2. Calculate an expression for dy/dx and d2y/dx2 in terms of t if the parametric pair is given as tan(x) = e^at and e^y = 1 + e^2at
Hint: Turn tan(x) = e^at and e^y = 1 + e^2at into expressions suited to your calculation.
I assume a is a constant. If tan(x) = exp(at) (where exp(x) means eˣ), then differentiating both sides with respect to t gives
sec²(x) dx/dt = a exp(at)
Recall that
sec²(x) = 1 + tan²(x)
Then we have
(1 + tan²(x)) dx/dt = a exp(at)
(1 + exp(2at)) dx/dt = a exp(at)
dx/dt = a exp(at) / (1 + exp(2at))
If exp(y) = 1 + exp(2at), then differentiating with respect to t yields
exp(y) dy/dt = 2a exp(2at)
(1 + exp(2at)) dy/dt = 2a exp(2at)
dy/dt = 2a exp(2at) / (1 + exp(2at))
By the chain rule,
dy/dx = dy/dt • dt/dx = (dy/dt) / (dx/dt)
Then the first derivative is
dy/dx = (2a exp(2at) / (1 + exp(2at))) / (a exp(at) / (1 + exp(2at))
dy/dx = (2a exp(2at)) / (a exp(at))
dy/dx = 2 exp(at)
Since dy/dx is a function of t, if we differentiate dy/dx with respect to x, we have to use the chain rule again. Suppose we write
dy/dx = f(t)
By the chain rule, the derivative is
d²y/dx² = df/dx
d²y/dx² = df/dt • dt/dx
d²y/dx² = (df/dt) / (dx/dt)
d²y/dx² = 2a exp(at) / (a exp(at) / (1 + exp(2at)))
d²y/dx² = 2 (1 + exp(2at))
2. Nora's bill at a store is $125. If she leaves a 2% tip for the gate keeper,
how much will the total bill be, including tip?
Answer:
$127.50
Step-by-step explanation:
All you have to do is $125 times 1.02 because it is adding to the price it is already.
$125 × 1.02.
Which is $127.50.
alguien podria ayudarme?
Answer:
con que?
Step-by-step explanation:
Write an equation of the perpendicular bisector of the segment with endpoints (3,-7) and (-5,3) writing non-integers as simplified fractions:
Answer:
Step-by-step explanation:
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Answer:
x=3
Step-by-step explanation:
What u should always do is look at the letters of the triangles given:
It will tell u that:
[tex] \frac{tu}{dc} = \frac{uv}{cb} [/tex]
Now we once again just sub in the values:
[tex] \frac{12}{9} = \frac{20}{4x + 3} [/tex]
we can simplify the fraction on the right
[tex] \frac{4}{3} = \frac{20}{4x + 3} [/tex]
And now we cross multiply
3×20=4(4x+3)
60=16x+12
60-12=16x
48=16x
Therefore :
x=3
the sum and product of zeroes are 4 and 1 respectively then the quadratic equation is
A. x² - 4x + 1 =0
B. x + 1=0
C 4x² +x +1 =0
D . x² + 7x+1 =0
Answer:
A. x²- 4x+ 1
option A is the answer
find the answer
fast
Answer:
i) 5y
Ii) 5y-3
iii) 5y×6
Iv)
Here is an encoded message, a message that has been converted into a code.
WRGDB LYD JRRG GDB.
Can you figure out what it says in English? How was the original message encoded?
7362*637 help please
Answer:
4689594
Step-by-step explanation:
solve the compound inequality 2(x-2)+7>-1 and 5-4x>9
Answer:
1) x > -2
2) x < -1
Step-by-step explanation:
1) 2(x - 2) + 7 > -1
2x - 4 + 7 > -1
2x + 3 > -1
2x > -4
x > -2
2) 5 - 4x > 9
-4x > 4
x < -1
Use the Pythagorean Theorem to find the distance, to the nearest tenth, between F(9,5) and G(-2, 2).
Answer:
Step-by-step explanation:
d = √((9 -(-2))² + (5 - 2)²)
d = √(11² + 3²)
d = √130
d = 11.401754250...
d = 11.4 units
Answer:
11.4 to the nearest tenth.
Step-by-step explanation:
Distance = sqrt((5-2)^2 + (9-(-2))^2)
= sqrt(3^2 + 11^2)
= sqrt 130
= 11.402
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Answer:
x=9
Step-by-step explanation:
since the triangles are similar, the sides are all in proportion. This means that:
[tex] \frac{uw}{eg} = \frac{uv}{fg} [/tex]
Now we can just sub in the sides:
[tex] \frac{91}{13} = \frac{56}{x - 1} [/tex]
simplify the first fraction
[tex] \frac{7}{1} = \frac{56}{x - 1} [/tex]
Now we can cross multiply
56=7(x-1)
56=7x-7
63=7x
Therefore:
×=9
Complete the explanation of how you can use a table of values, an equation, and
a qraph to determine whether a function represents a proportional relationship.
Answer:
Step-by-step explanation:
Two cities, A and B, are mapped on the coordinate plane. How far apart are they from each other?
I can’t help because I can’t see the coordinate plane.
what is 130mins into hours and minutes?
Answer:
Step-by-step explanation:
1 Hour = 60 minutes
60 + 60 = 120 minutes
120 minutes = 2 hours
Add 10 minutes
2 hours 10 minutes = 130 minutes
Beatrice watched two films at the theatre. The first she watched was 2 1/6 hours long and the second film was 1 5/6 hours long . Calculate the total length of the two films
Answer:
4 Hours
Step-by-step explanation:
2 1/6 = 13/6
1 5/6 = 11/6
13/6+11/6= 24/6
Simplify 24/6 which will give you 4
4. You have 36 pairs of running shoes. Let x be the
number of Nikes and y be the number of Adidas shoes
you own. You own twice as many Nikes as Adidas
shoes.
d
Write and solve a linear system of equations to find the
number of each brand of shoes.
Answer:
Nikes: 24 pairsAdidas: 12 pairsStep-by-step explanation:
The system of equations can be written ...
x + y = 36
x = 2y
__
The system can be solve by substituting for x:
(2y) +y = 36
y = 12 . . . . . . divide by 3
x = 2(12) = 24
There are 24 pairs of Nikes and 12 pairs of Adidas.
(Quick Please) 8x - 4 < -36 solve the equality show your work
Answer is -4
Step-by-step explanation:
8x-4< -36
8x < -36+4 (move [- 4] to the other side to find x)
8x < -32
8x < -4
Answer:
x < -4
Step-by-step explanation:
8x - 4 < -36
+4 +4 (Add 4 on both sides)
8x < -32
/8 /8 (Divide by 8 on both sides)
x < -4
1. The length of time, in hours, it takes an "over 40" group of people to play one soccer match is
normally distributed with a mean of two hours and a standard deviation of 0.5 hours. A sample of
size n = 50 is drawn randomly from the population. Find the probability that the sample mean is
between 1.8 hours and 2.2 hours.
The probability that the sample mean is between 1.8 hours and 2.2 hours. is; 0.99535
What is the Probability in Normal Distribution?
We are given;
Sample size; n = 50
Standard deviation; σ = 0.5
Mean; μ = 2
The formula to find the z-score for each sample mean is;
z = (x' - μ)/(σ/√n)
Thus, for x' = 1.8, we have;
z = (1.8 - 2)/(0.5/√50)
z = -2.83
For x' = 2.2, we have;
z = (2.2 - 2)/(0.5/√50)
z = 2.83
Thus, the probability that the sample mean is between 1.8 hours and 2.2 hours. is;
P(-2.83 < Z < 2.83) = 0.99535
Read more about Normal Distribution Probability at; https://brainly.com/question/4079902
#SPJ1
Amare runs 1\10 mile in 2\3 minute. What is his speed in miles per minute? Show your work
Answer:
60
Step-by-step explanation:
HELP ME! I WILL GIVE BRAINLIEST
Answer:
#1 matches with the pizza scenario
#2 matches with the present scenario
#3 matches with the Sarah scenario
Step-by-step explanation:
Look for keywords at the end of the questions and if they go hand and hand (such as in 7 hours / yield 20 servings) then they go together as a pair
Translate the phrase into a variable expression. Use the letter p to name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(7) for division
the total number of peanuts divided among 4 baseball fans
Answer:
p/4
Step-by-step explanation:
You have p amount of peanuts and 4 baseball fans, so you divide p among 4, which is p/4
Answer: its p/10
Step-by-step explanation: i just did it
Josh and Adelina are staff members for a political candidate. They are considering hiring callers who will call
voters and ask for donations.
Josh and Adelina define X as the amount donated by a given voter they call. Based on data from their volunteer
callers, the expected value of X is E(X) = $18.07.
Adelina says, "For every 100 voters we call, we can expect to bring in about $1,807 in total donations."
Josh says, "If we call a very large number of voters, the average donation will be close to $18.07."
Whose statement is correct based on the expected value?
According to the given expected value, it is found that Josh's statement is correct.
The interpretation of the expected value is that over a large number of trials, the average value will be close to the expected value.In this problem, the expected amount donated by a given voter they call is $18.07.
Hence, considering a very large number of voters called, the average amounts of their donations will be close to $18.07, hence, Josh's statement is correct.100 voters is not a large amount, hence the expected value should vary around $18.07, and we can't say that Adelina's statement is correct.You can learn more about expected value at https://brainly.com/question/25858347
Answer:
both correct :)
Step-by-step explanation:
pls help me
I am giving brainliest
Work out the highest common factor (HCF) of 180 and 240
If I am correct, I believe that it is 60
help me plzzzzzzzzzzzz
Answer:
9) 21
10) 70
11) 34
12) 31
13) 50
14) 31
15) 137
16) 101
Step-by-step explanation:
9)
20+40=60
60 + b =180 ( sum of the interior angles on a triangle is 180 )
b = 180 - 60
b = 120
39 + c + ? = 180 ( sum of the interior angles on a triangle is 180 ) c =120 ( vertically opposite angles are equal )
39 + 120 + ? = 180
159 + ? = 180
? = 180 - 159
? = 21
________________________________________________________________________________________
10)
60 + 65 + b = 180 ( sum of the interior angles on a triangle is 180 )
125 + b = 180
b = 180 - 125
b = 55
50 + b + c = 180 ( sum of the angels on a straight line is 180 )
50 + 55 + c = 180
105 + c = 180
c = 180 - 105
c = 75
35 + c + ? = 180
35 + 75 + ? = 180
110 + ? = 180
? = 180 - 110
? = 70
________________________________________________________________________________________
11)
84 + 36 + b = 180 ( sum of the interior angles on a triangle is 180 )
120 + b = 180
b = 180 - 120
b = 60
86 + b + ? = 180 ( sum of the interior angles on a triangle is 180 )
86 + 60 + ? = 180
146 + ? = 180
? = 180 - 146
? = 34
________________________________________________________________________________________
12)
35 + 23 + b = 180 ( sum of the interior angles on a triangle is 180 )
58 + b = 180
b = 180 - 58
b = 122
27 + c + ? = 180 ( sum of the interior angles on a triangle is 180 ) c =122 ( vertically opposite angles are equal )
27 + 122 + ? = 180
149 + ? = 180
? = 180 - 149
? =31
________________________________________________________________________________________
13)
115 + b = 180 ( sum of the angels on a straight line is 180 )
b = 180 - 115
b = 65
65 + 90 + c = 180 ( sum of the angels on a straight line is 180 )
155 + c = 180
c = 180 - 155
c = 25
155 + d = 180 ( sum of the angels on a straight line is 180 )
d = 180 - 155
d = 25
c + d + e = 180 ( sum of the interior angles on a triangle is 180 )
25 + 25 + e = 180
50 + e = 180
e = 180 - 50
e = 130
e + ? = 180 ( sum of the angels on a straight line is 180 )
130 + ? = 180
? = 180 - 130
? = 50
________________________________________________________________________________________
14)
35 + 20 + b = 180 ( sum of the interior angles on a triangle is 180 )
55 + b = 180
b = 180 - 55
b = 125
156 + c = 180 ( sum of the angels on a straight line is 180 )
c = 180 - 156
c = 24
c + e + ? = 180 ( sum of the interior angles on a triangle is 180 ) e= 125 ( vertically opposite angles are equal )
24 + 125 + ? = 180
149 + ? = 180
? = 180 - 149
? = 31
________________________________________________________________________________________
15)
b = 45 ( vertically opposite angles are equal )
b + 60 + c = 180 ( sum of the interior angles on a triangle is 180 )
45 + 60 + c = 180
105 + c = 180
c = 180 - 105
c = 75
68 + 75 + e = 180 ( sum of the angels on a straight line is 180 )
143 + e = 180
e = 180 - 143
e = 37
100 + 37 + j = 180 ( sum of the interior angles on a triangle is 180 )
137 + j = 180
j = 180 - 137
j = 43
j + ? = 180 ( sum of the angels on a straight line is 180 )
43 + ? = 180
? = 180 - 43
? = 137
________________________________________________________________________________________
16)
b = 75 ( vertically opposite angles are equal )
c = 45 ( vertically opposite angles are equal )
b + c + e = 180 ( sum of the interior angles on a triangle is 180 )
75 + 45 + e = 180
120 + e = 180
e = 180 - 120
e = 60
e + 79 + j = 180 ( sum of the angels on a straight line is 180 )
60 + 79 + j = 180
139 + j = 180
j = 180 - 139
j = 41
j + 60 + s = 180 ( sum of the interior angles on a triangle is 180 )
41 + 60 + s = 180
101 + s = 180
s = 180 - 101
s = 79
s + ? = 180 ( sum of the angels on a straight line is 180 )
79 + ? = 180
? = 180 - 79
? = 101
________________________________________________________________________________________
hope this helps☆☆☆
it took soooo long to do btw ⊙•⊙
find the value
9-2(--6-4)
PLEASE HELPPPP QUICKLY LOOK AT THE ATTACHED PHOTO FOR TE QUESTION!!!
Answer:
[tex]\sqrt 10y[/tex]
Step-by-step explanation:
10*[tex]\sqrt{y}[/tex] is [tex]\sqrt 10y[/tex]
[tex]\sqrt{100y}[/tex]
Step-by-step explanation:
Recall that
[tex]10 = \sqrt{100}[/tex]
So we can write our original expression as
[tex]10\sqrt{y} = \sqrt{100}\sqrt{y}[/tex]
[tex]\;\;\;\;\;\;\;\;\;=\sqrt{100y}[/tex]
What are the common factors of 24 and 36?
O A. 1,2,4,6, 12
O B. 1,2,3,4,6,12
C. 1,2,3,4,6,8,12
O D. 1,3,4,9,18
Answer:
B. 1,2,3,4,6,12
Step-by-step explanation:
Factors of 24: 1, 24, 2, 12, 3, 8, 4, 6
Factors of 30: 1, 36, 2, 18, 3, 12, 4, 9, 6,
PLS HELP NO LINKS
A cardboard box has the dimensions 2 ft, 1.5 ft, and 1.2 ft. What is the volume of the box?
A. 3.2 ft
B. 3.6 ft
C. 4.7 ft
D. 14.4ft
Answer:
3.6 cubic feet
Step-by-step explanation:
The volume of the box is simply the product of the 3 sides. so [tex]2ft \times 1.5ft \times 1.2 ft = 3.6 ft^3[/tex]