Answer: [tex]\frac{dy}{dx}[/tex] = [tex]\frac{ 7 - sin y }{ -6 y^{2} + x cos y }[/tex]
Step-by-step explanation:
Given data,
x sin y - 2y^3 - 5 = 7x
Differentiate with each term with respect to the independent variable,
[tex]\frac{d}{dx}[/tex] (x sin y) - [tex]\frac{d}{dx}[/tex] (2y^3) - [tex]\frac{d}{dx}[/tex] (5) = [tex]\frac{d}{dx}[/tex] (7x)
Apply to the product rule,
sin y * [tex]\frac{d}{dx}[/tex] (x) + x * [tex]\frac{d}{dx}[/tex] (sin y) - [tex]\frac{d}{dx}[/tex] (2 [tex]y^{3}[/tex]) - [tex]\frac{d}{dx}[/tex] (5) = [tex]\frac{d}{dx}[/tex] (7x)
Apply the chain rule,
sin y * [tex]\frac{d}{dx}[/tex] (x) + x* [tex]\frac{d}{dy}[/tex] (sin y) * [tex]\frac{dy}{dx}[/tex] - [tex]\frac{d}{dy}[/tex] (2 [tex]y^{3}[/tex])* [tex]\frac{dy}{dx}[/tex] - [tex]\frac{d}{dx}[/tex] (5) = [tex]\frac{d}{dx}[/tex] (7x)
Take out the coefficients,
sin y * [tex]\frac{d}{dx}[/tex] (x) + x * [tex]\frac{d}{dy}[/tex] (sin y) * [tex]\frac{dy}{dx}[/tex] -2 [tex]\frac{d}{dy}[/tex] ([tex]y^{3}[/tex]) * [tex]\frac{dy}{dx}[/tex] - [tex]\frac{d}{dx}[/tex] (5) = 7 * [tex]\frac{d}{dx}[/tex] (x)
Differentiate the constants and power functions,
sin y + x * [tex]\frac{d}{dy}[/tex] (sin y) * [tex]\frac{dy}{dx}[/tex] - 2 * 3 * [tex]y^{2}[/tex] * [tex]\frac{dy}{dx}[/tex] = 7
Differentiate sin (x),
sin y + cos y * [tex]\frac{dy}{dx}[/tex] - 2 * 3 * [tex]y^{2}[/tex] * [tex]\frac{dy}{dx}[/tex] = 7
Isolate,
[tex]\frac{dy}{dx}[/tex] = [ 7-sin y ] / (-6 [tex]y^{2}[/tex] + x cos y )
Therefore,
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{ 7 - sin y }{ -6 y^{2} + x cos y }[/tex]
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Hannah is the oldest of four siblings whose ages are consecutive integers the sum of their ages is 86 fine Hannah's age
Answer:
20, 21,22,23
Step-by-step explanation:
Consecutive means in order. Integers are the set of whole numbers and their opposites: ...-3,-2,-1,0 ,1,2,3...
Let x = the one sibling
Let x + 1 = the second sibling
Let x + 2 = the third sibling
Let x+4 = the fourth sibling.
If you add the four siblings together they equal 86
(x) + (x +1) + (x + 2) + (x+3) = 86 I put the parentheses in so that you can see each sibling, but it is not needed.
x + x+ 1 +x + 2 + x+ 3 = 86 Combine like terms
4x + 6 = 86 Subtract 6 from both sides
4x = 80 Divide both sides by 4
x = 20
The first sibling is 20, then 21, then 22 and finally 23
Check:
20 + 21 + 22 + 23 = 86
Given that xy = 36 and x - y = 5, Find the value of x² + y².
Answer:
97
Step-by-step explanation:
To find x² + y², use the identity (x - y)² = x² + y² - 2xy.
(x - y)² = x² + y² - 2xy
Substitute xy = 36 and x - y = 5 in the above formula,
5² = x² + y² - 2*36
25 = x² + y² - 72
Add 72 to both sides,
25 + 72 = x² + y²
x² + y² = 97
a blank chart shows open and close prices and highs and lows, but over a long time period it can also show pricing blank
Based on the information given, it can be deduced that the chart that is being described is the OHLC chart.
A statistical graph or chart is defined as the pictorial representation of statistical data in graphical form. The statistical graphs are used to represent a set of data to make it easier to understand and interpret statistical information.
It should be noted that an open-high-low-close chart (OHLC) chart simply means a type of chart that's used to illustrate the movements in the price of a financial instrument for a particular period of time.
The vertical line on the chart illustrates the price range over a unit of time. It's useful in assessing volatility as it shows the full price range of the period.
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If Fernando paid $450 for a netbook that was 75% of the original price, what was the original price?
Answer:
$600
Step-by-step explanation:
450 = 3/4 (because 75%=3/4)
450/3=150. 150 = 1/4, or 25%. Now it's just as simple as multiplying 150 4 times to get 100%, or the original cost, 150 times 4 equals 600. Therefore the notebooks original price is $600
Hazel and Luna are in different sections of MTH 134. They both took Test 1 and their instructors indicated that in each section, the scores fell into a normal distribution. Hazel made a score of 93 points and Luna made a score of 68 points. In Hazel's section, the Test 1 scores had a mean of 80 and a standard deviation of 8. In Luna's section, the mean was 40 with a standard deviation of 15. Use the Empirical Rule to determine which student did "better" and why.
Using z-scores, it is found that due to the higher z-score, Luna did better on the exam.
What are z-scores?The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.From the two bullet points, it is found that the student who did "better" is the one whose grade has the higher z-score.
For Hazel, the parameters are given as follows:
[tex]X = 93, \mu = 80, \sigma = 8[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (93 - 80)/8
Z = 1.625.
For Luna, the parameters are given as follows:
[tex]\mu = 68, X = 40, \sigma = 15[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (68 - 40)/15
Z = 1.87.
Due to the higher z-score, Luna did better on the exam.
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A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts
moving, the rabbit sees it and starts running away at a speed of 40 feet per second.
What should the fox's speed be to catch up to the rabbit in no more than 10 seconds?
Factor completely. x^8-1/81
Answer:
Step-by-step explanation:
[tex]\displaystyle\\ x^8-\frac{1}{81} \\\\x^8-\frac{1}{3^4} =\\\\x^8-(\frac{1}{3})^4 =\\\\x^{4*2}-(\frac{1}{3})^{2*2}= \\\\(x^4)^2-((\frac{1}{3} )^2)^2=\\\\(x^4-(\frac{1}{3})^2)(x^4+(\frac{1}{3} ) ^2)=\\\\(x^{2*2}-(\frac{1}{3})^2)(x^4+\frac{1^2}{3^2} )=\\\\((x^2)^2-(\frac{1}{3})^2)(x^4+\frac{1}{9})=\\\\(x^2-\frac{1}{3} )(x^2+\frac{1}{3})(x^4+\frac{1}{9})[/tex]
Find x for this equation
Show clear algebraic fraction
Step-by-step explanation:
cross multiply both sides
2(6x+1)=3(5x–2)
12x+2=15x–6
collect like terms
+2+6=15x–12x
8=3x
divide both sides by 3
8\3=3x\3
therefore, the final answer is
8\3
thank you
please mark as the brainliest
A population has SS= 50 and s^2 = 5. How many scores, (N).are in the population?
There are 11 scores, (N) in the population.
How many scores, (N) are in the population?The given parameters are:
Variance, s^2 = 5
Sum of squares, SS = 50
The variance of the population is calculated using
s^2 = SS/[N - 1]
So, we have
5 = 50/[N - 1}
Cross multiply
So, we have
5(N - 1) = 50
This gives
N - 1 = 10
Add 1 to both sides
N = 11
Hence, there are 11 scores, (N) in the population.
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Let f(x)= 3x^2+3.
Evaluate
lim h ==> 0 (f(2+h)-f(2))/h
[tex]f(x)=3x^2+3\hspace{5em}\displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \cfrac{[3(2+h)^2+3]~~ - ~~[3(2)^2+3]}{h} \\\\\\ \cfrac{[3(4+4h+h^2)+3]~~ - ~~[3(4)+3]}{h}\implies \cfrac{[(12+12h+3h^2)+3]~~ - ~~[15]}{h} \\\\\\ \cfrac{[12h+3h^2+15]~ - ~~[15]}{h}\implies \cfrac{12h+3h^2}{h}\implies \cfrac{h(12+3h)}{h}\implies 12+3h \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \lim_{h\to 0}~12 + 3h\implies 12+3(0)\implies \text{\LARGE 12}[/tex]
He wants to include a school and a hospital, which are 10 kilometers apart.
What should the distance between the school and the hospital be on the map?
The distance between the school and the hospital on the map is 8 cm
How to calculate the distance?Here, we want to find the distance between the school and the hospital on the map
The scale is that 4cm to 5km
So ;
if 4 cm = 5km
Then x cm = 10km
x * 5 = 4 * 10
5x = 40
x = 40/5
x = 8 cm
Therefore the distance between the school and the hospital on the map is 8 cm
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Jessica had $7 and her sister had $2. After their parents gave each of them an equal amount of money, Jessica had twice as much money as her sister. How much money did their parents give each of them?
Answer:
$3:00
Step-by-step explanation:
let 'x' be the money that the parents gave to Jane and her sister each
Jane will have 7+x dollars
Jane's sister will have 2 + x dollars
Jane had twice as much money as her sister thus
7 + x = 2(2 + x)
7 + x = 4 + 2x
4 + 2x = 7 + x
2x - x = 7 - 4
x = $3
the parents gave $3 to each.
Need to find the value of x
Answer:
x=2
Step-by-step explanation:
Because these angles are the same you can do: 10x-14=7x-8. By doing simple math you'll get x=3 as you answer
Answer:
x = -18/7 y simplified as -2.57143y
Step-by-step explanation:
to figure this out and find the excluded value, first set the denominator equal to 0, because fractions represent division and dividing by 0 isn't defined. that will give us 7x+18y=0.. move the variable to the right hand side and change it sign.. which will be 7x=-18y, now divide both side by 7, = x=-18/7y / -2.57143y
Identify the key characteristics of the parent fifth-root function f(x)=x Include the following domain, range, intervals where the function is increasing, decreasing, or constant, intercepts, whether the function is even, odd, or neither, whether the function is continuous or discontinuous, asymptotes, and end behavior. (4 pts.)
From the graph of the fifth root function, we have that:
The domain and the range are all real values.The function is increasing for all real values, and never decreasing nor constant.The x-intercept is of x = 0.The y-intercept is of y = 0.The function is odd.The function is continuous.The function has no asymptotes.The end behavior is that y -> - ∞ when x -> -∞ and y -> +∞ when x -> +∞.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence, since the given graph has no holes, and keeps going to infinity, we have that both the domain and the range are all real values.
Since the function has no holes, it is also continuous, and has no vertical asymptotes.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when x increases, y decreases.For this problem, we have that the function is moving right and up over it's entire domain, hence it is increasing for all real values, and never decreasing nor constant.
What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.Since the graph passes through the origin, we have that:
The x-intercept is of x = 0.The y-intercept is of y = 0.What are even and odd functions?In even functions, we have that f(x) = f(-x) for all values of x.In odd functions, we have that f(-x) = -f(x) for all values of x.If none of the above statements are true, the function is neither.For this problem, looking at the graph, we have the the second statement holds true for all values of x, hence the function is odd.
What is the end behavior of the function?It is given by the values of y when x -> ∞.
Hence:
For the end behavior, y -> - ∞ when x -> -∞ and y -> +∞ when x -> +∞.
Since f(x) -> ∞ when x -> ∞, the function has no asymptotes.
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Solve the equation
2(4-5x)=3(4x+3)
Answer:
-1 /22
Step-by-step explanation:
1his is a fraction kinda thing so put -1 at the top like a numerator and the 22 go at the bottom like the denominator
What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $900, if
it pays 7% fixed interest for the duration of the
bond?
yield = [?] %
Give your answer as a percent rounded to the nearest
hundredth.
The yield on the corporate bond of a face value of $1000 is 7.77%.
What is the percentage discount?
The percentage discount is the discount given on a product as compared to the given discount on 100 rupees.
Given, the face value of the bond is $1000.
Discounted price of the bond is $900.
Therefore, the fixed interest on the bond for that period will be
= $1000 × 7/100 = $70.
Now, the yield on that corporate bond = 70 × 100/900 % = 7.77% .
Hence, the yield on the corporate bond of a face value of $1000 is 7.77%.
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he table represents a linear equation. A two column table with 5 rows. The first column, x, has the entries, negative 10, negative 5, 10, 15. The second column, y, has the entries, 8, 7. 4, 3. Which equation shows how (–10, 8) can be used to write the equation of this line in point-slope form?
Equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)(x+ 10).
As given,
Given points of linear equation: (-10,8), (-5, 7) , (10,4), (15,3)
Consider (x₁, y₁)=(-10,8) and (x₂ ,y₂)=(-5,7)
Slope 'm'=(y₂-y₁)/(x₂-x₁)
=(7-8)/(-5+10)
=-1/5
Equation of line passing through (-10,8) in point slope form:
y-y₁=m(x-x₁)
⇒(y -8)=(-1/5)(x+10)
⇒y=1/5(-x+30)
Therefore, equation of the line in point slope form passing through (-10,8) for the given coordinates (-10,8), (-5, 7) , (10,4), (15,3) of linear equation is
(y - 8)=(-1/5)( x + 10).
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Can someone help me with this
thanks so much for the help!
The domain of the function is all the real numbers and the range is from -2 to 2.
What are domain and range?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
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.
In the image, we can see that the value of the function varies from -2 to 2 at all the possible values of the real numbers.
Therefore, the domain of the function is all the real numbers and the range is from -2 to 2.
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James invests his money in an account paying 3.7% interest compounded quarterly. What is the effective annual yield on this account?
Answer:
3.7517%
Step-by-step explanation:
take 3.7 and divide it by 4 to get 0.925
then apply 0.925% to x 4 times to find out the compounded rate
what is the GCF of 18 and 28?
Answer:2
Step-by-step explanation:
evaluate this please
Answer:
the answer would be x=8
Step-by-step explanation:
6×4=24
24/3=8
you’re buying 60 acres Of farmland at a cost of 372000
What is the cost per acre
What would be the cost for 70 acres
Answer:
Per acre will cost 6200
70 acres will cost 434,000
Step-by-step explanation:
you’re buying 60 acres Of farmland at a cost of 372000
1) What is the cost per acre
solutionIn order to find the cost per acre we divide the values which is;
➟ 372000 ÷ 60
➟ 6200
∴ it will cost 6200 per acre
2) What would be the cost for 70 acres
solutionto find how much it will cost for 70 acres we will multiply the value per acre by 70 which is;
➟ 6200 × 70
➟ 434,000
∴ it will cost 434,000 for 70 acres
Clare is cycling ata speed of 12. Miles per hour if she starts at a position chosen as zero what will
Clare will have traveled 9 miles in 45 minutes.
What is speed?The definition of speed is the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling.So, Clare is riding her bike at a speed of 12 miles per hour.
Her starting point is zero.Distance traveled in 45 minutes or 45/60 hours at the same speed will be = Speed Time
= 12 × 45/60= 45/5= 9 milesTherefore, Clare will have traveled 9 miles in 45 minutes.
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A jar contains 4 red marbles, 5 yellow marbles, 3 green marbles, and 3 blue marbles.
1. If two marbles are selected at random without replacing between draws, what is the probability that the outcome contains green and/or blue marbles only? (Round your answer to four decimal places.)
2. If three marbles are selected at random without replacing between draws, what is the probability that the outcome contains only green marbles? (Round your answer to four decimal places.)
3. If three marbles are selected at random with replacing between draws, what is the probability that the outcome contains no green marbles? (Round your answer to four decimal places.)
The required probability for a number of problems given is as follows, 1.) 1 / 3 2.) 1 / 5, and 3.) 1 / 4.
Here,
A jar consists of 4 red marbles, 5 yellow marbles, 3 green marbles, and 3 blue marbles.
Total number of marbles = 15
1) probability that the outcome contains green and/or blue marbles only,
= 2 / 6 = 1 / 3
2.) probability that the outcome contains only green marbles,
= 3 / 15 = 1 / 5
3.) the probability that the outcome contains no green marbles,
= 3 / 12 = 1 / 4
Thus, the required probability for a number of problems given is as follows, 1.) 1 / 3 2.) 1 / 5, and 3.) 1 / 4.
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How much would $500 invested at 9% interest compounded monthly be worth after 4 years ? A(t)=P(1+r/n)^nt
The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
[tex]\rm A = P \left ( 1 + \dfrac{r}{n} \right ) ^{nt}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.
For interest compounded monthly, the value of n is 12.
The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be
[tex]\rm A = 500 \left ( 1 + \dfrac{0.09}{12} \right ) ^{12 \times 4}[/tex]
Simplify the equation, then we have
A = 500 (1.0075)⁴⁸
A = 500 x 1.4314
A = $715.70
The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.
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Harriet counts 15 big boxes and 12 small boxes of notebooks. Each large box contains 189 notebooks, and each small box contains 79 notebooks. Estimate the total number of notebooks. Is your estimate an overestimate or an underestimate? Explain why it is better to have an overestimate than an underestimate. WILL GIVE 95 POINTS
Answer:15 big boxes with 189 notebooks each: 20 * 200 = 4,000
12 small boxes with 79 notebooks each: 10 * 80 = 800
4,000 + 800 = 4,800
There are approximately 4,800 notebooks, this is an overestimate as I rounded up.
Step-by-step explanation:
(2x+4)(x-4) multiply
Answer: 2x²-4x-16
Step-by-step explanation:
[tex](2x+4)(x-4)=\\2x(x)+2x(-4)+4(x)+4(-4)=\\2x^2-8x+4x-16=\\2x^2-4x-16[/tex]
For the following exercise, find the domain and range of the function below using interval notation.
Domain:
Range:
The domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
For domain :-
Since, the domain is the set of all allowed x inputs of a function.
The smallest x can get is x = -3 as shown by the left-most point.
The largest x can get is x = 7, though we can't actually reach this value due to the open hole at the right-most point.
The interval of all possible x values is -3 ≤ x < 7 which converts to the interval notation [-3, 7)
We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.
We can say "x is any number between -3 and 2, including -3 but excluding 2".
For range :-
Since, the range is the set of all allowed y inputs of a function.
The smallest x can get is x = -7 as shown by the left-most point.
The largest x can get is x = 6, though we can't actually reach this value due to the open hole at the right-most point.
The interval of all possible x values is -7 ≤ x < 6 which converts to the interval notation [-7, 6)
We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.
Hence, the domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.
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1.Solve for y.
y = 20
y = 120
y = 60
y = 10
The length of a rectangular parking area is four times the width. The perimeter is 150 yd . Find the length and width of the parking area.
The width of the rectangle = 15 yd
The length of the rectangle = 60 yd.
What is the Perimeter of a Rectangle?Perimeter of a rectangle = 2(length + width).
Given the following:
Width of the rectangle = w
Length of the rectangle = 4w
Perimeter of the rectangle = 150 yd.
Therefore:
2(4w + w) = 150
2(5w) = 150
10w = 150
10w/10 = 150/10
w = 15
Width of the rectangle = w = 15 yd
Length of the rectangle = 4w = 4(15) = 60 yd.
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