1 = 2, X2 = -8, X3 = 4, X4 = -8 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6
1) ∑X = X1 + X2 + X3 + X4
∑X = 2 + (-8) + 4 + 1 = -1
2) ∑Y = Y1 + Y2 + Y3 + Y4
∑Y = 3 + (-8) + 10 + 6
∑Y = -11
3) ∑ X² = X₁² + X₂² + X₃² + X₄²
∑X² = (2)² + (-8)² + (4)² + (1)²
∑X² = 85
4) ∑Y² = Y₁² + Y₂² + Y₃² + Y₄²
∑X² = (-3)² + (-8)² + (10)² + (6)²
∑X² = 209
Complete question is;
Two variables, X and Y assume the values X1 = 2, X2 = -5, X3 = 4, X4 = 1 and Y1 = -3, Y2 = -8, Y3 = 10, Y4 = 6, respectively. Calculate (a) ∑X, (b) ∑ Y, (c) ∑ X² (d) ∑ Y²
Read more about Sum of data at; https://brainly.com/question/15858152
#SPJ1
Which expression is equivalent to (27.3 5.9)47
O 211.3-1.95
O228-(-3) 20.94
O 27.3-5.04
O228-3-20.94
The correct answer is Option 4.
Please solve this question step by step explanation
The value of ∠B is 60 degrees
How to solve for B?The given parameters are
2∠A = 3∠B = 6∠C
Let the angles in a triangle ABC be ∠A, ∠B and ∠C.
The sum of these angles in the triangle ABC is
∠A + ∠B + ∠C = 180
Multiply the above equation by 2
2 * (∠A + ∠B + ∠C) = 2 * 180
Evaluate the product
2∠A + 2∠B + 2∠C = 360
Recall that 2∠A = 3∠B.
Substitute the above in the equation 2∠A + 2∠B + 2∠C = 360
3∠B + 2∠B + 2∠C = 360
This gives
5∠B + 2∠C = 360
Multiply the above equation by 3
3 * (5∠B + 2∠C) = 3 * 360
Evaluate the product
15∠B + 6∠C = 1080
Recall that 3∠B = 6∠C.
Substitute the above in the equation
So, we have:
15∠B + 3∠B = 1080
Evaluate the like terms
18∠B = 1080
Divide both sides by 18
∠B = 60
Hence, the value of ∠B is 60 degrees
Read more about angles at:
https://brainly.com/question/27682397
#SPJ1
Calculate the volume of a sphere that has a diameter of 7 meters.
Answer:
1436.76
Step-by-step explanation:
use the formula 4piR^3 to solveAnswer:
538.57 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
diameter ⇒ 7 m
∴ radius = d / 2
radius ( r ) = 7 / 2 = 3.5 m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 3.5 )³
V = 4 π × ( 3.5 )³
V = 4 π × 42.875
V = 4 π × 42.88
V = 12.56 × 42.88
V = 538.57 m³
cual es el valor de 15+b=23
Use a table of values to graph the function ƒ(x) = |x + 2| – 1. Select the correct graph below.
Please help me I’m stuck
Answer:
-1/3
5
Step-by-step explanation:
We need to complete
y = mx + b
with a slope, m, and with the y-intercept, b.
From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.
We now have y = mx + 5.
Now we need the slope.
We pick two points that are easy to read, (0, 5) and (3, 4).
m = slope = rise/run
To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.
Then we go left horizontally 3 units. The run is -3.
m = slope = rise/run = 1/(-3) = -1/3
Now we have the slope, so we can finish.
y = -1/3 x + 5
Answer:
-1/3
5
Explain why [tex]x[/tex] and [tex]3x + 5[/tex] are factors of the expression [tex]x(3x + 5)^{2}[/tex] and not terms of the expression.
[tex]x[/tex] and [tex]3x+5[/tex] are being multiplied to form the expression, and are not being added or subtracted.
Here, x and (3x+5) are given in the form of multiplication, instead of being separated by addition or subtraction. This is why x and (3x+5) are factors of the expression x(3x + 5)² and not terms of the expression.
What are terms and factors in an expression?
Terms of an expression can be a variable, a signed number, or a constant multiplied by one or more variables. On the other hand, the factors are the items that have been multiplied by another items. Any integer, variable, phrase, or lengthier expression can be a factor.
For instance, the expression 2x(y - 5) has three components: 2, x, and (y-3). These three components are its factors, since when multiplied, they produce the same expression. The factors may or may not be comprised of more than one terms.
Learn more about factors here:
https://brainly.com/question/24182713
#SPJ1
From the sample space S={1,2,3,4,...,15} a single number is to be selected at random. Given the following events, find the indicated probability.
A. the selected number is even
B. the selected number is a multiple of 4.
C. the selected number is a prime number.
P(BIA)
The probabilities of the given events are:
A. P(even) = P(A) = 7/15
B. P(multiple) = P(B) = 3/15
C. P(prime) = 6/15
D. P(B|A) = 3/7
What is probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.
P(E) = n(E)/n(S)
Calculation:The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
So, n(S) = 15
A. The selected number is even:
Consider the event as A.
The set of even numbers in the given sample is {2,4,6,8,10,12,14}
So, n(A) = 7
Then, the required probability is
P(A) = n(A)/n(S)
= 7/15
B. The selected number is a multiple of 4:
Consider the event as B.
The set of multiples of 4 in the given sample is {4,8,12}
So, n(B) = 3
Then, the required probability is
P(B) = n(B)/n(S)
= 3/15
C. The selected number is prime:
Consider the event as C.
The set of prime numbers in the given sample is {2,3,5,7,11,13}
So, n(C) = 6
Then, the required probability is
P(C) = n(C)/n(S)
= 6/15
D. calculate P(B|A):
Since events B and A are dependent events of the same sample,
n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is
P(B|A) = n(A∩B)/n(A)
⇒ P(B|A) = 3/7
Learn more about the probabilities here:
https://brainly.com/question/251701
#SPJ1
f(x)=2x-6 Match each transformation of f(x) with its description
The transformation of the function is illustrated below
How to match the transformation?Parent function is: f(x) = 2x - 6
Transformations are:
shifts f(x) 4 units down
f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10
stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24
shifts f(x) 4 units right
f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14
compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6
Learn more about function on:
https://brainly.com/question/25638609
#SPJ1
A projector enlarges an image in the ratio 20:1. What will be the size of an enlargement of a picture that is 8cm by 6cm?
Answer:
160 cm × 120 cm
Step-by-step explanation:
this means 1 cm turns into 20 cm.
so, 8 cm × 6 cm becomes
8×20 = 160 cm × 6×20 = 120 cm
Write your answer as a fraction in simplest form.
-1 3/4 • 2 1/8
Please help me with this geometry question
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
HJ = 23.5 in[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Take HJ = x, GH = y and GJ = z
x = y + 2z = x + y - 17x + y + z = 73put the value of x from equation 1 in equation 2
[tex]{ \qquad❖ \: \sf \:z = (y + 2) + y - 17} [/tex]
[tex]{ \qquad❖ \: \sf \:z = 2y - 15} [/tex]
now, put the value of x and z in equation 3
[tex]{ \qquad❖ \: \sf \:y + 2 + y + 2y - 15 = 73} [/tex]
[tex]{ \qquad❖ \: \sf \:4y - 13 = 73} [/tex]
[tex]{ \qquad❖ \: \sf \:4y = 86} [/tex]
[tex]{ \qquad❖ \: \sf \:y = 21.5 \: \: in} [/tex]
Now, we need to find HJ (x)
[tex]{ \qquad❖ \: \sf \:x = y + 2} [/tex]
[tex]{ \qquad❖ \: \sf \:x = 21.5 + 2} [/tex]
[tex]{ \qquad❖ \: \sf \:x = 23.5 \: \: in} [/tex]
[tex]{ \qquad \large \sf {Conclusion} :} [/tex]
HJ = 23.5 inIf R={(1,2),(2,3),(3,9),(4,5)} find R-1
Answer:
R-1={(2,1),(3,2),(9,3),(5,4)
Step-by-step explanation:
R-1={(2,1),(3,2),(9,3),(5,4) because (- 1) means reverse in relation
SAT Math Question
Correct Answer: D
I was confused with A and D while solving this problem.
I get why D is the right answer but why is A wrong?
I'm tentatively changing my answer to say this kind of relies on practical knowledge of how stores tend to operate. If 20 coupons are given out, the store has sold all 500 shirts, arguably at a loss to the retailer. They have to have more shirts in stock to be sold at full price because, well, that's how they make money. It's more likely that such a store would carry more than just 500 shirts at the start of each day, so A is (probably) wrong.
divide the difference of 20 and 6 by the product of 7 and 2
Step-by-step explanation:
Vocabulary (what the words mean):Divide, the same as ÷
divide 6 by 3
by is the same as the symbol
6 ÷ 3 = 2
Difference, This is another way of saying take away or minus
the difference of 6 and 3 is
6 - 3 = 3
Product, This is another word for multiply or times
the product of 2 and 3 is
2 × 3 = 6
Write as an equationdivide (÷) the difference of 20 and 6 (20 - 6) by the product of 7 and 2 (7 × 2)
so
(20 - 6) ÷ (7 × 2)
can you do the rest???
How many 4-digit numbers can be created using
the digits 1, 3, 5, 7, and 9 without repeating any
digits within that 4-digit number?
Answer:
120 four digit numbers can be created from the gives.
Step-by-step explanation:
Solution
You are given 5 digits in the givens.
1 3 5 7 9
Therefore
5 * 4 * 3 * 2 is the answer to your question. 4 and 3 and 2 determine that none of the digits can be repeated. That equals 120.
if (a+10) and a are in straight line find the value of a
Answer:
a=170
Step-by-step explanation:
(a+10)=180[because being a straight line]
or, a+10=180
or,a=180-10
a=170
Therefore,a=170
Ms. Oshiro teaches her 27 students to make folded-paper birds. Each student can make about 2 birds in 1 minute. About how many birds can all the students make in 55 minutes? A 3,000 B 1,500 C 100 D 60
Answer:
The answer is 2970
Step-by-step explanation:
Collectively, all the students can make about 54 books rds per minute (27 * 2)
Therefore in 55 minutes there should be 2970
(54*55) :)
Captain's Autos sells 22 used cars on
Monday, and 18 cars on Tuesday. This was
25% of the number of sales for the week.
How many cars did they sell altogether that
week?
Answer:
160
Step-by-step explanation:
22+18=40, and this was 25% of the cars.
So, 40(4)=160 cars were sold that week.
The number of cars Captain's Autos sold in total that week is 160.
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. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Number of used car on monday= 22
Number of cars on tuesday= 18
Now,
Let's call the total number of cars sold during the week "x".
We know that the number of cars sold on Monday and Tuesday is 25% of the total number of cars sold during the week. So we can write:
22 + 18 = 0.25x
Simplifying, we get:
40 = 0.25x
Dividing both sides by 0.25, we get:
x = 160
Therefore, by the unitary method the answer will be 160.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
A photograph is 3 in. longer than it is wide. When a 2-in. border is placed around the photograph, the total area of the photograph and the border is 108 in^2. Find the dimensions of the photograph.
width = 7
length = 10
Step-by-step explanation:
solve for the one letter that gets talked about the most
which is w or width
width = w
length = 3 + w
2 inch border means
width = w + 2
length = 3 + w + 2
area = length times width
area = ( 3 + w + 2 ) times (w + 2 )
108 = ( 3 + w + 2 ) times (w + 2 )
108 = ( w + 5 ) times (w + 2 )
( w + 5 ) times (w + 2 ) = 108
w^2 + 7w +10 = 108
w^2 + 7w - 98 = 0
going to make w = x
x^2+7x-98=0
(x-7)(x+14)
x = 7
x = -14
w=7
w= -14
cant have a negative measurement so w=7 is used
width = w
length = 3 + w
width = 7
length = 3 + 7 = 10
What are the intercept of 2X+3y= 6z=30
Answers:
A (15,0,0) ,(0,27,0) ,(0,0,-5)
B (15,0,0),(0,10,0) ,(0,0,5)
C (10,0,0),(0,15,0,)(0,0,5)
D (15,0,0),(0,10,0),(0,0,-5)
The intercepts of the given equations is as given in the task content is; Choice B; (15,0,0),(0,10,0) ,(0,0,5).
What are the intercepts of the equation as give in the task content?The x-intercept of the given equation can be determined by setting values of y and z to zero.
The y-intercept can be determined by setting x and z to zero.
While the z-intercept can be determined by setting x and y to zero.
Consequently, the X-intercept of the given equations is; 2x +3(0) = 30; x = 15.
Therefore, we have; (15,0,0)
The y-intercept is therefore; 2(0) +3y = 30; 3y = 30; y = 30/3 = 10 and. we have; (0,15,0)
And hence, the z-intercept is; z = 30/6 = 5.
Read more on intercept;
https://brainly.com/question/1884491
#SPJ1
Which of the following number 1001,1002,1004 will be the sum of 994 and a 2 digit number
The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.
What is a 2-digit number?A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.
A 2-digit number is any number between 10 and 99.
According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.
1001 - 994 = 7 (1 digit)1002 - 994 = 8 (1 digit)1004 - 994 = 10 (2 digit)Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.
Learn more about number at: https://brainly.com/question/17429689
#SPJ1