Answer:
[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]
Step-by-step explanation:
Given
[tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]y(1) = 0[/tex]
[tex]y'(1) =e[/tex]
Required
The solution
Differentiate [tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]y' = c_1e^x - c_2e^{-x}[/tex]
Next, we solve for c1 and c2
[tex]y(1) = 0[/tex] implies that; x = 1 and y = 0
So, we have:
[tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]0 = c_1 * e^1 + c_2 * e^{-1}[/tex]
[tex]0 = c_1 e + \frac{1}{e}c_2[/tex] --- (1)
[tex]y'(1) =e[/tex] implies that: x = 1 and y' = e
So, we have:
[tex]y' = c_1e^x - c_2e^{-x}[/tex]
[tex]e = c_1 * e^1 - c_2 * e^{-1}[/tex]
[tex]e = c_1 e - \frac{1}{e}c_2[/tex] --- (2)
Add (1) and (2)
[tex]0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2[/tex]
[tex]e = 2c_1e[/tex]
Divide both sided by e
[tex]1 = 2c_1[/tex]
Divide both sides by 2
[tex]c_1 = \frac{1}{2}[/tex]
Substitute [tex]c_1 = \frac{1}{2}[/tex] in [tex]0 = c_1 e + \frac{1}{e}c_2[/tex]
[tex]0 = \frac{1}{2} e+ \frac{1}{e}c_2[/tex]
Rewrite as:
[tex]\frac{1}{e}c_2 = -\frac{1}{2} e[/tex]
Multiply both sides by e
[tex]c_2 = -\frac{1}{2} e^2[/tex]
So, we have:
[tex]y=c_1e^x +c_2e^{-x[/tex]
[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}[/tex]
[tex]y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}[/tex]
Mitchell and his friends went to the candy store, where they can buy candy by the pound. Mitchell bought 1.2 pounds of candy. His friends bought 2.3 pounds and 1.8 pounds. About how many pounds of candy did they buy altogether?
rounding
Answer:
5.3 pounds
Step-by-step explanation:
1.2 plus 1.8 is 3 pounds
then you add 3 pounds plus 2.3 lbs and you get
5.3 pounds
Answer:
5.3
Step-by-step explanation:
If you add how much Mitchell bought (1.2) and how much his friends bought (2.3), (1.8) therefore the answer is 5.0 or rounded is just 5
The graphs below have the same shape. What is the equation of the blue graph?
Answer:
the answer is D
Step-by-step explanation:
Answer:
werwegwrvetvytby46bu46unu46e8mn667mmmm
Step-by-step explanation:m7
ui 6ei 67i77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777mmm
The question is in the image
Answer:
$9Step-by-step explanation:
f(x) = - 25 ( x - 9 )² + 200when x = 5 ,
f(5) = - 25 ( 5 - 9 )² + 200 = - 200
when x = 9 ,
f(9) = - 25 ( 9 - 9 )² + 200 = 200
when x = 10 ,
f(10) = - 25 ( 10 - 9 )² + 200 = 175
when x = 15 ,
f(15) = - 25 ( 15 - 9 )² + 200 = -700
∴ when price = $9
the company receive the maximum profit
Answer:
9$
Step-by-step explanation:
Which of the following is a radical equation?
Answer:
[tex]\sqrt{x} +3 =13[/tex]
Step-by-step explanation:
A radical equation is any equation in which a variable is under a root. This is the only equation in which x is under the square root, so this is the radical equation.
what is the equation of the line shown?
Answer:
y=1/2x+1/2
Step-by-step explanation:
the line intercepts at (0,0.5) which makes the y-intercept 1/2 and if you look at the slope, it increases 1 unit up and 2 units to the right so the slope is also 1/2
The equation of line is y= 1/2x+ 1/2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Take points from the graph as (-1, 0) and (3, 2).
So, slope of line = (2 - 0)/ (3 -(-1))
= 2/4
= 1/2
Now, slope- intercept form
y- 0 = 1/2 ( x-(-1))
y= 1/2x + 1/2
Hence, the equation of line is y= 1/2x+ 1/2
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
Select the correct answer.
A distribution center is redesigning two of its shipping boxes. The volume of these two boxes needs to be the same, and their dimensions are shown.
Write a system of equations to represent the volume of each box, y. Which statement describes the number and viability of the systems solutions?
Answer:
The system has two solutions, but only one is viable because the other results in negative side lengths.
Step-by-step explanation:
correct on edmentum or plato
help leee plzzzzzzzbbbnbbbb
Given: triangle RST is circumscribed about circle A.
m∠APT = _____°
Answer:
90
Step-by-step explanation:
From the given drawing, we have;
ΔRST is circumscribed about circle A
The center of the circle A = The point A
The line RT = A tangent to the circle A
The radius to the circle A = The line AP
According to circle theory, a line which is tangent to a circle is perpendicular to the radius of the circle drawn from the point of tangency
Where two lines are perpendicular to each other, then the angle formed between them = 90°
The angle formed between a tangent and the radius of the circle = m∠APT
Therefore;
m∠APT = 90°
find the discriminantof the quadratic equation root 2 X square + 7 x + 5 root 2
[tex]\displaystyle\ 2x^2+7x+5\sqrt{2} =0 \\\\\boxed{D=7^2-4\cdot2\cdot 5\sqrt{2} =49-40\sqrt{2} }[/tex]
Jamal bought a diamond ring at a 20% discount. He paid $2640 for the ring. Naomi bought a similar ring but was given a discount of $924. What was the percentage discount given to Naomi?
Answer: 72%
Step-by-step explanation:
Set Jamal's original ring price = x
[tex]x - x(0.2) = 2640\\x(1-0.2)=2640\\x(0.8)=2640\\x=\frac{2640}{0.8}=3300[/tex]
Jamal's original ring price = $3300
Set Naomi's discount = y
[tex]3300-3300(y)=924\\=3300(1-y)=924\\1-y=\frac{924}{3300} \\-y=\frac{924}{3300} -1\\y=1-\frac{924}{3300}=1-0.28=0.72[/tex]
Naomi's discount is 0.72 = 72%
WILL GIVE BRAINLIEST AND 20 POINTS!
PLEASE SHOW WORK1
f={(−2,−5),(3,−1),(1,−1)} and g={(1,1),(−1,−2),(−4,1),(−3,−1)}
Find (f+g)(1).
Answer:
[tex](f+g)(1)=0[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle f=\left\{(-2, -5), (3, -1), (1, -1)\right\}\text{ and } \\ \\ g = \left\{(1, 1), (-1, -2), (-4, 1), (-3, -1)\right\}[/tex]
And we want to find the value of (f + g)(1).
Recall that this is equivalent to:
[tex]=f(1)+g(1)[/tex]
According to the set, f(1) = -1 and g(1) = 1. Hence:
[tex]=(-1)+(1)=0[/tex]
PLEASE HELP!!!
Verify sin(180°- θ) = sin θ
SHOW WORK!!!
Answer:
see explanation
Step-by-step explanation:
Using the identity
sin(x - y) = sinxcosy - cosxsiny , then
sin(180 - θ)
= sin180cosθ - cos180sinθ
= (0) cosθ - (- 1)sinθ
= 0 + sinθ
= sinθ
Need help ASAP !!!!!!
answer:
to test whether agraph is linear
Score for Question 2: ___ of 5 points) 2. Write the equation of the circle in general form. Show your work.
Answer:
[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]
Step-by-step explanation:
Given
See attachment for circle
Required
The circle equation
First, we get the radius of the circle.
From the attachment, we have:
[tex]r = 3[/tex]
Next, the center of the circle
[tex](h,k) = (-1,1)[/tex]
The equation of the circle is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
This gives:
[tex](x - -1)^2 + (y - 1)^2 = 3^2[/tex]
[tex](x +1)^2 + (y - 1)^2 = 3^2[/tex]
Expand
[tex]x^2 + 2x + 1 + y^2 - 2y + 1 = 9[/tex]
Collect like terms
[tex]x^2 + y^2 + 2x - 2y + 1 + 1 - 9 = 0[/tex]
[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]
Hence, the equation in general form is:
[tex]x^2 + y^2 + 2x - 2y - 7 = 0[/tex]
Can someone help me with this math homework please!
Answer:
addition one is: (1/2) + 5x - (1/2)= 8 - (1/2)
muliplcation one is: (4x)(1/4)=(3) (1/4)
subtracting one is: 3x-4+4=12+4
division one is: 55/11 = 11x/11
Step-by-step explanation:
Hope this helps and good luck :)))
which of the gollowing cirxles lie completely within the third quadrant? Check all that apply
Option B
Option C
These two circles lie completely within the third quadrant
Answered by GAUTHMATH
jordan wants to save to buy a car and decides to open a banking account that is offering an interest rate of 4.5% compounded annually how much will jordan have in the account after 5 years it he deposits $7,000 today?
Answer:
8,723.27$
Step-by-step explanation:
Graph: Y - 3 = 1/2 (x+2)
Answer:
see graph
Step-by-step explanation:
Personally I put into slope intercept form before graphing
y - 3 = 1/2 (x+2)
y -3 = 1/2x + 1
y = 1/2x + 4
4 is y-intercept
1/2 is slope. [tex]\frac{Rise= 1}{Run= 2}[/tex]
Pier is a teacher
There are 13 boys and 17 girls in the class
Pier chooses one student at random
Workout the probability the student is a boy
Answer:
I think its 43%
Explanation
math
The probability of Pier choosing a boy is 0.43 or 43%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The total number of students in the class is:
13 boys + 17 girls
= 30 students
The probability of Pier choosing a boy is the number of boys in the class divided by the total number of students:
Probability of choosing a boy.
= number of boys / total number of students
Probability of choosing a boy.
= 13 / 30
Probability of choosing a boy.
= 0.4333 or approximately 0.43
Therefore,
The probability of Pier choosing a boy is 0.43 or 43%.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ2
What is the constant of variation, k, of the direct variation, y = for, through (5,8)?
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
The constant of direction variation givens a proportion that is maintained by both x and y values for all points of a line that it passes through.
Usually represented with the variable [tex]k[/tex], it is given by:
[tex]\frac{y}{x}=k[/tex] for coordinates (x, y).
This relationship can be written as [tex]y=kx[/tex] which is also the layout for a proportional relationship.
Since coordinates are written (x, y), for point (5, 8), substitute [tex]x=5, y=8[/tex] to get the constant of variation:
[tex]8=5k,\\k=\boxed{\frac{8}{5}}[/tex]
Answer:
8/5
Step-by-step explanation:
Given that y varies directly with x , therefore ,
[tex]\implies y \propto x[/tex]
Let k be the constant . Therefore ,
[tex]\implies y = k x[/tex]
When the point is (5,8) ,
[tex]\implies 8 = k * 5 \\\\\implies \underline{\underline{\boxed{ k =\dfrac{8}{5}}}}[/tex]
Hence the constant of variation is 8/5.
if two angles are supplementary, then what is the measurement of the missing angle, if one angle is 120?
Answer: 60°
Step-by-step explanation:
If two angles are supplementary, that means they add up to 180°.
Therefore, if one angle is 120°, the other missing angle can be calculated by:
180° - 120° = 60°
pls help will mark brainliest
Answer:
C
Step-by-step explanation:
The other answers have inputs (x) that have multiple outputs (y) which goes against the definition of a function. For example in answer D zero has both the outputs of 7 and 52 which can not happen in order to be a function. However outputs can have multiple inputs just not the other way around.
I need help with this it’s saying the “blank” Method would be the best for solving this system of equations
6x + 4y=8
-x+4y=12
Answer:
-12+4y=x..............1
6(-12+4y)+4y=8
-72+24y+4y=8
28y=80
y=3.33
-12+4(3.33)=x
1.32=x
Help and explain please !!!
Answer:
D
Step-by-step explanation:
f(x) = x-4
f(3.2) = -3.2-4
= -7.2
In a survey of 600 students in a school. 150 student were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee Find how many Students were taking neither tea nor coffee
Answer:
125
Step-by-step explanation:
600=150+225+100+X=475+X
600-475=125=X
X=125
Answer: 325 I believe!
Step-by-step explanation:
A farmer in China discovers a mammal
hide that contains 71% of its original
amount of C-14.
N = Noekt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
Step-by-step explanation:
I'm assuming you're looking for the age of the mammal hide, since there's no question here, but there's also nothing else to solve for. Remember a few things before we move on. First, if we are not told the initial amount with which we start, we have to assume that it's 100%. Second, remember that natural log and e are inverses of each other so they eliminate each other in application. Now to set up the problem. It looks like this:
[tex]71=100e^{-.0001t}[/tex] and begin by dividing both sides by 100 to get
[tex].71=e^{-.0001t}[/tex] and take the natural log of both sides. The other important thing to remember about the rules for logs and natural logs is that when you take the natural log of something, you are "allowed" to move the exponent down out front, which is why we do this. We cannot currently solve for t when it's stuck up there where it is right now. Taking the natural log allows us to bring that exponent down AND eliminate both the natural log and the e at the same time:
ln(.71) = -.0001t and we divide to solve for t:
[tex]\frac{ln(.71)}{-.0001}=t[/tex] and
[tex]\frac{-.3424903089}{-.0001}=t[/tex] so
t = 3424.9 years, or rounded, 3425 years.
x/5 = 2/3 = 5/y find the ratio from x to y
Answer:B
Step-by-step explanation:because im smart
The marked price of a fan is Rs 1,620 and selling price is Rs 1,539. Find the discount amount.
Answer:
rs. 81
Step-by-step explanation:
given,
mp. = 1620
sp. = 1539
now,
discount = mp - s.p = 1620 - 1539 = 81
Sila jogged 12 kilometers today and wants to know how far she traveled in feet. What error did Sila make while converting from kilometers to feet? StartFraction 12 kilometers Over 1 EndFraction times StartFraction 0.62 miles Over 1 kilometer EndFraction times StartFraction 5280 feet Over 1 mile EndFraction = 392,832 feet Sila put a wrong number in her calculator when multiplying the numerators. Sila's first fraction should be StartFraction 1 kilometer Over 0.62 miles EndFraction. Sila's last fraction should be StartFraction 1 mile Over 5280 feet EndFraction. Sila forgot to divide by 0.62.
Answer:
Sila put a wrong number in her calculator when multiplying the numerators.
Step-by-step explanation:
StartFraction 12 kilometers Over 1 EndFraction times StartFraction 0.62 miles Over 1 kilometer EndFraction times StartFraction 5280 feet Over 1 mile EndFraction = 392,832 feet
Correct calculation:
12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile
= (12km * 0.62 miles * 5280 feet) / (1 * 1 km * 1 mile)
= 39,283.2 feet
Sila's calculation:
12 km/ 1 * 0.6miles / 1km * 5280 feet / 1 mile
= 392,832 feet
Is 7 1/5 times 49 7/5 equivalent to 343
Step-by-step explanation:
7 1/5=36/5
49 7/5=252/5
[tex] \frac{36 \times 252}{5 \times 5} \\ = \frac{9072}{25} \\ = 362.88[/tex]
not equal to 343
Brainliest please~