Find the general solution of the given differential equation. cos^2(x)sin(x)dy/dx+(cos^3(x))y=1 g
If the given differential equation is
[tex]\cos^2(x) \sin(x) \dfrac{dy}{dx} + \cos^3(x) y = 1[/tex]
then multiply both sides by [tex]\frac1{\cos^2(x)}[/tex] :
[tex]\sin(x) \dfrac{dy}{dx} + \cos(x) y = \sec^2(x)[/tex]
The left side is the derivative of a product,
[tex]\dfrac{d}{dx}\left[\sin(x)y\right] = \sec^2(x)[/tex]
Integrate both sides with respect to [tex]x[/tex], recalling that [tex]\frac{d}{dx}\tan(x) = \sec^2(x)[/tex] :
[tex]\displaystyle \int \frac{d}{dx}\left[\sin(x)y\right] \, dx = \int \sec^2(x) \, dx[/tex]
[tex]\sin(x) y = \tan(x) + C[/tex]
Solve for [tex]y[/tex] :
[tex]\boxed{y = \sec(x) + C \csc(x)}
which follows from [tex]\tan(x)=\frac{\sin(x)}{\cos(x)}[/tex].
Choose the end behavior of the graph of each polynomial function.
Options
Falls to the left and rises to the right
Rises to the left and falls to the right
Rises to the left and rises to the right
Falls to the left and falls to the right
Using limits, the end behavior of the functions are given as follows:
a. Rises to the left and falls to the right.
b. Rises to the left and rises to the right.
c. Falls to the left and rises to the right.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In item a, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -5x^3 = -5(-\infty)^3 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -5x^3 = -5(\infty)^3 = -\infty[/tex]
Hence it rises to the left and falls to the right.
In item b, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 3x^6 = 3(-\infty)^6 = \infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 3x^6 = 3(\infty)^6 = \infty[/tex]
Rises to the left and rises to the right.
In item c, we have that, respectively, to the left and to the right.
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 20x^3 = 20(-\infty)^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 20x^3 = 20(\infty)^3 = \infty[/tex]
Falls to the left and rises to the right.
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8. How do outliers affect the mean of a data set?
OIt does not change.
It depends whether the outlier is a high outlier or a low outlier.
It decreases.
It increases.
Answer:
it depends on whether the outlier is a high outlier or a low outlier
Step-by-step explanation:
The mean of a data set is the average of the data set. So if I had the data set {5, 2, 10} the average would be (5+2+10)/3 = 5.667. Now if I added an outlier like 10,000 it would increase the mean significantly. It changes it significantly but I cannot say whether it increases or decreases it without knowing the value of the outlier, since if I had the outlier -10,000 that would decrease the mean, but I had the outlier 10,000 it would increase it. So it depends on whether the outlier is a high outlier or a low outlier
A sequence of numbers begins with 12 and progresses
geometrically. Each number is the previous number
divided by 2.
Which value can be used as the common ratio in an
explicit formula that represents the sequence?
N/H
02
06
O 12
Answer:
1/2
Step-by-step explanation:
since every time you divide by 2, the common ratio is 1/2
Betty has the option of using three types of tables in her coffee shop:
square tables with a side length of 36 inches
rectangular tables 20 inches wide and 73 inches long
round (circular) tables with a diameter of 42 inches.
Which type of table has the largest area?
a.)
Square tables
b.)
Rectangular tables
c.)
Round tables
d.)
The tables all have the same area.
Answer:
The rectangular table
Step-by-step explanation:
Square table: 36*36=1296
Rectangular table: 20*42=1460 [tex]in^{2}[/tex]
Circular table: [tex]\pi * 21^{2}[/tex]≅1384
Find the range for the given domain: {-2, -1, and 0} and the function is y = 3x2.
The range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.
What is range?
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that:-
The range for the given domain: {-2, -1, and 0} and the function is y = 3x².
The range will be the value of y at each given value of the domain.
Domain: { -2, -1, 0 }
y = 3x²
At x = -2 → y = 3 ( -2)² = 12
At x = -1 → y = 3 (-1)² = 3
At x = 0 → y = 3 (0) = 0
Therefore range of the function at domain {-2, -1, and 0} will be { 12 , 3 and 0}.
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Martin uses of a gallon of paint to cover of a wall. What is the unit rate at which Martin paints in walls per gallon?
The unit rate at which Martin paints in walls per gallon is 1 7/25 walls per gallon
Unit rateUnit rate of paint per gallon = Quantity of wall / gallon of paint
= 4/5 ÷ 5/8
= 4/5 × 8/5
= (4 × 8) / (5 × 5)
= 32/25
= 1 7/25 walls per gallon
Complete question:
Martin uses 5/8 of a gallon of paint to cover4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon
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What is the solution set for Ix+3| =5?
S-8 and s-8
s=-2 and s=2
s=-8 and s=2
s = 2 and s= 8
The area of a rectangle, A = l • w is represented by the expression 24x^6y^15. Which could be the dimensions of the rectangle?
After calculating the value, l & w could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
Calculation:The inquiry relates to the laws of indices
where, [tex]x^{a} * x^{b}=x^{a+b}[/tex]
Provided the query, A= [tex]24x^{6}y^{15}[/tex]
[tex]2* 12[/tex] might be used to calculate the length and width of 24.
Hence,
[tex]x^{6}=x^{5} * x^{1} =x^{5+1}[/tex]
& [tex]y^{15}= y^{8} * y^{7} =y^{8+7}[/tex]
So, it can be written as,
A=l * w
⇒ [tex]24x^{6}y^{15}[/tex] = [tex]2x^{5}y^{8}[/tex] * [tex]12xy^{7}[/tex]
Therefore, it is concluded that the dimensions of the rectangle could be [tex]2x^{5} y^{8}[/tex] & [tex]12x^{} y^{7}[/tex].
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Which pair of ratios makes a proportion?
A. 1/4 and 5/25
B. 1/4 and 7/24
C. 1/4 and 10/48
D. 1/4 and 9/36
Answer:
D. 1/4 and 9/36Step-by-step explanation:
If two ratios make a proportion then it can be shown as:
a/b = c/d ⇒ ad = bcLet's verify the answer choices with this method
A. 1/4 and 5/25
1*25 = 4*525 = 20, incorrect, not a proportionB. 1/4 and 7/24
1*24 = 4*7 24 = 28, incorrect, not a proportionC. 1/4 and 10/48
1*48 = 4*1048 = 40, incorrect, not a proportionD. 1/4 and 9/36
1*36 = 4*936 = 36, correct, this is a proportionAdam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours
Step-by-step explanation:
im sorry but im not sure about this question
Answer:
334.488 miles
Step-by-step explanation:
You don't have a specific request on what I should answer, if it was distance then here's your answer
Laurel has an area in her yard that is in the shape of a parallelogram. It has a base of 30 feet and a height of 22 feet. She wants to cover this area with wildflower seeds. She finds out that 1 ounce of seeds covers 125 square feet of ground. How many ounces of seeds does she need to cover this area?
Answer:
Laurel has to cover this area with 2.64 ounces of seeds.
Step-by-step explanation:
Given
Base of Parallelogram = 30ft
Height of Parallelogram = 22ft
Area of Parallelogram = 1/2*base*height
Therefore, Area of Parallelogram = 1/2*30*22
= 330sq. ft
Given
One ounce of seed covers 125 sq. ft
Hence, No. of ounces needed to cover 330 sq. ft= 330/125
= 2.64
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What value of a make the equation 14-a=19-12
[tex]14-a=19-12\\14-a=7\\a=14-7\\a=7[/tex]
Answer:
7
Step-by-step explanation:
14-a=19-12
14-a=7
14-7=a
7=a
Combine like terms
Complete the statements about the cross sections of cylinders and cones.
The cross section parallel to the base of a cone is a
The cross section parallel to the base of a cylinder is a
The cross section perpendicular to the base of a cone is a
The cross section perpendicular to the base of a cylinder is a
The cross-section parallel to the base of a cone is a circle
The cross-section parallel to the base of a cylinder is a circle
The cross-section perpendicular to the base of a cone is a triangle
The cross-section perpendicular to the base of a cylinder is a rectangle
he tables represent the functions f(x) and g(x). A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, f(x), has the entries, negative 5, negative 3, negative 1, 1, 3, 5. A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, g(x), has the entries, negative 13, negative 9, negative 5, negative 1, 3, 7. Which input value produces the same output value for the two functions?
A function assigns the values. The input value that produces the same output value for the two functions is 1.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given tables the x is the input while f(x) and g(x) are the outputs of the respective functions. Therefore, the input for which the two given functions will return the same output is 1.
Hence, the input value that produces the same output value for the two functions is 1.
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Help me please I need this for tomorrow please please
ST
6
9
10
Which phrase best describes the translation from the graph y = 2x² to the graph of y = 2x² + 5?
O 5 units up
O 5 units down
O 5 units right
O 5 units left
The answer to the question is 5 units up.
if 9^x=25, what does 3^x equal?
Answer:
[tex]3^x=5[/tex]
Step-by-step explanation:
Given:
[tex]9^x=25[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^x=25[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2x}=25[/tex]
Apply the same exponent rule:
[tex]\implies (3^x)^2=25[/tex]
Square root both sides:
[tex]\implies \sqrt{(3^x)^2}=\sqrt{25}[/tex]
[tex]\implies 3^x=5[/tex]
The distance between points A and B is 15. The coordinates of point A are (1, 18) and the
coordinates of B are (13, z). Solve for the two values of z. Show your work to prove your
answer.
Answer:
9 and 27
Step-by-step explanation:
let me know if you want an explanation
Which expression is equivalent to (startfraction 4 m n over m superscript negative 2 baseline n superscript 6 baseline endfraction) superscript negative 2? assume m not-equals 0, n not-equals 0.
The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].
From the principle of indices we get,
Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]
Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]
Multiplication, [tex]a^{mn}=(a^m)^n[/tex]
negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]
Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
Calculating we get,
[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae
[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]
[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices
[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula
Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].
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Answer:
b
Step-by-step explanation:
edge 23
Fraction
4 5/6 -2 2/7 - 1 3/14
Answer:
1.3 or 1.333333
Step-by-step explanation:
Just do it!
2
Select the correct answer.
What is the solution to the equation?
3+√3x5 = x
O A.
-2 and -7
OB.
2 and 7
O C.
-2
OD. 7
The solution to the equation is x = 7 , -2 , Option C and D is the right answer.
What is an Equation ?An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.
It is given that the equation is
[tex]\rm 3 +\sqrt{3x - 5}= x[/tex]
Taking square on both sides
3x-5 = (x-3)²
3x-5 = x² +9 -6x
x² -9x -14 = 0
x² -7x +2x -14 = 0
x(x-7) +2(x-7) = 0
(x-7)(x+2) = 0
x =7 , x = -2
Therefore the solution to the equation is x = 7 , -2 , Option C and D is the right answer.
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Two open cylinders have the same radius but one is twice as long as the other.
a) Calculate the volume of the two cylinders and compare them using a final statement (sentence).
b) Calculate the surface area of the two cylinders and compare them using a final statement (sentence). If you notice a relationship between volume and surface area,add it to your final
statement. (God bless anyone who can help me ).
Answer:
shown below
Step-by-step explanation:
a) V = h(pi)r²
let x = height
and c = the constant radius
V1 = 2x(pi)c²
V2 = x(pi)c²
let c = random number, such as 2
let x = 3
2x(pi)4
x(pi)4
pi(4) = 12.57
3 x 12.57 = 37.7
6 x 12.57 = 75.4
We can compare these ans realise that the cylinder with double the height will also have double the volume.
b) SA = h(pi)2c
SA1 = 2x(pi)2c
SA2 = x(pi)2c
let c = 2
let x = 3
2(3)(pi)(2(2))
6(pi)4
24(pi)
3(pi)(2)(2)
3(pi)(4)
12(pi)
I don't need to finish the calulation to see that this is also halved. So the surface area of the one with the double length is twice the surface area of the one with a smaller height.
Comparatively, both the volume and surface area are doubled when the height is doubled.
QED.
Reposting this question since no one helped last time
Answer:
450 N
Step-by-step explanation:
Since you have the VOLUME and the HEIGHT of the prism, you can calculate the AREA of the prism base :
18 m^3 / 3 m = 6 m^2 area
Now you are given pressure = force / area
75 n/m^2 = force / 6 m^2
6 *75 = force = 450 N
Answer:
450 newtons
Step-by-step explanation:
To solve for the force, we first need to find the area. (Force = Pressure × Area)
[tex]Area = \frac{volume}{height} = \frac{18m^{3} }{3m} = 6m^{2}[/tex]
Now we just substitute this number into [tex]Force = Pressure * Area[/tex] and get that [tex]Force = 75newtons/m^{2} * 6m^{2} = 450 newtons[/tex]
(p.s. Units are very important! This question doesn't require any unit
conversions, but others might.)
Five hundred ten of 650 high school students said that pizza was their favorite food in the school cafeteria.
what is the margin of error? round to four decimal places.
0.0005
0.0003
0.0161
0.0322
If Five hundred ten of 650 high school students said that pizza was their favorite food. The margin of error is 0.0322.
Margin of errorGiven:
Sample proportion=Five hundred ten=510
Sample size=650
Hence:
Margin of error=z×√p×(1-p)/n
Margin of error=2√510/650× (1-510/650)÷650
Margin of error=2√0.78461538×(1-0.78461538)÷650
Margin of error=2√0.78461538×0.21538462÷650
Margin of error=2√0.168994085÷650
Margin of error=2√0.0002599909
Margin of error=0.0322
Therefore the correct option is D.
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If 5 men or 10 women can complete any work in 50 days. Than in how many days 8 men and 4 women complete that whole work?
Firstly, let’s assume the the whole capacity the work requires is 1.
Then, let’s see how 1 man can do in 50 days: 1/5.
Further, let’s see how 1 man can do in 1 day : 1/(5×50) = 1/250.
Similarly, let’s see how 1 woman can do in 1 day: 1/(10×50) = 1/500.
Now, we have 8 men, and they can do 8*1/250 in 1 day, which is 4/125.
Besides, we have 4 women, and they can do 4×1/500 in 1 day, which is 1/125.
Therefore, all people we have can do 4/125 + 1/125 of the work in 1 day, which is 1/25.
As a result, the work takes 1/(1/25)= 25 days.
Help me with steps please!
Answer:
18, 36, 54
Step-by-step explanation:
Find the least common multiple of 6 and 9:
Multiples of 6: 6, 12, 18, ......
Multiples of 9: 9, 18, 27, ......
We see that 18 is the least common multiple of 6 and 9.
Additional multiples of 18 are 36 and 54.
If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.
How to estimate an integer which is divisible by 6 and by 9?Consider the statement as a contradiction.
The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.
Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product [tex]$2 \times 3 \times 3=18$[/tex] exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of [tex]$2 \times 2 \times 3 \times 3=36$[/tex] which exists also not divisible by 54.
Therefore, the correct answer is option e) 54.
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A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids.
A hexagon is shown. The hexagon is comprised of 2 congruent isosceles trapezoids. The bases of the trapezoid have lengths of 5 and 8. The height of the trapezoid is 3.
The volume of the prism is 234 cubic units. What is the height of the prism?
3 units
4 units
6 units
8 units
Answer:
the answer is 4 units im pretty sure
Step-by-step explanation:
The height of the prism is 6 units.
The correct option is C.
What is a prism?A prism is a polyhedron in three dimensions with two identical ends.
To find the height of the prism, we need to use the formula for the volume of a prism, which is:
Volume = Base area x Height
Since the prism has two congruent hexagonal bases, we can find the base area by adding the areas of the two congruent isosceles trapezoids.
The area of an isosceles trapezoid is given by the formula:
Area = ((b1 + b2) / 2) x h
where b1 and b2 are the lengths of the two parallel bases, and h is the height of the trapezoid.
In this case, the two parallel bases have lengths of 5 and 8, and the height of each trapezoid is 3, so the area of one trapezoid is:
Area = ((5 + 8) / 2) x 3 = 19.5 square units
The base area of the prism is then:
Base area = 2 x 19.5 = 39 square units
We are given that the volume of the prism is 234 cubic units, so we can use the formula for the volume of a prism to find the height:
Volume = Base area x Height
234 = 39 x Height
Height = 6 units
Therefore, the height of the prism is 6 units.
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Find the y-intercept and the slope of the line.
6x-2y=5
Answer:
m=3
b=(0,5)
Step-by-step explanation:
Make "t" subject by algebra:-
s=ut+at2