The differential equation
dy/dx = x sin(x ²) / y
is separable as
y dy = x sin(x ²) dx
Integrate both sides:
∫ y dy = ∫ x sin(x ²) dx
∫ y dy = 1/2 ∫ 2x sin(x ²) dx
∫ y dy = 1/2 ∫ sin(x ²) d(x ²)
1/2 y ² = -1/2 cos(x ²) + C
Solve for y implicitly:
y ² = -cos(x ²) + C
Given that y = 1 when x = 0, we get
1² = -cos(0²) + C
1 = -cos(0) + C
1 = -1 + C
C = 2
Then the particular solution to the DE is
y ² = 2 - cos(x ²)
Solving explicitly for y would give two solutions,
y = ± √(2 - cos(x ²))
but only the one with the positive square root satisfies the initial condition:
√(2 - cos(0²)) = √1 = 1
-√(2 - cos(0²)) = -√1 = -1 ≠ 1
So the unique solution to this DE is
y = √(2 - cos(x ²))
i need to find the area of a rectangle using the formula A=b*h the height is 810 cm the base is 10 meters...i know i need to convert, but how do i set up the equation to gigute/work this this out?
Answer:
81000[tex]cm^{2}[/tex] or 8.1[tex]m^{2}[/tex]
Step-by-step explanation:
1m = 100cm
10m = 1000cm
a= b*h
a= 1000cm * 810cm
= 810000[tex]cm^{2}[/tex]
1[tex]m^{2}[/tex] = 10000[tex]cm^{2}[/tex]
810000[tex]cm^{2}[/tex] = 8.1[tex]m^{2}[/tex]
Sarah bought a pair of shoes that were $64 but we’re on sale for $46 sales tax is 6% how much does she pay for the shoes
Answer:
43,24$
Step-by-step explanation:
46$ — 100%
x$ — 6%
46 · 6/100
2,76$
46$ - 2,76$ = 43,24$
I don't know if this helps
Simplify the expression:
10+10v–10+10v
Answer:
20v
Step-by-step explanation:
answer
20 v. hope helpful answer. 10+10v-10+10 =20
A bakery offers a sale price of $2.80 for 6 muffins. What is the price per dozen?
The price per dozen muffins is
Answer:
$5.60 or 5.52
Step-by-step explanation:
Step one multiply 2 to 2.80 (Since 6 muffins cost $2.80, a dozen should be 6 times 2. Because a dozen is 12, so half of a dozen is 6, and multiply half by 2 and, you will get the answer.)
[tex]2 \times 2.80 = 5.60[/tex]
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds. a) What is the probability that a drum meets the guarantee
Answer:
0.6844 = 68.44% probability that a drum meets the guarantee.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 101.8 pounds and a standard deviation of 3.76 pounds.
This means that [tex]\mu = 101.8, \sigma = 3.76[/tex]
What is the probability that a drum meets the guarantee?
Probability of at least 100 lbs of solvent, which is 1 subtracted by the p-value of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 101.8}{3.76}[/tex]
[tex]Z = -0.48[/tex]
[tex]Z = -0.48[/tex] has a p-value of 0.3156.
1 - 0.3156 = 0.6844
0.6844 = 68.44% probability that a drum meets the guarantee.
anyone could help a little?
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Answer:
a) 100
b) 15 miles
Step-by-step explanation:
Each small square on the graph represents 1 person.
a) To the right of distance = 30 miles, there are 4 groups of 25 small squares, so 100 people travel 30+ miles.
__
b) To the right of distance = 15, there are (11 +6×5)×5 = 205 small squares. That is 205 people travel more than 15 miles to work. Sam may travel about 15 miles to work.
Explain how System becomes equivalent to System 2.
System 1:
Ax + By = C
LX + My = N
System 2:
Ax + By = C
(A-L)X+(B-M)y=C-N
O The first equation in System 1 is the sum of the equations in System 2. The second equation in System 2 is the first equation in System 2.
O The first equation in System 1 is the difference of the equations in System 2
The second equation in System 1 is the first equation in System 2
© The second equation in System 2 is the sum of the equations I System 1. The first equation in System
is the first equation in System 1.
• The second equation in System
the difference of the equations in System 1. The first equation in System 2 is the first equation in System
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Answer:
D
Step-by-step explanation:
The first equation of System 2 is the first equation of System 1.
The second equation has an x-coefficient of (A-L). The coefficients of x in System 1 are A and L, so (A-L) is their difference. The second equation of System 2 is the difference of the equations in System 1.
__
This is described by Choice D:
The second equation in System 2 is the difference of the equations in System 1. The first equation in System 2 is the first equation in System 1.
Given the function f(x) = 0.5|x - 4| + 6, for what values of x is f(x) = 7
Answer:
6 or 2
Step-by-step explanation:
f(x) = 0.5|x - 4| + 6
0.5|x - 4| + 6 = 7
0.5|x - 4| = 7-6
0.5|x - 4| = 1
|x - 4| = 2
x -4 = ± 2
x-4 = 2 ==> x = 6
x-4 = -2 => x = 2
so the value of x = 6 or 2
Which conversions from scientific notation to standard notation are true? Select the four correct answers
The options are missing, so i have attached them.
Answer:
options B, E, G & H are correct.
Step-by-step explanation:
A) We are given;
1.71 × 10³ = 0.00171
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point to the right of 1.71 three times because the exponent is 3.
Thus, the proper conversion is;
1.71 × 10³ = 1710
B) We are given;
8.05 × 10^(5) = 805000
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point five times to the right of 8.05 because the exponent is 5.
Thus, the proper conversion is;
8.05 × 10^(5) = 805000
C) We are given;
2.4 × 10⁴ = -24000
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point four times to the right of 2.4 because the exponent is 4.
Thus, the proper conversion is;
2.4 × 10⁴ = 24000
D) We are given;
8.25 × 10^(-3) = -8250
For this conversion, the exponent attached to 10 is negative. This means we will have to move the decimal point three times to the left of 8.25 because the exponent is -3.
Thus, the proper conversion is;
8.25 × 10^(-3) = 0.00825
E) We are given;
7.09 × 10^(-6) = 0.00000709
For this conversion, the exponent attached to 10 is negative. This means we will have to move the decimal point six times to the left of 7.09 because the exponent is -6.
Thus, the proper conversion is;
7.09 × 10^(-6) = 0.00000709
F) We are given;
3.99 × 10^(5) = 300,099
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point five times to the right of 3.99 because the exponent is 5.
Thus, the proper conversion is;
3.99 × 10^(5) = 399,000
G)We are given;
8 × 10^(7) = 80,000,000
For this conversion, the exponent attached to 10 is positive. This means we will have to move the decimal point seven times to the right of 8 because the exponent is 7.
Thus, the proper conversion is;
8 × 10^(7) = 80,000,000
H) We are given;
1.03 × 10^(-4) = 0.000103
For this conversion, the exponent attached to 10 is negative. This means we will have to move the decimal point four times to the left of 1.03 because the exponent is -4.
Thus, the proper conversion is;
1.03 × 10^(-4) = 0.000103
Looking at all the options as well as the proof I got, only options B, E, G & H are correct.
I need help with this math problem please
Answer:
C) 3(x+7)²
Step-by-step explanation:
Answer:
A) (3x + 21)(x + 7)
Step-by-step explanation:
If we look at the equation we can see that it is a quadratic equation, therefore we can factor it in the following way...
[tex]3x^{2} + 42x + 147 = 3x^{2} + 21x + 21x + 147 = 3x(x + 7) + 21(x + 7) = (3x + 21)(x + 7)[/tex]
Therefore the answer is A)
A tree with a height of 8 ft casts a shadow 14 feet long on the ground. How high is another tree that casts a shadow which is 21 feet long?
Answer:
12
Step-by-step explanation:
Do 8 divided by 14 =0.571428571
times that by 21 = 12
Write a story to match the equation x + 2 1/2 = 10 . Explain what x represents in your story. Solve the equation. Explain or show your reasoning.
x + 2 1/2 = 10
x + 0.5 = 10
x = 9.5
Someone donated 2 toys and one-half of a toy. Someone donated a random out of toys and we had 10 toys in total.
x equal that mystery amount of toys that were dontated.
What are the domain and range of the function hx) = 5x+3+1?
-10
8
2.
-10
6
4
-8
10
- 2
6
s
-10
O domain: all real numbers greater than 1
range: all real numbers
O domain: all real numbers
Step-by-step explanation:
domain : i think is x > 4/3
range : y >4
A tire on a car has an outside diameter of 3 6.90 inches what angle in radians does the tire turn while traveling 1 mile
Answer:
well... uhm...its...uhm... 39.9
Step-by-step explanation:
Write an equation for the following problem,
"Ross decides to go ice skating with his friends.
The rink charges $8 to rent skates and $7.50 for
each hour. Write an equation to find the total
cost (C) if he skates for 3 hours.?"
Answer:
c= $8 +($7.50×3)
Step-by-step explanation:
The number of adults at an amusement park, measured in hundreds of people, is represented by the function a(w)=−0.4w^2+5w+9, where w is the number of weeks since the amusement park opened for the season.
The number of children at the same amusement park, measured in hundreds of people, is represented by the function c(w)=−0.2w^2+9w+12, where w is the number of weeks since the amusement park opened for the season.
What function, f(w) , can be used to determine how many more children than adults are at the amusement park any week during the season?
Answer:
0.2w^2+4w+3
Step-by-step explanation:
a(w)=−0.4w^2+5w+9
c(w)=−0.2w^2+9w+12
We want to find the how many more children than adults
f(w) = c(w) - a(w)
= −0.2w^2+9w+12 - ( −0.4w^2+5w+9)
Distribute the minus sign
= −0.2w^2+9w+12 +0.4w^2-5w-9
Combine like terms
= 0.2w^2+4w+3
An electronics firm claims that the proportion of defective units of a certain process is 5%. A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot. On a particular occasion, the bury found 5 items defective. a) What is the probability of this occurrence, given that the claim of 5% defective is correct
Answer:
0.0006 = 0.06% probability of this occurrence
Step-by-step explanation:
For each unit, there are only two possible outcomes. Either it is defective, or it is not. The probability of an unit being defective is independent of any other unit, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
An electronics firm claims that the proportion of defective units of a certain process is 5%.
This means that [tex]p = 0.05[/tex]
A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot.
This means that [tex]n = 15[/tex]
a) What is the probability of this occurrence?
Probability of 5 defective items, whch is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.05)^{5}.(0.95)^{10} = 0.0006[/tex]
0.0006 = 0.06% probability of this occurrence
math
A hemispherical tank is filled with water and has a diameter of 4 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?
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Answer:
1046 pounds
Step-by-step explanation:
The volume of the hemisphere is given by the formula ...
V = 2/3πr³
where r is the radius, or half the diameter.
The radius is (4 ft)/2 = 2 ft, so the volume of the tank is ...
V = (2/3)π(2 ft)³ = 16/3π ft³ ≈ 16.755 ft³
Then the weight of the water in the tank is ...
(16.755 ft³)(62.4 lb/ft³) ≈ 1045.52 lb
The total weight of the water is about 1046 pounds.
Mike is building a model of a classic car: a '67 Chevy Impala. The scale is 1 in : 48 in. The actual length of the car is 213.2 inches. How long will the model be? Round to the nearest tenth.
What is 7% of 300 pounds
Answer:
21
Step-by-step explanation:
Of means multiply
7% * 300
Change to decimal form
.07 * 300
21
Are 1/3 and 3/6 equal equivalent fractions?
The ______ are (is) used to determine the amount of money that an organization would save if it used a particular test in place of the test it currently uses to select employees.
Answer:
The correct answer is the "Brogden-Cronbach-Gleser formula".
Step-by-step explanation:
Brogden introduced the BCG approach towards the conclusion of the nineteenth century as well as developed it considerably mostly throughout a 1965 guidebook by Cronbach as well as Gleser.This model was used to determine the monetary value of another profit derived from either the usage of the content or the selection criterion beneath defined parameters.Area of shaded region
Answer:
what are you asking
Step-by-step explanation:
You need a 30% alcohol solution. On hand, you have a 780 mL of a 15% alcohol mixture. You also have 90%
alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?
You will need ____ mL of the 90% solution?
PLEASE HELP!!! BRAINLIEST! FOR MY FINAL!!!
Answer:
195 mL of the 90% solution
Step-by-step explanation:
Let the number of mL of 90% mixture = x
Hence, our equation is
780mL × 15% + x mL × 90% = (780mL + x) 30%
117 + 0.9x = 234 + 0.3x
Collect like terms
0.9x - 0.3x = 234 - 117
0.6x = 117
x = 117/0.6
x = 195 mL
Therefore, You will need 195 mL of the 90% solution
Jasmine recorded the number of minutes she spent doing homework each day during the months of March and April
The box plot shows her data for March
March
0
5
10
15
20
25
30
35
40
45
50
Time Spent Doing Homework (minutes)
Her data for April is given in the table
0 5 10 15
20 25 30 30 30
30 30 30 30
35 40 40 40 45
45 45 45 50 50 55 60 65 65 75
Select all true statements about the data
DA Jasmine spent more minutes doing homework during the month of April.
B
The mean value
greater for the month of April
C. The median value is greater for the month of April
D. Based on the interquartile range, there is greater variability for the month of April
Answer:
Option A,B,C and D is correct
Step-by-step explanation:
As we can see , the data set for April month has longer time duration taken for completing homework as compared to the time taken during the month of April. Hence, option A is correct.
Option B is also correct because most of the instance of time taken for doing homework is greater for month of April as compared to the month of March
Median value for the month of march = 25 and median value for the month of April is (30+35)/2 = 32.5. Hence, Option C is correct
There is greater variability for the month of April. Hence, option D is correct
Geometry. BD is tangent to circle O at C, mAEC=280, and mACE=80. Find mDCE.(The figure is not drawn to scale.)
A. 100
B. 50
C. 120
D. 60
Which is the graph of g(x) =[x+3]?
Answer:
B
Step-by-step explanation:
10 ft
8 ft
Find the perimeter of this figure to
the nearest hundredth. Use 3.14 to
approximate a.
P = [?] ft
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Answer:
40.56 ft
Step-by-step explanation:
The length of the semicircle of diameter 8 ft is ...
(1/2)(π)(d) = (π/2)(8 ft) = 4π ft ≈ 4×3.14 ft = 12.56 ft
Then the sum of the lengths of all of the sides of the figure is ...
P = 10 ft + 8 ft + 10 ft + 12.56 ft = 40.56 ft
The perimeter of the figure is about 40.56 ft.
2. On this spinner, the pointer is spun once. The colour is recorded.
The pointer is spun a second time. The colour is recorded.
a) Suppose you win if you spin the same colour on both spins.
What are your chances of winning?
b) Suppose you win if you spin two different colours.
What are your chances of winning?
Answer:
A=25% B=75%
Step-by-step explanation:
So first lets make a sample space. (Im using red, blue, green, and yellow)
rr, rb, rg, ry
br, bb, bg, by
gr, gb, gg, gy
yr, yb, yg, yy
So for A its 4/16 or 1/4=25%
For B its 12/16=3/4=75%
Help me plz I’m too slow for this
Answer:
160 units²
Step-by-step explanation:
Surface area of the square pyramid = a² + 2al
Where,
a = side length of the square = 8
l = slant height of the triangular face = 6
Plug in the values
Surface area of the square pyramid = 8² + 2*8*6
= 64 + 96
= 160 units²