The argument; if he did not get a good wage, then he must not have studied medicine is valid.
What is valid proof?Let P represent "He studies medicine"
Let Q represent "He gets a good job"
Let R represent "He gets a good wage"
The argument can be written as:
P → Q
Q → R
¬R
∴ ¬P (conclusion: he did not study medicine)
Assume for contradiction that the argument is invalid:
P → Q
Q → R
¬R
P (assumption for contradiction: he studied medicine)
Use modus ponens to derive Q from (5) and (1):
Q (from 1 and 5 using MP)
Use modus ponens again to derive R from (6) and (2):
R (from 2 and 6 using MP)
This contradicts ¬R in (3), so our assumption in (5) must be false. Therefore, we can conclude that the argument is valid:
¬P (from contradiction of assumption in (5))
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If z=(x+y)e^y and x=5t and y=1−t^2, find the following derivative using the chain rule. Enter your answer as a function of t.
dz/dt= ?
By the chain rule, if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then
[tex]\dfrac{\mathrm dz}{\mathrm dt} = \dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt} + \dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
We have [tex]f(x,y)=(x+y)e^y[/tex], for which
• [tex]\dfrac{\partial f}{\partial x} = e^y[/tex]
• [tex]\dfrac{\partial f}{\partial y} = e^y + (x+y)e^y = (x+y+1)e^y[/tex]
and [tex]x(t)=5t[/tex] and [tex]y(t)=1-t^2[/tex], so that
• [tex]\dfrac{\mathrm dx}{\mathrm dt} = 5[/tex]
• [tex]\dfrac{\mathrm dy}{\mathrm dt} = -2t[/tex]
Putting everything together, we get
[tex]\dfrac{\mathrm dz}{\mathrm dt} = 5e^y - 2t(x+y+1)e^y \\\\ \dfrac{\mathrm dz}{\mathrm dt} = 5e^{1-t^2} - 2t(5t-t^2+2)e^{1-t^2} = \boxed{\left(2t^3-10t^2-4t+5\right)e^{1-t^2}}[/tex]
The solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].
What is the Chain rule?The chain rule explains how to calculate a composite function's derivative.
What is a composite function?If you may write [tex]f(g(x))[/tex] , a function is composite. It's a function within a function, or a function of a function, in other words.
By the chain rule, we can write if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then,
[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]
As it is given to us, [tex]f(x,y)=(x+y)e^y[/tex], therefore, we can write,
[tex]\dfrac{\partial f}{\partial x}=e^y[/tex][tex]\dfrac{\partial f}{\partial y}=e^y+(x+y)e^y=(x+y+1)e^y[/tex]And x(t)=5t, while y(t)=1-t², So,
[tex]\dfrac{dx}{dt}=5[/tex][tex]\dfrac{dy}{dt}=-2t[/tex]Now, Substitute all the values together, in the equation,
[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]
Substituting the values we will get,
[tex]\dfrac{dz}{dt} &=(5 \times e^y)+[-2t(x+y+1)e^y]\\\\[/tex]
[tex]=5e^{1-t^2}-2t(5t-t^2+2)e^{1-t^2}\\\\=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex]
Hence, the solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].
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Help please due today
A factory makes 3.65 meters of masking tape every second. How many meters of masking
tape can the factory make in 4 seconds?
Answer:
i think 14.6
Step-by-step explanation:
pls mark bainlyest
You have two cards with a sum of (-12) in your hand.
Add two more cards but the total of cards stay the same
Answer:
you could have a 6 and then a -6
or a 3 and a -3
or 0 and 0
have 2 cards with the same number but one is negative
Step-by-step explanation:
A rectangle has an area of 48 cm2 and a perimeter of 38 cm. What are the dimensions of the rectangle?
The dimensions of the rectangle will be 3 cm. and 16 cm..
Solution:
First, calculating the area of the rectangle, based on these dimensions,
Formula for the area of a rectangle:
A=LW
A=(3)(16), or A=(16)(3)
A=48 cm²✔
So, now we know that these dimensions satisfy the area of the rectangle, but do they satisfy the perimeter of the rectangle?
Now, calculating the perimeter of the rectangle, based on these dimensions,
Formula for the perimeter of a rectangle:
P=2(L+W)
P=2(3+16), or 2(16+3)
P=2(19)
P=38 cm ✔
Now, we know that both of these dimensions satisfy both of the given conditions. So, the final answer is that the two dimensions of the rectangle are 3 cm. and 16 cm.. I hope that this answer helped you find what you were looking for. Enjoy your day, and take care.
State the domain of each function.
1. [tex]g(a)=\sqrt{1+a^{2}}[/tex]
2. [tex]f(x)=\frac{2}{x} + \frac{4}{x+1}[/tex]
Please show your work, as the steps are the only reason I'm asking.
Answer:
[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]
[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]
Step-by-step explanation:
Question-1:we want to figure out the domain of the following function:
[tex] \displaystyle g(a) = \sqrt{1 + {a}^{2} } [/tex]
remember that, the domain of an even root function are all values of x for which the redicand is positive or 0 that is being said the domain of the function g(a) belong to [tex]\mathbb{R}[/tex] . another way to think about it, the domain of square root function f(x) belong to x≥0. In this case we have square variable in the redical so when we input a negative number, it yields a positive number with that said the domain of the function g(a) belong to all the real numbers.Thus,
[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]
Question-2:we'd like to find the domain of the following function:
[tex] \displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1}[/tex]
in order to do so we need to simplify it further,so simplify addition in order to do so the first step is to figure out the LCM of the denominator i.e x(x+1) ⇒ x²+x, secondly divide the denominator of every fraction by the LCM and multiply the result by the numerator of very fraction ,then finally add them therefore,
[tex] \displaystyle f(x)=\frac{2x + 2+4x}{ {x}^{2} + x } \\ \displaystyle \boxed{\frac{6x + 2}{ {x}^{2} + x }} [/tex]
we know that the domain of a rational function are all the values of x for which the denominator is different than 0.
the denominator of the function would be 0 when x=0 and -1 thus,
[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]
and we're done!
The Torrence family has a rectangular, in-ground pool in their yard. It holds 1700 ft of water. If it is 17 ft wide and 4 ft deep,
what is the length of the pool
9514 1404 393
Answer:
25 ft
Step-by-step explanation:
The volume is given by the formula ...
V = LWD . . . . . the product of length, width, depth
Solving for L, we have ...
L = V/(WD) = (1700 ft³)/((17 ft)(4 ft)) = 100/4 ft = 25 ft
The length of the pool is 25 ft.
need help with some khan academy stuff
Answer:
2.2 % per minute
35 minutes
Step-by-step explanation:
(0,23%) and (30, 89%)
We can find the slope
m = ( y2-y1)/(x2-x1)
= (89-23)/(30-0)
66/30
=2.2 % per minute
To get to full change we need 100-23 = 77 %
77% * 1 minute/ 2.2 % =35 minutes
J is the midpoint of CT
If:
CJ= 5x – 3 and
JT = 2x + 21
Find CT.
Answer:
74
Step-by-step explanation:
Since J is the midpoint, that just means that both CT and JT are going to be the same length. With that information we can create an equation and solve for x.
5x - 3 = 2x + 21
5x = 2x + 24
3x =24
x = 8
Now to find the length of CT, we will add both equations to find the total length.
5x - 3 + 2x + 21
5(8) - 3 + 2(8) + 21
40 - 3 + 16 + 21
37 + 16 + 21
53 + 21
74
Best of Luck!
Answer:
CT = 74
Step-by-step explanation:
J = the midpoint of CT
CJ = JT
5x – 3 = 2x + 21
+3 +3
------------------------
5x = 2x + 24
-2x -2x
-------------------------
3x = 24
x = 8
Now, we know that CT = CJ + JT
= 5x - 3 + 2x + 21
= 7x + 18
now our x value we found was 8 right? Plug that in here.
= 7 (8) + 18
= 56 + 18
= 74
Find the output, k, when the input, t, is -7.
k= 10t - 19
k=
Answer:
Here is the answer . hope this helps.
I apologize for asking this again but I need help finding the complementary angles, ASAP
Answer:
2nd option is correct
∠AEF and ∠FED , ∠AEG and ∠CEG
Step-by-step explanation:
1st option is a supplementary and even 3rd and 4th options
brainliest to best answer
Answer:
2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
so 2x1=2 so -2x-1=2
if its wrong i dont now cause im silly
PLS PLS PLS IM BEGGING YOU, HELP ME, i’ve been trying so hard to solve this for hours and i still dont get it :( pls help me
Answer:
m=79
t=54
Step-by-step explanation:
yes these are the answers
Answer:
angle t = 54 degrees
angle m=79(alternate angles)
Step-by-step explanation:
angle p=126 degrees
angle z=79 degrees
angle p + angle t=180(allied angles)
126 + t =180
t =180-126
t = 54 degrees
u=79(vertically opposite angles)
therefore;
angle m=79(alternate angles)
Calculate the difference and enter it below.
-19-(-10)
Answer here
Answer:
+1 is the answer
Step-by-step explanation:
-19-(-10)
-19+10
+1
If 32^2^c= 8^cC+7, what is the value of c?
Answer:
C=3
Step-by-step explanation:
Jaya's mother is 5 years more than three times her age. Find Jaya's age if her mother is 44 years old.
Answer:
Jaya is 13 years old.
Step-by-step explanation:
Let's assume Jaya's age to be x years old.
Jaya's mothers age is (3*x)+5.
3x+5=44
3x=39
x=13.
Three foreign languages are offered at Cliff High School. 1/6 of the students take French, 1/5 take Spanish, and 1/3 German. Which
fraction represents the number of students taking a foreign language at Cliff HS?
Answer:
1/3
Step-by-step explanation:
4. Los usuarios del transporte público llegan en forma aleatoria e independiente a una para de autobús. La tasa media de llegada es 10 persona por minuto.
a. Calcule la probabilidad de que no llegue ninguna persona en un lapso de un minuto.
b. Calcule la probabilidad de que lleguen tres o menos personas en un lapso de un minuto.
c. De que no llegue ninguna persona en un lapso de 15 segundos. d. De que llegue por lo menos una persona en un lapso de 15 segundos
Answer:
Step-by-step explanation:
What are two ways you could represent the expression 3-4n
There are not just "the two ways" to represent this expression. There are two ways, surely, but they are not the only ways as implied.
You could expose 4 and get something like [tex]4(\frac{3}{4}-n)[/tex] or expose 3 and get something like [tex]3(1-\frac{4}{3}n)[/tex].
But you could also say something like [tex]3-(1+3)n=3-n-3n=-3(n-1)-n[/tex]... in fact there are a lot of ways to write any expression.
Hope this helps :)
evaluate x^2 when x=5
Answer:
25
Step-by-step explanation:
x = 5
x^2 = 5^2 = 5*5 = 25
Answer:
25
Step-by-step explanation:
5*5=25
Simplify the following expression. 2p – 10 – 4p – 7
Answer:
the answer is-2p-3
hope is helpful
Answer:
2p – 10 – 4p –7
–2p –17
I hope I helped you^_^
solve the equation -7 x = -28
-7 x = -28
Divide both sides by -7.
x = 4
Please help
Solve the inequality.
|14 – 5x] > 8
[?]
x <
or x >
A
Answer:
x< -4/1 or x > 6/5
If our answers are different, just say so :)
solve -5x+y=1 and 9x-2y=4 using multiplication and then elimination.
Answer:
x = - 6, y = - 29
Step-by-step explanation:
Elimination:
2*(-5x + y = 1) = -10x + 2y = 2
9x - 2y = 4 = + (9x - 2y = 4) =
-x = 6
x = -6
9(-6)-2y=4
-54-2y=4
-2y=58
y=-29
I =∫▒dx/(x^2 √(x^2+4))
What is the midpoint of (-2,3) and (4,5)
If 3x+2=5/9, what is the value of −3x+8?
Answer:
[tex] \frac{85}{9} [/tex]
Step-by-step explanation:
hopefully the picture is clear and understandable!
:)
Help!
Which expression is equivalent to—
Answer:
2a
Step-by-step explanation:
[tex] \frac{4a + 4}{2a} \times \frac{ {a}^{2} }{a + 1} [/tex]
➡️ [tex] \frac{4(a + 1)}{2} \times \frac{a}{a + 1} [/tex]
➡️ [tex] = 2a[/tex] ✅
The formula for determining the pressure, p, exerted on an object at a depth, h, below the surface of a liquid is p = s + dgh, where s is the atmospheric pressure, d is the density of the liquid, and g is the acceleration due to gravity.
(Pls Explain in Simple terms)
Answer:
The formula for determining the pressure, p, exerted on an object at a depth, h, below the surface of a liquid is p = s + dgh,
S...
Find the length of UT.
12
T
14
W
2x+2
2x + 5
V
A. 32
B. 43
O o
C. 21
D. 39
9514 1404 393
Answer:
A. 32
Step-by-step explanation:
The relationship between segment lengths is ...
WT·WU = WC·WV
14(2x +2) = 12(2x +5)
28x +28 = 24x +60
4x = 32
2x = 16
Then the measure we're after is ...
UT = WT +WU = 14 +(16 +2)
UT = 32