[tex]\text{Given that,}\\\\\text{Area} = 12 b^7 b b^4 =12 b^{12}\\\\\text{Width} = 4a^2 b^2\\\\\text{Now,}\\\\\text{Length} \times \text{Width} =\text{Area} \\\\\implies \text{Length} = \dfrac{\text{Area}}{\text{Width}}=\dfrac{12b^{12}}{4a^2 b^2} = \dfrac{3b^{10}}{a^2}[/tex]
Y=1/2x-5
What is the slope?
Answer: 1/2
Step-by-step explanation:
Slope is the number in front of x
Answer:
The slope of the line or m is represented by 1/2. x and y are coordinates on the line and -5 represents the y-intercept. The used for this equation is y = mx + b. M = slope and b is the y-intercept
Step-by-step explanation:
Hope I made sense to you.
find the point (x,y) on the curve where dy/dx = 0
a. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx} = \dfrac{dy}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]
Given that [tex]y=e^t+e^{-t}[/tex] and [tex]x=e^{-t}[/tex], we have the derivatives
[tex]\dfrac{dy}{dt} = e^t -e^{-t}[/tex]
[tex]\dfrac{dx}{dt} = -e^{-t}[/tex]
and so
[tex]\dfrac{dy}{dx} = \dfrac{e^t - e^{-t}}{-e^{-t}} = 1-e^{2t}[/tex]
Set this equal to zero and solve for t :
[tex]1-e^{2t} = 0[/tex]
[tex]1 = e^{2t}[/tex]
[tex]\ln(1) = \ln\left(e^{2t}\right)[/tex]
[tex]0 = 2t \ln(e)[/tex]
[tex]0 = 2t[/tex]
[tex]t=0[/tex]
This value of t corresponds to x = e⁰ = 1 and y = e⁰ - 1/e⁰ = 1 - 1 = 0. So the only point on the curve where the derivative dy/dx is zero is (1, 0).
b. Compute the second derivative. Since dy/dx is a function of t, we'll momentarily replace it with f(t). By the chain rule,
[tex]\dfrac{d^2}{dx^2} = \dfrac d{dx} \dfrac{dy}{dx} = \dfrac{df}{dx} = \dfrac{df}{dt}\cdot\dfrac{dt}{dx} = \dfrac{df}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]
We have
[tex]\dfrac{df}{dt} = -2e^{2t}[/tex]
and we've already committed dx/dt. So
[tex]\dfrac{d^2}{dx^2} = \dfrac{-2e^{2t}}{-e^{-t}} = 2e^{3t} [/tex]
Substitute the first and second derivative into the differential equation:
[tex]\left(\dfrac{d^2y}{dx^2}\right)^2 + \dfrac{dy}{dx} - 1 = 0[/tex]
[tex]\left(2e^{3t}\right)^2 + (1-e^{2t}) - 1 = 0[/tex]
[tex]4e^{6t} -e^{2t}= 0[/tex]
[tex]e^{2t} (4e^{4t} - 1) = 0[/tex]
[tex]4e^{4t} - 1 = 0[/tex]
[tex]4e^{4t} = 1[/tex]
[tex]e^{4t} = \dfrac14[/tex]
[tex]\ln\left(e^{4t}\right) = \ln\left( \dfrac14\right)[/tex]
[tex]4t \ln(e) = -\ln(4)[/tex]
[tex]4t = -\ln(4)[/tex]
[tex]t = -\dfrac{\ln(4)}4[/tex]
A right triangle is shown in the graph. Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points) Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points) Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points)
Answer:
Part A, write out the equation by subtracting the vertex from x and y, then set it equal to the radius square. All of this information is given in the picture. Then the domain is all the x's and the range is all the y's starting at the center and going out 10 in each direction since 10 is the radius.
Step-by-step explanation:
Use the circle formula that you learned in lesson 3.02 using the given points. Remember this quiz was open note and your formula should be in your notes. Also, it should be familiar to you from Geometry and middle school math where you first learned about circles:)
3х – 11 = 22 solve x
Answer:
x=11
Step-by-step explanation:
3x-11=22
3x-11+11=22+11
3x=33
3x/3=33/3
x=11
Step-by-step explanation:
3x = 22 + 11
3x = 33
3x = 33/3
3x = 11
Find The nth Term of this number sequence
18, 16, 14, 12
a = 18
d = 16 - 18 = -2
an = a + (n - 1) × d
an = 18 + (n - 1) × (-2)
an = 18 - 2n + 2
an = -2n + 20
Determine whether the graphs of given pair of equations are parallel,
perpendicular, or neither. 2x+5y=15
3x+5y=15
Answer:
Neither because x can't equal 3 and equal 2 at the same time and 2x + 5y doesn't equal 3x + 5y. 3x is > 2x by one x
Step-by-step explanation:
Hope this answer works for you!
Below are the graphs of the functions y=2x and y3x What is the same about both lines?
sole the inequality x-8>-4
Answer:
[tex]x>4[/tex]
Based on this, we know the correct number line will be an empty bubble with a line going to the right of 4.
Step-by-step explanation:
[tex]x-8>-4[/tex]
add 8 to both sides of the inequality
[tex]x>4[/tex]
how many times can 2 go into 67
fourth grade help
Answer:
Step-by-step explanation:
To answer this, divide 67 by 2, writing the answer as a mixed number:
67
---- = 33 1/2
2
thus, 2 can go into 67 33 times, keeping in mind that there's a remainder (1/2).
Help me please!!!!!!!!!!!
What is the equation of the line that has a slope of 3 and goes through the point (-3,5)?
A. Y=3x +4
B. Y= 3x - 14
C. Y= 3x - 4
D. Y= 3x + 12
Answer:
C. y=3x-4
Step-by-step explanation:
I just know trust me
Solve for w.
16w–w–12w–2w=13
w=
Answer:
w = win
Step-by-step explanation:
w=13
Answer:
w = 13
Step-by-step explanation:
16w - w = 15w
15w - 12w = 3w
3w - 2w = w
w = 13
name the parts mentioned in the figure below
please answer this
Answer:
O - point
CD- chord
AB- diametre
I dont know PO sorry
Answer:
O is the center.
AB is the diameter.
OP is a radius.
CD is a tangent.
By the way the combination of letters is the two points that it relates too.
Step-by-step explanation:
hope this helps. . .<3
1. 2y +8x =70
2. 2y = 8x- 70
3. y= 8x- 70
What’s the slope and y intercept for these equations?
Can you give me some hint please
Describe how the point-slope formula is useful when writing the equation of a trend line
Step-by-step explanation:
if you observe the graph the y values increase as the x value increase.
so it has a possitive association.
if the value of y increase as the value of the x increase then data has positive association.
Multiply (4-5i)(4+i)
Answer:
this is the correct answer happy
A single card is drawn at random from a standard 52 card deck. Work out the following probabilities in their simplest form: P(4)= P(not 4)=
Answer:
Step-by-step explanation:
Total Number of possible outcomes = 52
Getting a jack from a deck of 52 cards for a certain event (A) = 4
The Probability (A) = 4/ 52
= 1 / 13 = 0.07
Hope you like it please mark as brainliest.
Order of operations and cross
reduce:
I got 20/3 but I think I’m wrong
Answer:
130/81
simplified: 1 49/81
Step-by-step explanation:
I did the math
Is the following relation a function?
X. Y
-1. -2.
2. 3
3. 1
6. -2
Answer:
Step-by-step explanation:
x y
−1 −2
2 3
3 1
6 −2
Answer:
no
Step-by-step explanation:
6 and -2 is not a function
How much is 2+10.
Please help me i dont know
Will give brainliest
Answer: 12
2 + 10
12
:)
Answer: 12
Step-by-step explanation: just add 2 to 10
What is the prime factorization of 270?
270 = 2 x 3 x 3 x 3 x 5 = 2 x 3^3 x 5
ok done. Thank to me :>
Answer:
2x3x3x3x5
Step-by-step explanation:
if your doing this on time4learning lesson type 5x2x3x3x3 to get it right it worked for me but it didnt work in any other order
Find complex numbers z=(x,y) such that
[tex]z ^{2} = - 5 - 12i[/tex]
Answer:
I don't know..,.............,,.,.......,
Dеtеrmіnе tһе rаnցе օf tһе fսnсtіօn f(х) = 3х - 5 ԝһеn tһе ԁօmаіn іѕ {-4, 2, 9}.
Answer:
range is { - 17, 1, 22 }
Step-by-step explanation:
Substitute the values from the domain (input) into f(x) for range
f(- 4) = 3(- 4) - 5 = - 12 - 5 = - 17
f(2) = 3(2) - 5 = 6 - 5 = 1
f(9) = 3(9) - 5 = 27 - 5 = 22
range is { - 17, 1, 22 }
¿Cuál es la pendiente perpendicular a la pendiente m = 3 ?
Answer:
The slope of a line perpendicular to a vertical line is zero.
Step-by-step explanation:
Function or non functional? Pls help ty :3
help quick due in 10 minutes you will be reported if you spam Ivan is 75 inches tall if his brother Logan was 5 inches shorter, he would be exactly half Evan's height How tall is Logan? Enter your answer as a decimal in the box,
Answer:
35
Step-by-step explanation:
if not correct I'm very very sorry I tried my best for this</3
Do you think you could use a multiply a 4 digit number by a 1 digit number
Answer:
line them up straight with the bottom number and the top number.
A square is 3 inches by 3 inches. What is its area
Answer:
9
Step-by-step explanation:
Because area is multipication, you need to multiply legth and width. So 3x3=6. Hope it helps! :)
11.2+X=-24.7. what is X
After doing some quick calculations, we can determine that X = −35.9
I hope this helps! :)
Answer:
x = -35.9
Step-by-step explanation:
Subtract both sides by 11.2 11.2 - 11.2 equals zero leaving x on one side.
x = - 24.7 - 11.2
A negative minus another negative number is a larger negative number.
x= -24.7 - 11.2 = -35.9
x = -35.9
. Consider the set {7,8,9), a subset of this set includes:
{2,3}
b. {5,63
c. none of these
d. {10,11
Answer:
Option "C" none of these is the correct answer.
Step-by-step explanation:
The subset of the set {7, 8, 9} must have the elements of this set only.
Hope this helps :)