[tex]\( f(2) = \ln \left( \frac{14}{3} \right) \)[/tex]. You can calculate this value to get a numerical result.
To find the particular solution [tex]\( y = f(x) \)[/tex] to the given differential equation [tex]\( \frac{dy}{dx} = \frac{x^2 + 1}{e^y} \)[/tex] with the initial condition [tex]\( f(1) = 0 \)[/tex] and then evaluate [tex]\( f(2) \),[/tex] we can follow these steps:
1. Separate variables:
[tex]\[ e^y dy = (x^2 + 1) dx \][/tex]
2. Integrate both sides:
[tex]\[ \int e^y dy = \int (x^2 + 1) dx \][/tex]
[tex]\[ e^y = \frac{1}{3} x^3 + x + C \][/tex]
3. Apply the initial condition [tex]\( f(1) = 0 \):[/tex]
[tex]\[ e^0 = \frac{1}{3} (1)^3 + 1 + C \][/tex]
[tex]\[ 1 = \frac{1}{3} + 1 + C \][/tex]
[tex]\[ C = \frac{2}{3} \][/tex]
So, the particular solution is:
[tex]\[ e^y = \frac{1}{3} x^3 + x + \frac{2}{3} \][/tex]
4. Solve for y :
[tex]\[ y = \ln \left( \frac{1}{3} x^3 + x + \frac{2}{3} \right) \][/tex]
Now, we need to find f(2), which means finding the value of y when x = 2:
[tex]\[ y = \ln \left( \frac{1}{3} (2)^3 + 2 + \frac{2}{3} \right) \][/tex]
[tex]\[ y = \ln \left( \frac{8}{3} + 2 + \frac{2}{3} \right) \][/tex]
[tex]\[ y = \ln \left( \frac{14}{3} \right) \][/tex]
can you graph 6=6? infinite solutions
Answer:6 = 6 represents a true statement because 6 is always equal to 6. When graphed on a coordinate plane, this equation would result in a straight line at y = 6, which means that every point on the line corresponds to a solution of the equation. Since the line extends infinitely in both directions, there are infinitely many solutions to this equation.
Step-by-step explanation:
2. Graph each equation using a table of values.
(a)) y = 3x - 1
Make an x and y table, and pick any values to plug in for x in the equation.
I will use the numbers from -2 to 2
Now plug in the values you picked for x into the equation to find its y-value
x = -2
y = 3x - 1 Plug in -2 for x
y = 3(-2) - 1
y = -6 - 1
y = -7
x = -1
y = 3x - 1
y = 3(-1) - 1
y = -3 - 1
y = -4
Do the same for the rest of the numbers, and graph each point and draw a line connecting them.
use the fact that 2 1/2 divided by 1/8 equals 20 to find 2 1/2 divided by 5/8.
Answer:
The value of the expression is 4.
Step-by-step explanation:
Consider the provided information.
We have given that:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]
Now we need to find the value of:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =?[/tex]
Consider the provided fact:
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20[/tex]
Multiply [tex]\frac{1}{5}[/tex] both sides.
[tex]\dfrac{1}{5}\times \dfrac{2\dfrac{1}{2} }{\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]
[tex]\dfrac{1\times2\dfrac{1}{2} }{5\times\dfrac{1}{8} } =20\times\dfrac{1}{5}[/tex]
[tex]\dfrac{2\dfrac{1}{2} }{\dfrac{5}{8} } =4[/tex]
Hence, the value of the expression is 4.
The graph of which function has a minimum located at (4, –3)?
f(x) = one-halfx2 + 4x – 11
f(x) = –2x2 + 16x – 35
f(x) = one-halfx2 – 4x + 5
f(x) = 2x2 – 16x + 35
Answer:
f(x) = 1/2x^2 – 4x + 5 (the third option)
Step-by-step explanation:
I looked it up on a graphing calculator.
The quadratic function that has a minimum located at (4, -3) is:
[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]
Which function has a minimum located at (4, -3)?All the options are quadratic functions, so we need to find the one with a leading coefficient positive, which also has a vertex at (4, -3).
The 3 ones with positive leading coefficients are:
[tex]f(x) = (1/2)*x^2 + 4x -11[/tex]
[tex]f(x) = (1/2)*x^2 - 4x + 5[/tex]
[tex]f(x) = 2x^2 - 16x + 35[/tex]
The vertex of the first one is at:
[tex]x = -4/(2*1/2) = -4[/tex]
The x-value of the vertex must be x = 4, so we can discard this.
For the second quadratic function the x-value of the vertex is:
[tex]x = -(-4)/(2*1/2) = 4[/tex]
Then the y-value of the vertex is:
[tex]f(4) = (1/2)*4^2 - 4*4 + 5 = -3[/tex]
Then the vertex is at (4, -3), so this is the correct option.
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Which is the value of this expression when a = 5 and k = negative 2? (3^2 a^-3)(3 a^-4)^-2
Answer: C 25/9
Step-by-step explanation:
What is 15x when x=4
Answer:
60
Step-by-step explanation:
15*4=60
The 15x when x = 5 will be 60.
What is the arithmetic operator?
Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
x = 4
Now,
15x is nothing but we need to multiply 15 with x
So,
15x = 15 × 4
15x = 60
Hence,The 15x when x = 5 will be 60.
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Translate the following sentence into an equation. The sum of twice a number x and 13 is two less than three times x.
Question 20 options:
a)
2x + 13 = 3x – 2
b)
2(x + 13) + 3x – 2
c)
2x + 13 = 2 – 3x
d)
2x + 13 = 3(x – 2)
Answer:
2x + 13 = 3x - 2
Step-by-step explanation:
This should be the answer
Answer:
its 2
Step-by-step explanation:
Use the drawing tools to form the correct answers on the graph. Plot the zeros of this function: f(x) = (x – 1)(x – 7).
The answer is in the graph picture
The zeros of the function f(x) = (x - 1)(x - 7) are 1 and 7
The function is given as:
f(x) = (x - 1)(x - 7)
Set the function to 0.
So, we have:
f(x) = (x - 1)(x - 7) = 0
This gives
(x - 1)(x - 7) = 0
Split
(x - 1) = 0 or (x - 7) = 0
Remove brackets
x - 1 = 0 or x - 7 = 0
Solve for x
x = 1 or x = 7
Hence, the zeros of the function are 1 and 7
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Polynomial equation when zeros are -4, -2, 1, 4
Step-by-step explanation:
Given,
The zeros of the polynomial are - 4, - 2, 1 and 4
To find, the polynomial equation = ?
We know that,
The polynomial equation = (x - A)(x - B)(x - C)(x - D)
= (x + 4)(x + 2)(x - 1)(x - 4)
= [(x + 4)(x - 4)] [(x + 2)(x - 1)]
= ([tex]x^{2}-16[/tex])([tex]x^2-x+2x-2[/tex])
= ([tex]x^{2}-16[/tex])([tex]x^2+x-2[/tex])
= [tex]x^{4}+x^{3}-2x^{2}-16x^{2}-16x+32[/tex]
= [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex]
Thus, the required poynomial equation is [tex]x^{4}+x^{3}-18x^{2}-16x+32[/tex].
What is 4x4 i need to know
Answer: 16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
4x4 is 4 groups of four.
You can visibly show this by doing four lines of four dots.
••••
••••
••••
••••
count those dots, you get 16
Kevin has an after-school delivering advertising after 9 weeks he had earned a mean of $24 per week how much does he need to earn in the 10th week to increase his mean weekly earnings to $25
Answer:
$34
Step-by-step explanation:
So he earns $24 per week (ima just say p/w to make it shorter) meaning he earned around $216 in total. To get to $25 p/w, you have to get $250 in total from the 10 weeks. So $250 - $216 = $34.
⭐ Answered by Foxzy0⭐
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6v+13b=377
4v+9b=259
Answer:
v = 13
b = 23
Step-by-step explanation:
To solve this system of equations, we can negate one equation and add it to other to cancel out one variable.
Looking at v and b, the coefficients are 6, 4 and 13, 9, respectively.
It would be easier to use the LCM of 6 and 4
[tex]E_1 : 6v + 13b = 377\\E_2: 4v + 9b = 259\\\\4E_1 + (- 6)E_2:\\24v + 52b = 1508\\-24v - 54b=-1554\\\\0v -2b = -46\\-2b = -46\\b = 23\\\\4v + 9(23) = 259\\4v + 207 = 259\\4v = 52\\v = 13\\\\6(13) + 13(23)\\78 + 299\\377[/tex]
How many groups of 14 are in 28?
Answer:
there are 2 groups
Step-by-step explanation: 14 x 2 = 28
If you need 100 trucks for every 1500 yards, how many will you need for 1000 yards ?
Identify the x intercept and y intercept of the line 2x-4y=-12
The x-Intercepts of the line 2x - 4y = -12 is -6 and the y-intercept is 3.
To identify the x and y intercepts of the line, we set one variable to zero and solve the equation for the other variable.
For the x-intercept, we set y=0 and solve for x in the equation: 2x - 4(0) = -12, hence x = -6.
For the y-intercept, set x=0 and solve for y in the equation: 2(0) - 4y = -12, hence y = 3.
Therefore, the x-intercept is -6 and the y-intercept is 3
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4 times a number divided by 3 is 5 more than that number divided by 2 what is the value of that number
Answer:
x=6
Step-by-step explanation:
Let the number be x
Then 4 times a number divided by 3 is 5 more than that number divided by 2 gives the equation:
[tex] \frac{4x}{3} = \frac{x}{2} + 5[/tex]
Multiply through by the LCD, which is 6.
[tex] 6 \times \frac{4x}{3} = 6 \times \frac{x}{2} + 5 \times 6[/tex]
Cancel out to obtain:
[tex] 2 \times 4x =3 \times x + 30[/tex]
[tex]8x = 3x + 30[/tex]
Group similar terms
[tex]8x - 3x = 30[/tex]
Simplify the LHS
[tex]5x = 30[/tex]
Divide both sides by 5 to get:
[tex]x = 6[/tex]
Lisa purchased a concert ticket on a website. The original price of the ticket was $85. She used a coupon code to receive a 20% discount. The website applied a 10% service fee to the discounted price. Lisa's ticket was less than the original price by what percent?
Answer:
10%
Step-by-step explanation:
The original price of the ticket was $85 and she had a discount of 20%. Since the website applied a 10% service fee to her discount price, then Lisa'a ticket would be 10% less than the original price.
Help please I really need it
Answer:
X-Intercept is -45. (Answer would be (-45,0))
Step-by-step explanation:
You can use Desmos which is a graphing calculator to figure out the answer. Plug the equation into Desmos and it will show you a line and where the x-intercept is. And boom, you got your answer.
56∙9÷14∙ 1/3
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help
Answer:
Result = 12
Step-by-step explanation:
Fractions
Fractions are the general expression for rational numbers, defined as
[tex]\displaystyle \frac{a}{b}, \ b\neq 0[/tex]
Where a and b are integer numbers. Some operations with fractions have special rules than those with integers. The product of two or more fractions is
[tex]\displaystyle \frac{x}{y}\cdot \frac{w}{z}\cdot \frac{r}{s}=\frac{xwr}{yzs}[/tex]
We'll use that rule to operate the numbers given in the question:
[tex]\displaystyle 56\cdot \frac{9}{14}\cdot \frac{1}{3}=\frac{504}{42}[/tex]
The fraction can be simplified to an integer by dividing it
[tex]\displaystyle \frac{504}{42}=12[/tex]
Answer:The Answer is 12.
Step-by-step explanation:
When going through a step by step problem you always wanna go from the left to right.(Unless you have parentheses)
56*9=504
504/14=36
36*1/3=12
There for, you answer is 12.
Hope this helped you. Remember Stay Positive!
72% of the students in Math 6th at AZVA are currently passing mastering their lessons. If 324 students are currently mastering their Math lessions, how many students are in Math 6th?
a) Use a percent equation OR set up a proportion that will use to solve the problem.
b) Solve the problem. Show your work.
Answer:
Step-by-step explanation:
72% of the students in math 6 = 324
let x represent the students in math 6
turn ur percent to a decimal
0.72x = 324
x = 324 / 0.72
x = 450 students <===
Answer:
its 233.28
Step-by-step explanation:
cuz i took a test and this was the right answer
length of a rectangle is 4 more than its breadth.represent in the form equation
Answer:
L = B + 4
Step-by-step explanation:
Let the breadth be B
Let the length be L
But from the question, we were told that the length is 4 more than the breadth. This is expressed as
L = B + 4
Multiply.
(x-6)(5x-4)
O
A. 5x^2-30x + 24
B. 5x^2 - 34x + 24
c. 5x^2 - 26x-24
D. 5x^2 - 30x-24
Someone help me with this please. I can’t figure It out.
Answer:
Complementary angles
Step-by-step explanation:
Complementary angles add up to 90 degrees
Sarai is mixing a solution. She pours all the liquid from a full small beaker into a larger beaker. The liquid fills the large beaker to 15% of its capacity. If the small beaker holds 300 mL, how much does the large beaker hold?
Answer:
2000 ml
Step-by-step explanation:
Given: Sarai pours all the liquid from a full small beaker into a larger beaker.
The liquid fills the large beaker to 15% of its capacity.
The small beaker holds 300 ml.
Lets assume capacity of large beaker to hold be "x".
As given, Sarai pours all the liquid from a full small beaker into a larger beaker
∴ [tex]15\% \times x= 300\ ml[/tex]
⇒ [tex]0.15x= 300[/tex]
Dividing both side by 0.15
⇒[tex]x= \frac{300}{0.15}[/tex]
∴ [tex]x= 2000\ ml[/tex]
Hence, the large beaker can hold 2000 ml of liquid.
What is the prime factorization of 40?
2 times 5
2 times 20
2 times 2 times 2 times 5
2 times 2 times 4 times 5
Answer:
C.
Step-by-step explanation:
2 times 2 times 2 times 5 = 40
The prime factorization of 40 is 2 times 2 times 2 times 5, which can be written as 2^3 * 5. So, option C, "2 times 2 times 2 times 5," is the correct prime factorization of 40.
The prime factorization of the number 40 is 2^3 * 5. To arrive at this factorization, we break down 40 into its prime factors. We start by dividing 40 by the smallest prime number, 2. Since 40 is even, it can be divided by 2 evenly, resulting in 20. We continue this process until we can no longer divide by 2, which leaves us with 20. Now, we try to divide 20 by the next smallest prime, which is also 2. This division gives us 10. Once again, we divide by 2, and we are left with 5. Since 5 is a prime number, we cannot further divide it. Therefore, we have prime factorized 40 as 2 * 2 * 2 * 5, which can be expressed as 2^3 * 5, where the exponent 3 indicates that we have three 2s multiplied together, and the 5 is the prime factor on its own.
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A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 4 divided by ft for the legs and $ 16 divided by ft for the hypotenuse, write the total cost C of construction as a function of h.
Answer:
[tex]\frac{8h}{\sqrt{2}} + 16h[/tex]
Step-by-step explanation:
First we need to compute the side length as a function of h
So x be the side length of the right isosceles triangle, in Pythagorean formula we have
[tex]x^2 + x^2 = h^2[/tex]
[tex]2x^2 = h^2[/tex]
[tex]x = \frac{h}{\sqrt{2}}[/tex]
The cost for the legs is
[tex]C_l = 4*2x = \frac{8h}{\sqrt{2}}[/tex]
The cost for the hypotenuse is
[tex]C_h = 16h[/tex]
So the total cost in term of h is
[tex]C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h[/tex]
The total cost C of construction as a function of h is C = 16 / h + 8√2 / h
The pen is in the shape of an isosceles right angle. This means one of the
angle is 90 degrees and 2 sides of the triangle are equal and the base angles
are equal too.
Using pythagora's theorem
Therefore,
x² + x² = h²
2x² = h²
x² = h² / 2
x = √h²/ √2 = h/√2
cost of the legs = 4 / h/√2 + 4 / h /√2 = 8√2 / h
cost of the hypotenuse = 16 / h
Total cost = 16 / h + 8√2 / h
C = 16 / h + 8√2 / h
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1. There were 88 birds in the tree and then b of the birds flew away. Write an expression that shows how many birds are in the tree now.
2. Brice had $73 and then he earned d more dollars. Write an expression that shows how much money he has now.
3. Kurt's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.
pls help I will mark brainlist if correct !! :))
Morse code is a way to transmit text using a series of dots or dashes. The Morse Code for "Add" is shown. What fraction of the shapes are dots in the Morse code for "Add"
Add in Morse code is :
.—..-..
There are 8 total symbols, 5 of them are dots.
The fraction would be 5/8 are dots.
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
The Morse Code for Add is:
.__.._..
There are 5 dots and 3 dashes, so there are 8 figures in total. The fraction is 5 divided by the total number of symbols, which is 8. So the answer is [tex]\frac{5}{8}[/tex]
Write the Equation of the line in slope intercept form
(0, -3), (7.5,0)
Answer:
Step-by-step explanation:
First, start off by solving for the slope using this formula:
[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Then, plug in the values: [tex]\frac{0-(-3)}{7.5-0}[/tex]
Solve the equation: [tex]\frac{3}{7.5}[/tex]
That's your slope.
Then plug in one of the coordinates given in the problem for x and y and solve this equation:
y=[tex]\frac{3}{7.5}[/tex]x+b
Hope that helped!!! :)