Answer:
remember the chain rule:
h(x) = f(g(x))
h'(x) = f'(g(x))*g'(x)
or:
dh/dx = (df/dg)*(dg/dx)
we know that:
z = 4*e^x*ln(y)
where:
y = u*sin(v)
x = ln(u*cos(v))
We want to find:
dz/du
because y and x are functions of u, we can write this as:
dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/du) = 1/(u*cos(v))*cos(v) = 1/u
(dy/du) = sin(v)
Replacing all of these we get:
dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)
= 4*e^x*( ln(y)/u + sin(v)/y)
replacing x and y we get:
dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))
dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)
Now let's do the same for dz/dv
dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)
(dy/dv) = u*cos(v)
then:
dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]
replacing the values of x and y we get:
dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]
dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]
Rajah / Diagram 5 (b) Dalam Rajah 6, PQ ialah tangen sepunya dua bulatan. AQ dan BQ ialah tangen bagi bulatan yang masing-masing berpusat E dan F. Cari nilai x dan y. In Diagram 6, PQ is the common tangent of two circles. AQ and BQ is the tangent to the circles with centre E and F respectively. Find the value of x and y. [3 markah.
Answer:
36281629273781646181993836619946527189119292937467482919198$7473828191927364732818919283838292927383883829118661552621718919191019284746617171819001187373765252728
Step-by-step explanation:
173899918377+28910873638282
Which of the following expressions is not equivalent to the others?
Answer:
Im going to guess the second one
Step-by-step explanation:
It's the only one that does not have more than one negative fraction.
A movie theater has a seating capacity of 283. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2060 on a sold out night, how many children, students, and adults attended
Answer: adults = 79
children = 158
student = 46
Step-by-step explanation:
Let a = adults
Let c = children
Let s = student
From the information given,
a + c + s = 283 ....... i
c/a = 2, c = 2a ....... ii
5c + 7s + 12a = 2060 ...... iii
Put the value of c = 2a into equation i
a + c + s = 283
a + 2a + s = 283
3a + s = 283
s = 283 - 3a
Note that c = 2a
From equation iii
5c + 7s + 12a = 2060
5(2a) + 7(283 - 3a) + 12a = 2060
10a + 1981 - 21a + 12a = 2060
10a + 12a - 21a = 2060 - 1981
a = 79
Note c = 2a
c = 2 × 79 = 158
Since a + c + s = 283
79 + 158 + s = 283
s = 283 - 237
s = 46
adults = 79
children = 158
student = 46
X+ 1
If g(x)=
X-2 and h(x) = 4 – x, what is the value of (g•)(-3)?
ola Mo Nional
15
2
18
what are the coordinates of the point that is 1/6 of the way from a(14 -1) to b(-4 23)
9514 1404 393
Answer:
(11, 3)
Step-by-step explanation:
That point is ...
P = a + (1/6)(b -a) = (5a +b)/6
P = (5(14, -1) +(-4, 23))/6 = (70-4, -5+23)/6 = (11, 3)
The point of interest is (11, 3).
Answer:
The coordinates of the point that is 1/6 of the way from a to b is thus (11, 3)
Step-by-step explanation:
Let's look first at the x coordinates of the two given points: 14 and -4. From 14 to -4 is a decrease of 18. Similarly, from y = -1 to y = 23 is an increase of 24.
Starting at a(14, -1) and adding 1/6 of the change in x, which is -18, we get the new x-coordinate 14 + (1/6)(-18), or 14 - 3, or 11. Similarly, adding 1/6 of the increase in y of 24 yields -1 + 4, or 3.
The coordinates of the point that is 1/6 of the way from a to b is thus (11, 3)
insert a digit in a place of each "..." to make numbers that are divisible by 6 if it is possible: 4...6
Answer:
1 There is no number that make it divisible by 6 with no decimals
2 1,4,7
Step-by-step explanation:
2 23718/6= 3953
23748/6= 3958
23778/6= 3963
The population of retired citizens in Minneapolis is 86700. If the population increases at a rate of 8.9% each year. What will the population of retirees be in 7 years? Write an exponential growth model for the future population P(x) where r is in years: P(x) = What will the population be in 7 years? (Round to nearest person)
Answer:
157,476 people
Step-by-step explanation:
the formula :
P(x) = 86700. (1+ 0.089)^r
for r = 7
=> P(x) = 86700 × (1+ 0.089)^7
= 86700 × (1.089)^7
= 86700 × 1.8163
= 157,476 people
f(x) = 4x*x is a function?
Answer:
yes it is
Step-by-step explanation:
Can someone help me with this problem?
what's the value of the function f(x)= 2x+5 if x=3
Answer:
f(x) = 2(3) + 5
= 6 + 5 = 11
y = 11
x = 3
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6
Answer:
[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder
[tex][-21,\infty)[/tex] --- interval notation
Step-by-step explanation:
Given
[tex]-3a - 15 \le -2a + 6[/tex]
Required
Solve
Collect like terms
[tex]-3a + 2a \le 15 + 6[/tex]
[tex]-a \le 21[/tex]
Divide by -1
[tex]a \ge - 21[/tex]
Rewrite as:
[tex]-21 \le a[/tex]
Using set builder
[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]
Using interval notation, we have:
[tex][-21,\infty)[/tex]
* Insert a digit to make numbers that are divisible by 6 if it is possible:
234_6
Answer:
i put in 3 to make 23436 because 36 is divisible by 6
find the degree of polynomial of the following
[tex]3x^{3} - x ^{5} [/tex]
Answer:
the degree is the value of the biggest exponent = 5 (fifth degree)
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Since the highest power of x is 5, the degree of the polynomial x
3
−9x+3x
5
is 5.
Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x =0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
|error| <= _________
Answer:
0.0032
Step-by-step explanation:
We need to compute [tex]e^{0.4}[/tex] by the help of third-degree Taylor polynomial that is expanded around at x = 0.
Given :
[tex]e^{0.4}[/tex] < e < 3
Therefore, the Taylor's Error Bound formula is given by :
[tex]$|\text{Error}| \leq \frac{M}{(N+1)!} |x-a|^{N+1}$[/tex] , where [tex]$M=|F^{N+1}(x)|$[/tex]
[tex]$\leq \frac{3}{(3+1)!} |-0.4|^4$[/tex]
[tex]$\leq \frac{3}{24} \times (0.4)^4$[/tex]
[tex]$\leq 0.0032$[/tex]
Therefore, |Error| ≤ 0.0032
How to answer this question
Answer:
(0.3049 ; 0.3751)
Step-by-step explanation:
The confidence interval for proportion can be obtained using the relation :
Phat ± Zcritical * [√phat(1-phat) / n]
phat = x / n
Sample size, n = 700
x = 238
phat = 238/700 = 0.34
Zcritical at 95% = 1.96
C.I = 0.34 ± 1.96 * [√0.34(1-0.34) / 700]
C.I = 0.34 ± 1.96 * 0.0179045
C. I = 0.34 ± 0.0350928
Lower boundary = 0.34 - 0.0350928 = 0.3049
Upper boundary = 0.34 + 0.0350928 = 0.37509
(0.3049 ; 0.3751)
On dividing 12x³ by 4x the quotient is …..
Answer:
12x^3 is equivalent to
12x*12x*12x which if we multiply is
1728x
we divide by 4x
1728x divided by 4x=432x
Hope This Helps!!!
Answer:
3x^2
Step-by-step explanation:
when u divide 12x^3/4x....u divide 12/4=3 along with the x also..tat is x^3/x=x^2
Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.
Week Sales (1,000s of gallons)
1 17
2 22
3 20
4 24
5 18
6 17
7 21
8 19
9 23
10 21
11 16
12 23
(a) Using a weight of
1
2
for the most recent observation,
1
3
for the second most recent observation, and
1
6
for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.)
Compute four-week and five-week moving averages for the time series.
Week Time Series Moving
Value Average Forecast
1 17
2 22
3 20
4 24
5 18
6 17
7 21
8 19
9 23
10 21
11 16
12 23
(b) Compute the MSE for the four-week moving average forecasts. (Round your answer to two decimal places.)
Compute the MSE for the five-week moving average forecasts. (Round your answer to two decimal places.)
(c) What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? MSE for the three-week moving average is 11.12.
Answer:
Use suitable identity to find the product (3-2x)(3+2x).Find the remainder when x³+ 3x²+3x+1 is divided by x+1.On a plane surface we can find straight lines.8√15 + 2√3The decimal form of 36 100(a-b)³ = a ³- ........ 3 + 3ab²-b³In the Cartesian plane the horizontal line is called .........The coefficient of x² in 2-x²+ x³ is -1.√225 is an irrational number.The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).
kxndjdkdkdkkdkskskdkdjdjdjskskskdjdjddjd
Answer:
Not a functionFunctionFunctionNot a functionNot a functionHope this helps!
An arch is in the form of a parabola given by the function h = -0.06d^2 + 120, where the origin is at ground level, d meters is the horizontal distance and h is the height of the arch in meters.
Graph this function on your graphing calculator then complete the following statements.
The height of the arch is: ------- m
The width to the nearest meter, at the base of the arch is ------ m
Answer:
See attachment for graph
The height of the arch is: 120 m
The width to the nearest meter, at the base of the arch is 22 m
Step-by-step explanation:
Given
[tex]h = -0.06d^2 + 120[/tex]
Solving (a): The graph
See attachment for graph
Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.
Solving (b): The height
The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,
Hence:
[tex]height = 120[/tex]
Solving (c): The width
The curve touches the horizontal axis at two different points.
[tex]x_1 = -11[/tex]
[tex]x_2 = 11[/tex]
The absolute difference of both points represents the width.
So:
[tex]Width = |x_2 - x_1|[/tex]
[tex]Width = |11 - -11|[/tex]
[tex]Width = |11 +11|[/tex]
[tex]Width = |22|[/tex]
Hence:
[tex]Width = 22[/tex]
Suppose 46% of politicians are lawyers. If a random sample of size 662 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Answer:
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose 46% of politicians are lawyers.
This means that [tex]p = 0.46[/tex]
Sample of size 662
This means that [tex]n = 662[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.46[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194[/tex]
What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?
p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So
X = 0.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.46}{0.0194}[/tex]
[tex]Z = 2.06[/tex]
[tex]Z = 2.06[/tex] has a p-value of 0.9803
X = 0.42
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.42 - 0.46}{0.0194}[/tex]
[tex]Z = -2.06[/tex]
[tex]Z = -2.06[/tex] has a p-value of 0.0197
0.9803 - 0.0197 = 0.9606
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
5a2 + b(a2 + 5) + b2
[tex]\rightarrow\sf {5a}^{2} + {b(a}^{2} + 5) + {b}^{2} [/tex]
Solution:[tex]\rightarrow\sf {5a}^{2} + {b(a }^{2} + 5) + {b}^{2} \\ = \sf {5a}^{2} + {ba}^{2} + b \times 5 + {b}^{2} \\ = \large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]
Answer:[tex]\rightarrow\large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]
[tex]\color{red}{==========================}[/tex]
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ
Two different formulas of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formula 1 is σ12=1.5, and for formula 2 it is σ22=1.2. Two random samples of size n1=15 and n2=20 are tested, and the mean octane numbers observed are x¯1=89.0 fluid ounces and x¯2=92.2 fluid ounces. Assume normality.
a. Test the hypothesis that the formulations are equal versus the hypothesis that formulation 2 produces a higher mean road octane number than formulation 1. Calculate z0=
b. Calculate a 95% two-sided confidence interval on the mean difference road octane number.
Answer:
Step-by-step explanation:
a)
zo=(89.0-92.2)/sqrt((1.5/15)+(1.2/20))
zo=-8.00
p-value=0.0000
Reject the null hypothesis.
b)
95% confidence interval for difference
=(89-92.2)+/-1.96*sqrt((1.5/15)+(1.2/20))
=-3.2+/-0.78
=(-3.98, -2.42)
The distribution of the number of apples trees a farmer can plant each day is bell-shaped and has a mean of 62 and a standard deviation of 8. Use the empirical rule to help you answer the following. What is the approximate percentage of trees planted between 38 and 68
Answer:
The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Step-by-step explanation:
The Empirical Rule 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.
In this problem, we have that:
Mean of 62, standard deviation of 8.
What is the approximate percentage of trees planted between 38 and 86?
38 = 62 - 3*8
86 = 62 + 3*8
So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Find the solution for this system of equations.
2x + 4y = 8
x = 3y − 6
Answer:
[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]
Substitute for x in equation (a) :
[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]
Substitute for y in equation (b) :
[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]
2x+4y =8
x=3y-6 ——> x–3y=–6
x–3y = – 6 ] ×(–2) ——> –2x +6y=12
2x+4y=8
–2x+6y =12
__o_o____
0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2
2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0
(x,y) —> (0,2)
A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 15 ft3/min, how fast is the water level rising when the water is 8 inches deep
Answer:
7.5 ft³/min
Step-by-step explanation:
Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.
Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²
So, V = Ah = 2h = 2(10 - x)
The rate of change of volume is thus
dV/dt = d[2(10 - x)]/dt = -2dx/dt
Since dV/dt = 15 ft³/min,
dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min
Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt
= -dx/dt
= -(-7.5 ft³/min)
= 7.5 ft³/min
And the height at this point when x = 8 inches = 8 in × 1 ft/12 in = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft
Pls answer? Last one for today!
Step-by-step explanation:
You look for the common factor of both of them which in this case is 5, therefore it's
5(x+7)..just divide 5 in 5x and in 35
if 8km=5miles.how many miles are in 56m?
Answer:
89.6 miles
Step-by-step explanation:
[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{56}[/tex]
5x = 448
x=89.6
Step-by-step explanation:
if 8km=5
x =56km
5x=8×56
5x=448
x=89.6 miles
Which of the following equations describes this graph?
A. y=(x-1)^2-
B. y=(x-3)^2+2
C. y=(x+1)^2-2
D. y=(x-2)^2+3
Answer:
The choose (A)
y=(x-1)²-2
In order for the parallelogram to be a
rhombus, x = [?].
(5x + 25)
(12x + 11)
A parallelogram is also a rhombus if the diagonal is a bisector of an angle enclosed by the two adjacent sides of a parallelogram.
In our case it means,
[tex]5x+25=12x+11[/tex]
[tex]7x=14\implies x=\boxed{2}[/tex]
Hope this helps.
In order for the parallelogram to be a rhombus, ,For the parallelogram to be a rhombus, x must be equal to 2.
To determine the value of x that would make the parallelogram a rhombus, we need to compare the lengths of its opposite sides. In a rhombus, all four sides are equal in length. So, we can equate the lengths of the opposite sides of the parallelogram and solve for x.
Given that one side has a length of (5x + 25) and the opposite side has a length of (12x + 11), we can set up the following equation: 5x + 25 = 12x + 11
To solve for x, we can start by isolating the x term on one side of the equation. We can do this by subtracting 5x from both sides: 25 = 12x - 5x + 11 Simplifying the equation further: 25 = 7x + 11 Next, we can isolate the x term by subtracting 11 from both sides: 25 - 11 = 7x 14 = 7x Finally, we can solve for x by dividing both sides by 7: 14/7 = x x = 2 Therefore, for the parallelogram to be a rhombus, x must be equal to 2.
To know more about parallelogram here
https://brainly.com/question/970600
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PLEASE HELP I DONT NEED EXPLANATION JUST THE EQUATION IM IN A TEST RN HELP ASAP THANK YOU SO MUCH :)))
Answer:
[tex]-x^{2}[/tex]
Step-by-step explanation:
It simple really its just a reflection over the x-axis making it a negative towards the parent function
Answer:
The answer is -x²
Step-by-step explanation:
Hope this helps :)
