Answer:
[tex]y = -4ln(x^3 - 9x + 3) + C\\[/tex]
Step-by-step explanation:
Given the differential equation [tex]\frac{dy}{dx} = \frac{36-12x^2}{x^3-9x+3}\\ \\[/tex], we will use the variable separable method to solve the differential equation as shown;
[tex]\frac{dy}{dx} = \frac{36-12x^2}{x^3-9x+3}\\ \\dy = \frac{36-12x^2}{x^3-9x+3}dx\\ \\\\\\integrate \ both \ sides\\\\\int\limits dy = \int\limits\frac{36-12x^2}{x^3-9x+3}dx\\ \\\\using\ substitution\ method \ to \ solve \ RHS\\\\\int\limits\frac{36-12x^2}{x^3-9x+3}dx\\\\let \ u = x^3-9x+3; du/dx = 3x^2-9\\\\dx = du/3x^2-9\\\\\int\limits\frac{36-12x^2}{x^3-9x+3}dx\\\\ = \int\limits\frac{36-12x^2}{u}*\frac{du}{3x^2-9} \\\\= \int\limits\frac{12(3-x^2)}{u}*\frac{du}{3(x^2-3)}\\\\[/tex]
[tex]= \int\limits\frac{-12(x^2-3)}{u}*\frac{du}{3(x^2-3)}\\\\= -4\int\limits \frac{du}{u}\\ = -4lnu + C\\= -4ln(x^3 - 9x + 3)[/tex]
The differential solution becomes:
[tex]y = -4ln(x^3 - 9x + 3)[/tex][tex]+C[/tex]
Find the values for k so that the intersection of x=2k and 3x+2y=12 lies in the first quadrant.
Answer:
Values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.
Step-by-step explanation:
Given two lines:
[tex]x=2k[/tex] and
[tex]3x+2y=12[/tex]
To find:
Values of 'k' such that the intersection of given two lines lie in the first quadrant.
Solution:
In 1st quadrant, the values of [tex]x[/tex] and [tex]y[/tex] both are positive.
So, let us find out intersection of the two lines.
Intersection of the two lines can be found by solving the two equations for the values of [tex]x[/tex] and [tex]y[/tex].
Given that [tex]x=2k[/tex] to be in the first quadrant, the value of k must be positive.
Let us put [tex]x=2k[/tex] in the equation [tex]3x+2y=12[/tex] to find the intersection point.
[tex]3 \times 2k + 2y=12\\\Rightarrow 6k+2y=12\\\Rightarrow 2y=12-6k\\\Rightarrow \bold{y=6-3k}[/tex]
For y to be positive:
[tex]6 - 3k \geq 0\\\Rightarrow 3k \leq 6\\\Rightarrow k \leq 2[/tex]
So, values of k can be 0, 1, or 2 such that intersection of the given lines lie in the 1st quadrant.
If each square in the grid has a side length of 8 mm, what is the width of the rectangle? Do not include units (mm) in your answer. Type your answer below as a number (example: 5, 3.1, 4 1/2, or 3/2)
Answer:
See Explanation
Step-by-step explanation:
The question required attachment; however, follow the following steps to answer your question.
See Attachment
Considering the horizontal plane of the gird.
Count the number of the squares in that plane;
This gives 4
Multiply 4 by length of each side of a square;
[tex]Perimeter = 8mm * 4[/tex]
[tex]Perimeter = 32mm[/tex]
Mitchell travels from the US to Canada, where he exchanges 150 US dollars for Canadian dollars. He then spends 20 Canadian dollars, returns to the US, and exchanges the remaining money back to US dollars. How many US dollars does Mitchell have remaining? 129.46 130.00 130.66 134.59
Answer: $130.66
Step-by-step explanation:
Answer:
130.66
Step-by-step explanation:
i took the asignment
Let F(x, y, z) = 3xi+ 2yj and let σ be the cube with opposite corners at (0, 0, 0) and (5, 5, 5), oriented outwards. Find the flux of the flow field F across σ.
Use the divergence theorem,
[tex]\displaystyle\iint_{\partial\sigma}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\iiint_\sigma\mathrm{div}\mathbf F(x,y,z)\,\mathrm dV[/tex]
We have
[tex]\mathrm{div}\mathbf F(x,y,z)=\dfrac{\partial(3x)}{\partial x}+\dfrac{\partial(2y)}{\partial y}+\dfrac{\partial0}{\partial z}=5[/tex]
so that the flux across [tex]\sigma[/tex] is equal to 5 times the volume of the cube. The cube itself has edge length 5, so its volume is [tex]5^3=125[/tex], making the flux [tex]5^4=\boxed{625}[/tex].
Find sin 2x, cos 2x, and tan 2x from the given information. sin x = -3/5, x in quadrant 3.
Answer:
[tex]\sin 2x = \frac{24}{25}[/tex] , [tex]\cos 2x = \frac{7}{25}[/tex], [tex]\tan 2x = \frac{24}{7}[/tex]
Step-by-step explanation:
The sine, cosine and tangent of a double angle are given by the following trigonometric identities:
[tex]\sin 2x = 2\cdot \sin x \cdot \cos x[/tex]
[tex]\cos 2x = \cos^{2}x -\sin^{2}x[/tex]
[tex]\tan 2x = \frac{2\cdot \tan x}{1-\tan^{2}x}[/tex]
According to the definition of sine function, the ratio is represented by:
[tex]\sin x = \frac{s}{r}[/tex]
Where:
[tex]s[/tex] - Opposite leg, dimensionless.
[tex]r[/tex] - Hypotenuse, dimensionless.
Since [tex]x[/tex], measured in sexagesimal degrees, is in third quadrant, the following relation is known:
[tex]s < 0[/tex] and [tex]y < 0[/tex].
Where [tex]r[/tex] is represented by the Pythagorean identity:
[tex]r = \sqrt{s^{2}+y^{2}}[/tex]
The magnitude of [tex]y[/tex] is found by means the Pythagorean expression:
[tex]r^{2} = s^{2}+y^{2}[/tex]
[tex]y^{2} = r^{2}-s^{2}[/tex]
[tex]y = \sqrt{r^{2}-s^{2}}[/tex]
Where [tex]y[/tex] is the adjacent leg, dimensionless.
If [tex]s = -3[/tex] and [tex]r = 5[/tex], the value of [tex]y[/tex] is:
[tex]y = \sqrt{(5^{2})-(-3)^{2}}[/tex]
[tex]y = -4[/tex]
Then, the definitions for cosine and tangent of x are, respectively:
[tex]\cos x = \frac{y}{r}[/tex]
[tex]\tan x = \frac{s}{y}[/tex]
If [tex]s = -3[/tex], [tex]y = -4[/tex] and [tex]r = 5[/tex], the values for each identity are, respectively:
[tex]\cos x = -\frac{4}{5}[/tex] and [tex]\tan x = \frac{3}{4}[/tex].
Now, the value for each double angle identity are obtained below:
[tex]\sin 2x = 2\cdot \left(-\frac{3}{5} \right)\cdot \left(-\frac{4}{5} \right)[/tex]
[tex]\sin 2x = \frac{24}{25}[/tex]
[tex]\cos 2x = \left(-\frac{4}{5} \right)^{2}-\left(-\frac{3}{5} \right)^{2}[/tex]
[tex]\cos 2x = \frac{7}{25}[/tex]
[tex]\tan 2x = \frac{2\cdot \left(\frac{3}{4} \right)}{1-\left(\frac{3}{4} \right)^{2}}[/tex]
[tex]\tan 2x = \frac{24}{7}[/tex]
Use the Distance Formula to find the distance between the two points in polar coordinates. (Round your answer to one decimal place.) (8, 0.2), (9, 1.7)
Answer:
Distance= 1
Step-by-step explanation:
Distance be points using polar coordinates
Distance= √(8² +9² -2(8)(9)cos(0.2-1.7)
Distance=√(64 + 81-(144)cos(-1.5))
Distance= √(145-143.9506)
Distance=√ 1.0493
Distance= 1.0243
Distance= 1
Marcus bought w childrens's movie tickets for $5 each and n adult's movie tickets for $11 each. Write an algebraic expression for total amount Marcus spent.
Answer:
5w+11n
:D
Hope this helped!
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Which of the following numbers is not a
prime number?
A. 2
C. 11
B. 3
D. 27
Answer:
27, it is divisible by 1, 3, 9, and 27
Step-by-step explanation:
The advertised weight of a Snickers Fun Size bar is 17 grams. What proportion of candy bars in this sample weigh less than advertised
Answer:
0.412
Step-by-step explanation:
Given the stem plot figure out which ones are below 17g.
So: 7g / 17g = 0.412 which is the proportion
Question 1
Solve the equation.
-9h= - 27
Answer:
h=3
Step-by-step explanation:
-9h= - 27
Divide each side by -9
-9h/-9= - 27/-9
h = 3
Answer:
h = 3
Step-by-step explanation:
Step 1: Divide both sides by -9
[tex]\frac{-9h}{-9} =\frac{-27}{-9} \\h=3[/tex]
Therefore the h = 3
What is “35 is 60% of what number?”
Answer:
58.33
Step-by-step explanation:
35 isn't exactly 60% of an number but by rounding you will get 58.33
The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of
the completely inflated balloon is 784 cm², how long will it take for the balloon to fully inflate?
Use SA=4r2
7 seconds
10 seconds
49 seconds
196 seconds
Answer:
7 seconds
Step-by-step explanation:
The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second.
surface area of the completely inflated balloon is 784 cm²
SA=4r²
784= 4r²
784/4= r²
196 = r²
14cm = r
Yhe radius of the complete inflated balloon is 14cm
If the ball inflate at the rate of 2 cm per seconds
Then it took 14/2 = 7 seconds to inflate fully
Will give brainiliest to whoever answers it and gives it step by step please help me
Answer:
The first blank is 6.
The second blank is 7.
Step-by-step explanation:
The square root of 41 is between 6 and 7.
6 square is 36
7 square is 49.
So, the square root of 41 should be between 6 and 7.
The first blank is 6.
The second blank is 7.
Two angles of a triangle measure 12º and 40°.
What is the measure of the third angle of the triangle?
A. 38°
B. 48°
C. 128°
D. 308
Answer:
12+40= 52
180-52=128
Step-by-step explanation:
Angles in a triangle add up to 180
so if two sides are given , they must be added and subtracted from 180.
which gives us 180-52=128
Answer:
the angle is 128°
the right answer is C
Step-by-step explanation:
the angles of a triangle are always 180°
thus
the angle of the the triangle = 180° - (12°+40°)
= 180- 52° = 128°
Y A chemist can purchase a 10% saline solution in 500 cubic centimeter containers, a 20% saline solution in 500 cubic centimeter containers, and a 50% saline solution in 1,000 cubic centimeter containers. He needs 12,000 cubic centimeters of 30% saline solution. How many containers of each type of solution should he purchase in order to form this solution
Step-by-step explanation:
ultimately you need to end up with 30% solution
with 10%, 20%, and 50%, you are forced to tamper with the various percentages to reach the desired goal.
Since it is an even 12,000 (i.e. no 12500) and you have no hard container volumes to deal with, therefore find the easiest combination to reach 30%. In this case, (10%+50%)/2 = 30%
So therefore you need 12000 cubic centimeters of liquid, half of it being 50% and half being 10%.
12000/2 = 6000 cubic centimeters each
for 50%, each container is 1,000 cubic centimeters, so 6000/1000 =6 containers for 10% each container is 500 cubic centimeters, so 6000/500 = 12 containers
Therefore, you need 6 containers of 50% solution and 12 containers of 10% solution.
PLEASE HELP (05.04 LC) The image below is a triangle drawn inside a circle with center O: (5 points) Which of the following expressions shows the area, in square inches, of the circle? (π = 3.14) Select one: a. 3.14 ⋅ 2 b. 3.14 ⋅ 3 c. 3.14 ⋅ 22 d. 2 ⋅ 3.14 ⋅ 22
Answer:
The area of the circle is:
[tex]3.14\, *\,2^2 \,\,in^2[/tex]
Step-by-step explanation:
If the diameter of the circle is 4 inches, then its radius is half of that (that is 2 inches), and we can use the formula for the area of a circle:
[tex]Area=\pi\,R^2\\Area= \pi\,(2\,\,in)^2\\Area=3.14\,(4)\,in^2[/tex]
The area of the circle is : [tex]3.14\, *\,2^2 \,\,in^2[/tex]
A local gym has 2 types of cardio machines, treadmills and elliptical machines. There are 38 cardio machines in all. There are 10 more treadmills than there are elliptical machines. How many elliptical machines are at the gym? 9 elliptical machines 14 elliptical machines 24 elliptical machines 28 elliptical machines
Answer:
14 elliptical machines
Step-by-step explanation:
t = # of treadmills
e = # of elliptical machines
t + e = 38
t = e + 10
Substitute:
e + 10 + e = 38
2e = 28
e = 14
At the dairy farm, two cows produce enough milk to fill 7 equal sized buckets. Each cow produces the same amount of milk. What is the rate per bucket per cow?
Answer:
3.5 buckets per cow
Step-by-step explanation:
Given
[tex]Buckets = 7\ equal\ sized[/tex]
Required
Determine the rate per bucket per each cow
From the question, we understand that both cows produced same quantity of milk;
And since, they're are two cows
Milk produced by each cow is calculated by dividing number of buckets by 2; as follows;
[tex]Each\ cow = \frac{7}{2}\ buckets[/tex]
[tex]Each\ cow = 3.5\ buckets[/tex]
Hence, the rate is 3.5 buckets per cow
Daniel says that when the irrational number 7√3 is multiplied by any rational number, the product is always an irrational number. What value for the rational number disproves Daniel's claim?
Answer: 0
============================================
Explanation:
When we multiply 0 by any number, we get 0 as a result
x*0 = 0
0*x = 0
for any number x.
The number 0 is rational since we can write it as a fraction of two integers
0 = 0/1
If Daniel were to correct his statement to say "multiply by any nonzero rational number", then his statement would be correct that the result is irrational.
----------------------------------------------
Extra info:
Here's a proof showing why Daniel's claim is correct if we consider nonzero rational numbers
Let p be a nonzero rational number, so p = a/b for integers a,b where neither a or b are zero
Let q be an irrational number. We cannot write q as a ratio of two integers
The claim is that p*q is irrational. For now let's assume the opposite. So assume p*q is rational. This means p*q = r/s for integers r,s
This would be the same as (a/b)*q = r/s which solves to q = (r/s)*(b/a) = (rb)/(sa) making q rational, but that contradicts the fact we made q irrational earlier.
Therefore, the assumption p*q is rational cannot be the case, and p*q must be irrational.
If there were 1,000 cars in a line with an average car length of 10.8 feet, how long would the line be in feet? Assume that the cars are lined up bumper-to-bumper.
Answer:
10,800 feet
Step-by-step explanation:
1000 * 10.8 because there are 1000 cars each 10.8 feet long
Need Help This Is A Tricky One
Answer:
28th floor........
Step-by-step explanation:
...
Answer:
28
Step-by-step explanation:
current position: 9
down 4 floors: 9-4 = 5
up 7 floors: 5+7 = 12
up 8 floors: 12+8 = 20
up 8 floors: 20+8 = 28
A population has a standard deviation of 50 A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is:_________.
a. 5
b. 9.8
c. 650
d. 609.8
Answer:
B. 9.8Step-by-step explanation:
The formula for calculating the margin of error is expressed as shown;
Margin of error = Z * S/√n
Z is the z-score at 95% confidence interval = 1.96
S is the standard deviation = 50
n is the sample size = 100
Substituting this values into the formula above;
Margin of error = 1.96 * 50/√100
Margin of error = 1.96 * 50/10
Margin of error = 1.96 * 5
Margin of error = 9.8
Hence the margin of error is 9.8
Emma jogs 2 miles along the beach in 1 3 of an hour. If she travels at a constant rate, how far will she jog in an hour? 1. Use the known information to write a rate.
Answer:oufonsrgonsrgnrsosgnsogwo0on93rhskgv oaoef
Step-by-step explanation:
iaeiuaefiaef ebf efa fcade emma jog 123e oefofoinsfnfsaefosefnhsfnalnfaogh
The within-subjects F is the non-independent groups equivalent of the one-way ANOVA. True or False?
Answer: True.
Step-by-step explanation:
The one-way analysis of variance usually (abbreviated as one-way ANOVA). is a method that is used to compare the means of two or more samples ( by make use of the F distribution). This method only applies to numerical response data, the "Y", usually one variable, and numerical or (usually) categorical input data, the "X", always one variable, hence the reason it’s know as "one-way" beca it takes it account one variae at a time.
(4x-x^3+3)-(2x^2-3x^3+1)
Answer:
2 (x^3 - x^2 + 2 x + 1)
Step-by-step explanation:
Simplify the following:
-(2 x^2 - 3 x^3 + 1) - x^3 + 4 x + 3
Factor -1 out of -3 x^3 + 2 x^2 + 1:
--(3 x^3 - 2 x^2 - 1) - x^3 + 4 x + 3
(-1)^2 = 1:
3 x^3 - 2 x^2 - 1 - x^3 + 4 x + 3
Grouping like terms, 3 x^3 - x^3 - 2 x^2 + 4 x - 1 + 3 = (-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1):
(-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1)
3 x^3 - x^3 = 2 x^3:
2 x^3 - 2 x^2 + 4 x + (3 - 1)
3 - 1 = 2:
2 x^3 - 2 x^2 + 4 x + 2
Factor 2 out of 2 x^3 - 2 x^2 + 4 x + 2:
Answer: 2 (x^3 - x^2 + 2 x + 1)
Answer:
Step-by-step explanation:
4x - x^3 + 3 - 2x^2 + 3x^3 - 1
2x^3 - 2x^2 + 4x + 2 is the solution
what is 1/4 divided by 3/8
Answer: 2/3
Step-by-step explanation:
Answer: 2/3
Step-by-step explanation:It can sometimes be difficult to divide fractions, such as 1/4 divided by 3/8. When we divide two fractions, such as 1/4 ÷ 3/8, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.
5. A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci. a) In testing the scientist's belief, write the appropriate hypotheses at 0.05 level of significance.
Complete Question
A scientist believes the concentration of radon gas in the air is greater that the established safe level of 4 pci or less. The scientist tests the composition for 36 days finding an average concentration of 4.4 pci with a sample standard deviation of 1 pci.
a) In testing the scientist's belief, write the appropriate hypotheses:
[tex]H_o:[/tex] Ha:
b) What decision should be made?
Answer:
a
The null hypothesis is [tex]H_o : \mu \le 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
b
There is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 4 \ pci[/tex]
The sample size [tex]n = 36 \ days[/tex]
The sample mean is [tex]\= x = 4.4 \ pci[/tex]
The standard deviation is [tex]\sigma = 1 \ pci[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 4 \ pci[/tex]
The alternative hypothesis is [tex]H_a : \mu > 4 \ pci[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t = \frac{ 4.4 - 4 }{ \frac{ 1}{ \sqrt{36} } }[/tex]
=> [tex]t =2.4[/tex]
The p-value is mathematically represented as
[tex]p-value = P(Z > 2.4 )[/tex]
From the z-table
[tex]P(Z > 2.4 ) = 0.008[/tex]
[tex]p-value =0.008[/tex]
So from this obtained value we see that
[tex]p-value < \alpha[/tex] so we reject the null hypothesis
Hence we can conclude that there is sufficient evidence to conclude that the concentration of radon gas in the air is greater that the established safe level of 4pci or less
Find the scale ratio for the map described below 1 mm (map) = 50 km (actual) The scale ratio is 1 to ?
Answer:
1 : 50,000,000
Step-by-step explanation:
The given scale (with units) is ...
1 mm : 50 km
If we convert both units to meters, so we can give the scale as a pure number, then we have ...
10^-3 m : 5×10^4 m = 1 : 5×10^7 = 1 : 50,000,000
The values in the following matrix are treatment means from a two-factor study. One of the means is missing. What value for the missing mean would result in no main effect for Factor A?
B1 B2
A1 6 8
A2 12 ?
a. 14
b. 10
c. 12
d. 2
(Please explain)
Answer: D) 2
the value for the missing mean would result in no main effect for Factor A is 2
Step-by-step explanation:
Given that;
B1 B2
A1 6 8
B1 12 ?
To find the missing mean;
lets missing mean be x
Here mean of A1
( 6 + 8 ) / 2 = 14 / 2 = 7
Now mean of A2
(12 + x ) / 2 = 7
x + 12 = 14\x = 14 -12 = 2
Therefore the value for the missing mean would result in no main effect for Factor A is 2
so option d) is the correct answer
Answer:
b
Step-by-step explanation:
Solve the following
(q+9)/5 +8Q = 11 - Q
Answer:
mark it as brainlist plzz