Answers
Given
e ˣʸ = sec(x ²)
take the derivative of both sides:
d/dx [e ˣʸ] = d/dx [sec(x ²)]
Use the chain rule:
e ˣʸ d/dx [xy] = sec(x ²) tan(x ²) d/dx [x ²]
Use the product rule on the left, and the power rule on the right:
e ˣʸ (x dy/dx + y) = sec(x ²) tan(x ²) (2x)
Solve for dy/dx :
e ˣʸ (x dy/dx + y) = 2x sec(x ²) tan(x ²)
x dy/dx + y = 2x e ⁻ˣʸ sec(x ²) tan(x ²)
x dy/dx = 2x e ⁻ˣʸ sec(x ²) tan(x ²) - y
dy/dx = 2e ⁻ˣʸ sec(x ²) tan(x ²) - y/x
Since e ˣʸ = sec(x ²), we simplify further to get
dy/dx = 2 tan(x ²) - y/x
Related Questions
Simplify the expression. Express your answer as an improper fraction in simplest form.
Answers
Answer:
Step-by-step explanation:
3/40 is the correct answer
SOMEONE PLEASE HELP ME WITH THIS AND EXPLAIN EACH ONE AND HOW YOU DID IT PLEASE MY TEACHER SUCK AND ILL GIVE YOU BRAINLY IF U GET IT RIGHT!!!!
Answers
Answer:
a)
d)
Step-by-step explanation:
It's easiest to reduce each statement to its simplest form for comparison
Our test statement can be reduced by combining like terms
16x - 12 -24x + 4 = -8x - 8
this becomes our new gold standard
a) 4 + 16x - 12(1 + 2x)
apply the distributive property by multiplying terms in parenthesis by -12
4 + 16x - 12 - 24x
combine terms
-8x - 8 Yeaah, We have a winner as it exactly matches our gold standard.
b) 40x - 16 is already in simplest terms and does NOT match the gold standard.
c) 16x - 24x - 4 + 12
has the same cardinal values as the original, but differing signs, reducing gives -8x + 8
Not quite the same as a plus sign occurs where a negative exists in our gold standard.
d) -8x - 8 is already in simplest terms and exactly matches our gold standard. Yeah!
e) 10(1.6x - 1.2 - 2.4x + 4)
apply distributive property by multiplying each term in parenthesis by 10
16x - 12 - 24x + 40
combine like terms
-8x + 28 does NOT match our gold standard
Given: ABCD is a trapezoid,
AB= 13, CD = 14,
BC = 5, and AD= 20.
Find: A
ABCD
Answers
Answer:
A=13×13
=169sqr.units
Solve.
x² + 5x – 2=0
Answers
Answer:
1
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
2
+
5
−
2
=
0
x^{2}+5x-2=0
x2+5x−2=0
=
1
a={\color{#c92786}{1}}
a=1
=
5
b={\color{#e8710a}{5}}
b=5
=
−
2
c={\color{#129eaf}{-2}}
c=−2
=
−
5
±
5
2
−
4
⋅
1
(
−
2
)
√
2
⋅
1
Step-by-step explanation:
this should help
by finding A B and c
of the quadratic then applying the quadratic formula.
I hope this helps !!
1) A book contains 192 pages. A boy reads x complete pages everyday.if he has not finished the book after 10days, find the highest possible value of x
Answers
9514 1404 393
Answer:
19
Step-by-step explanation:
After x days, the boy will have read 10x. If this is less than 192, we have ...
10x < 192
x < 192/10
x < 19.2
If x is an integer, the largest possible value x could have is 19.
Find the midpoint of the line segment joining (–4, –2) and (2,8)
Show all work
Answers
Answer:
Mid- point =(-4+2/2, -2+8/2)
=(-2/2,6/2)
=(-1,3)
The mid point of the line segment joining (–4, –2) and (2,8) is (-1, 3)
Mid point formulamid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Therefore,
(-4, -2)(2, 8)
x₁= -4
x₂ = 2
y₁ = -2
y₂ = 8
Hence,
mid point = (-4 + 2 / 2, -2 + 8 / 2)
mid point = (-2 / 2, 6 / 2)
mid point = (-1, 3)
learn more on mid point here: https://brainly.com/question/1501820
At which times could Rory's phone have been plugged into the charger? Select three options.
Answers
Answer:
what three options bro where are the options
Answer:
9 hours, 11 hours, 19 hours.
A box contains orange balls and green The number of more four the number of orange If there 38 balls how many green balls and how balls are there in the box ?
Answers
let number of green balls= x
let number of orange balls=x+4
x+x+4=38
2x=38-4
2x=34
x=17
number of green balls=17
number of orange balls=21
Simplify the given equation.
6 - (3x+10) + 4(2 - x) = 15
O 4-7 x = 15
O4 - 4 x= 15
O 12 - 7 x= 15
Answers
Answer:
-7x-11
Step-by-step explanation:
expand brackets
6-3x-10+8-4x=15
4-7x=15
move 15 to left side
-7x-11
Answer:
4-7x=15
Step-by-step explanation:
[tex]6 - (3x + 10) + 4(2 - x) = 15 \\ 6- 3x - 10 + 8 - 4x = 15 \\ - 7x = 15 + 10 - 8 - 6\\ - 7x = 11 \\ the \: same \: one \: is \\ 4 - 7x = 15[/tex]
In a recent survey for an upcoming city mayoral election, people were asked to name the political party they identified with and also the
the candidate they were going to vote for.
• Of the 150 people who identified themselves as Democrats, 133 said they would vote for the Democratic candidate. The rest said to
vote for the Republican.
. Of the 160 people who identified themselves as Republican, 142 said they would vote for the Republican candidate. The rest said ti
vote for the Democrat.
Complete the two-way frequency table for this situation.
B I u X
x
Font Sizes
A
А
E E 3 E3
Identify Party
Democrat Republican Total
Democratic
Voted
Republican
Total
Characters used: 89 / 15000
Submit
Answers
This question is solved using relative frequency concepts, finding the following two way frequency table, with the - separating the values:
0.4290 - 0.0540 - 0.4839
0.0581 - 0.4581 - 0.5161
0.4871 - 0.5121 - 1
-------------------------------------------------------------------------------
Relative frequency:
The relative frequency of a to b is given by a divided by b.
-------------------------------------------------------------------------------
Democratic:
Total of 150 + 160 = 310 voters.
Of the 150 Democrats, 133 voted for the Democrat and 150 - 133 = 17 voted for the Republican.
The frequencies are:
[tex]\frac{133}{310} = 0.4290, \frac{17}{310} = 0.0548[/tex]
Proportion of democratic voters is:
[tex]\frac{150}{310} = 0.4839[/tex]
Thus, the first line is: 0.4290 - 0.0540 - 0.4839
-------------------------------------------------------------------------------
Republican:
Of the 160 Republicans, 142 voted for the Republican and 160 - 142 = 18 voted for the Democrat.
The frequencies are:
[tex]\frac{18}{310} = 0.0581, \frac{142}{310} = 0.4581[/tex]
The proportion of republican voters is:
[tex]\frac{160}{310} = 0.5161[/tex]
Thus, the second line is: 0.0581 - 0.4581 - 0.5161
-------------------------------------------------------------------------------
Third line:
0.4290 + 0.0581 = 0.4871
0.0540 + 0.4581 = 0.5121
0.4839 + 0.5161 = 1
Thus, the third line is: 0.4871 - 0.5121 - 1
-------------------------------------------------------------------------------
Two-way frequency table:
The two-way frequency table is:
0.4290 - 0.0540 - 0.4839
0.0581 - 0.4581 - 0.5161
0.4871 - 0.5121 - 1
A similar question is given at: https://brainly.com/question/24337228
Answer:
Democratic 133 18 151
Republican 17 142 159
Total 150 160 310
Step-by-step explanation:
A hole the size of a photograph is cut from a red piece of paper to use in a picture frame. On a coordinate plane, 2 squares are shown. The photograph has points (negative 3, negative 2), (negative 2, 2), (2, 1), and (1, negative 3). The red paper has points (negative 4, 4), (4, 4), (4, negative 4), and (negative 4, negative 4). What is the area of the piece of red paper after the hole for the photograph has been cut? 17 square units 25 square units 39 square units 47 square units Mark this and return
Answers
Answer:
its d 47
Step-by-step explanation:
yep yep
Answer:
D: 47
Step-by-step explanation:
Edge 2022
How do you expand ln(1/49^k)
Answers
Answer:
There are a few rules that we can use here:
ln(a^x) = x*ln(a)
ln(a) - ln(b) = ln(a/b)
ln(1) = 0
So here we want to expand:
ln(1/49^k)
First we can use the second property to get:
ln(1/49^k) = ln(1) - ln(49^k)
using the third property, we have:
ln(1/49^k) = ln(1) - ln(49^k) = 0 - ln(49^k)
ln(1/49^k) = - ln(49^k)
Now we can use the first property to get:
ln(1/49^k) = - k*ln(49)
Now we can use the fact that:
49 = 7*7 = 7^2
then:
- k*ln(49) = -k*ln(7^2) = -2*k*ln(7)
So we have:
ln(1/49^k) = (-2*ln(7))*k
We can expand it anymore because this is a real number "(-2*ln(7))" times a variable k.
An automobile manufacturer has given its van a 47.2 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 47.0. Assume the population standard deviation is known to be 1.9. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answers
Answer:
Test statistic = 1.664
Step-by-step explanation:
The hypothesis :
H0 : μ = 47.2
H1 : μ ≠ 47.2
Given that :
Sample mean, xbar = 47
Sample size, n = 250
Standard deviation, σ = 1.9
The test statistic :
(xbar - μ) ÷ (σ/√(n))
T = (47 - 47.2) ÷ (1.9/√(250))
T = (0.2 / 0.1201665)
Test statistic = 1.664
what is the answer for this question?
1. Dayne has three investment portfolios: A, B and C. Portfolios A, B and C together are worth a total of $175000, portfolios A and B together are worth a total of $143000, while portfolios A and C together are worth a total of $139000.
Use Cramer’s Rule to find the value of each portfolio.
Answers
Answer:
The correct answer is:
Portfolio A = $107,000
Portfolio B = $36,000
Portfolio C = $32,000
Step-by-step explanation:
According to the question,
[tex]A+B+C=175000[/tex]...(1)
[tex]A+B = 143000[/tex]...(2)
[tex]A+C=139000[/tex]...(3)
Now,
From (1) and (2), we get
⇒ [tex]Portfolio \ C = (1)-(2)[/tex]
[tex]=175000-143000[/tex]
[tex]=32000[/tex]...(4)
From (1) and (3), we get
⇒ [tex]Portfolio \ B =(1)-(3)[/tex]
[tex]=175000-139000[/tex]
[tex]=36000[/tex]...(5)
From (1), (4) and (5), we get
⇒ [tex]Portfolio \ A = (1)-(4+5)[/tex]
[tex]=175000-(36000+32000)[/tex]
[tex]=175000-68000[/tex]
[tex]=107000[/tex]
Thus the above is the correct answer.
A general contractor is constructing a building that requires a concrete foundation that is to be 20 feet by 22 feet and 24 inches thick. If the local home supply store sells concrete for $ 110 per cubic yard, what will be the cost of the concrete for the foundation?
Express your answer rounded up to the next whole dollar.
Answers
Answer:
$38427
Step-by-step explanation:
Surface Area Formula: A=2(wl+hl+hw) where l=length w=width h=height
A=2((20(22))+(22(2))+(20(2)) = 1048ft^2
3 ft = 1yds -> 1048 ft = 349 1/3 yds
349 1/3(110)= 38426.66666
$38427
Answer: $2,613,600
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit conversion and a rectangular prism.
When there are multiple units occurring in the same question, then we should convert all the units into one by different conversion factors.
A rectangular prism is a three-dimensional figure that has 6 sides that are rectangles.
1 foot = 12 inches
1 yard = 3 feet
V (rectangular prism) = w · l · h
Solve:
24 inches = 24 / 12 = 2 feet
$110 per cubic yard = 110 × 3³ = $2970 per cubic feet
V = w · l · h
V = (20) (22) (2)
V = 880 feet³
880 × 2970 = $2,613,600
Hope this helps!! :)
Please let me know if you have any questions
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $30.8, and the standard deviation is known to be $8.2. How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39
Answers
Answer:
A sample of 1699 would be required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation is known to be $8.2.
This means that [tex]\sigma = 8.2[/tex]
How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39?
This is n for which M = 0.39. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.39 = 1.96\frac{8.2}{\sqrt{n}}[/tex]
[tex]0.39\sqrt{n} = 1.96*8.2[/tex]
[tex]\sqrt{n} = \frac{1.96*8.2}{0.39}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*8.2}{0.39})^2[/tex]
[tex]n = 1698.3[/tex]
Rounding up:
A sample of 1699 would be required.
i need y’alls help !!
Answers
Answer for this prob
What is the volume of this rectangular pyramid?
______ cubic feet
Answers
Answer:
Step-by-step explanation:
L = 4 ft
W = 3 ft
H = 7 ft
volume = LWH/3 = 28 ft³
The cost, c, for mailing books is a function of the number of books, b. The
cost to mail books is $0.50 per book plus a $3.00 flat fee
Answers
Answer:
c = 3.00 + .50b
Step-by-step explanation:
The cost is the flat fee plus the cost per book times the number of books
c = 3.00 + .50b
c = 0.5b + 3
b (number of books) is the slope
3 (the flat fee) is the y-intercept
hope this helps!
Factor: x^3-2x^2-8x
1. (x-4)(x+2)
2. x(x+4)(x-2)
3. x(x-4)(x+2)
4. (x-4)(x^2+2x)
Answers
Answer:
x( x-4)(x+2)
Step-by-step explanation:
x^3-2x^2-8x
First factor out the greatest common factor x
x( x^2 -2x -8)
What 2 numbers multiply to -8 and add to -2
-4*2 = -8
-4+2 = -2
x( x-4)(x+2)
a)
3. A bag contains chocolates: 3 Snickers, 5 Hershey Bars, 6 Kit-Kat Bars, 6 Milky Ways
Without replacing any of the chocolates back to the bag
a) What is the probability of selecting 2 Snickers?
b) What is the probability of selecting a Snickers and Hershey Bar in that order?
c) What is the probability of selecting a Milky Way and a Kit Kat bar in that order?
Answers
The probability of selecting 2 Snickers is 3/190. The probability of selecting a Snickers and Hershey Bar in that order is 3/76. The probability of selecting a Milky Way and a Kit Kat bar in that order is 18/190.
Number of Snickers = 3
Number of Hershey Bars = 5
Number of Kit-Kat Bars = 6
Number of Milky Ways = 6
Total number of chocolates = 20
a) What is the probability of selecting 2 Snickers?
= 3/20 × 2/19
= 3/190
The probability of selecting 2 Snickers is 3/190
b) What is the probability of selecting a Snickers and Hershey Bar in that order?
= 3/20 × 5/19
= 3/76
The answer is 3/76
c) What is the probability of selecting a Milky Way and a Kit Kat bar in that order
= 6/20 × 6/19
= 18/190
The probability is 18/190
Read related link on:
https://brainly.com/question/13604758
Which of the following will help increase productivity?
Answers
Circled one please help
Answers
Formula-
If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}
Symbol that can be used-
The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".
Hope it helps you... pls mark brainliest if it helped you.
Find the least common multiple of 14 and 22.
Answers
154
Step-by-step explanation:
14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154,…
22: 22, 44, 66, 88, 110, 132, 154,…
The least common multiple is 154
Find m2 ABD.
A
D
40°
B
C
Answers
40°
Step-by-step explanation:
m∠ABD = m∠DBC because they’re being split equally among m∠ABC
Therefore, m∠ABD = 40°
Find the slope of the line through the pair of points. (7.-10) and (-6, -3)
Answers
Answer:
Fraction form: 7/-13
Decimal form:-0.53846153846154
lvnununuunkmviodjoifmvujibg ibzf
r
Answers
Answer:
speaking giberish
Step-by-step explanation:
cos it is just a word that is rare
work for 12 hours and earn $140 find the unit rate
Answers
Answer:
11.60
Step-by-step explanation:
To find unit rate, you need to use the formula:
(amount of money) ÷ (amount of hours)
Since we have both, we can plug in
140 ÷ 12 will give you approximately 11.6
So, you receive $11.60 every hour.
Lainey is looking for a new apartment and her realtor keeps calling her with new listings. The calls only take a few minutes, but a few minutes here and there are really starting to add up. She's having trouble concentrating on her work. What should Lainey do? a) Tell her realtor she can only receive text messages O b) Limit the time spent on each call O c) Turn off her phone until she is on a break O di Call her realtor back when customers won't see her on the phone
Answers
a...cause she's having trouble concentrating,for her to work she needs to tell her realtor she can only receive text messages it enables her to know the process of the house hunt
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C (3y +5e√x)dx + (10x + 3 cos y2)dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2
Answers
By Green's theorem, the line integral
[tex]\displaystyle \int_C f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy[/tex]
is equivalent to the double integral
[tex]\displaystyle \iint_D \frac{\partial g}{\partial x} - \frac{\partial f}{\partial y} \,\mathrm dx\,\mathrm dy[/tex]
where D is the region bounded by the curve C, provided that this integrand has no singularities anywhere within D or on its boundary.
It's a bit difficult to make out what your integral should say, but I'd hazard a guess of
[tex]\displaystyle \int_C \left(3y+5e^{-x}\right)\,\mathrm dx + \left(10x+3\cos\left(y^2\right)\right)\,\mathrm dy[/tex]
Then the region D is
D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}
so the line integral is equal to
[tex]\displaystyle \int_0^1\int_{x^2}^{\sqrt x} \frac{\partial\left(10x+3\cos\left(y^2\right)\right)}{\partial x} - \frac{\partial\left(3y+5e^{-x}\right)}{\partial y}\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \int_{x^2}^{\sqrt x} (10-3)\,\mathrm dy\,\mathrm dx \\\\ = 7\int_0^1 \int_{x^2}^{\sqrt x} \mathrm dy\,\mathrm dx[/tex]
which in this case is 7 times the area of D.
The remaining integral is trivial:
[tex]\displaystyle 7\int_0^1\int_{x^2}^{\sqrt x}\mathrm dy\,\mathrm dx = 7\int_0^1y\bigg|_{y=x^2}^{y=\sqrt x}\,\mathrm dx \\\\ = 7 \int_0^1\left(\sqrt x-x^2\right)\,\mathrm dx \\\\ = 7 \left(\frac23x^{3/2}-\frac13x^3\right)\bigg|_{x=0}^{x=1} = 7\left(\frac23-\frac13\right) = \boxed{\frac73}[/tex]
