Answer: f(0) = 0
Step-by-step explanation: anything multiplied by 0 is 0.
The value of [tex]f'(0)=\frac{-2}{5}[/tex]
What is Derivative of a function?
The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument
It is denoted by f ' ( x ) = dy / dx
Given data ,
Let the function be f ( x ) = [tex]ln(x + 4 + e^{-3x} )[/tex]
To differentiate f ( x ) ,
Let [tex]y=ln(a)[/tex] , where [tex]a=x+4+e^{-3x}[/tex]
So ,
[tex]e^{y} =a[/tex]
Using this function , we can write
[tex]e^{y} = x + 4 + e^{-3x}[/tex]
On differentiating , we get
[tex]e^{y}\frac{dy}{dx} = 1 + 0 -3e^{-3x}[/tex]
Dividing by [tex]e^{y}[/tex] on both sides , we get
[tex]\frac{dy}{dx} = \frac{ 1-3e^{-3x}}{e^{y} }[/tex]
We know , [tex]e^{y} =a[/tex]
And [tex]e^{y}=x+4+e^{-3x}[/tex]
So , [tex]\frac{dy}{dx} = \frac{ 1-3e^{-3x}}{x+4+e^{-3x} }[/tex]
Therefore [tex]f'(x)=\frac{dy}{dx} = \frac{ 1-3e^{-3x}}{x+4+e^{-3x} }[/tex]
Now , [tex]f'(0)=\frac{1-3e^{0}}{0+4+e^{0} }[/tex]
[tex]f'(0)=\frac{-2}{5}[/tex]
Hence , the value of [tex]f'(0)=\frac{-2}{5}[/tex]
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Carol invested $2,560 into two accounts. One account paid 6% interest and the other paid 8% interest. She earned 7.25% interest on the total investment in one year. How much money did she put in each account? Use the general formula, I=Prt, to model simple interest applications, where I is equal to the interest, P is equal to the product of the principal, r is equal to the rate, and t is equal to the time.
Answer:
The amount she put in the account that paid 6% interest = x = $960
The amount she put in the account that paid 8% interest = y = $1600
Step-by-step explanation:
Carol invested $2,560 into two accounts. One account paid 6% interest and the other paid 8% interest. She earned 7.25% interest on the total investment in one year.
I=Prt, to model simple interest applications, where I is equal to the interest, P is equal to the product of the principal, r is equal to the rate, and t is equal to the time.
Step 1
We have to calculate the total interest earn on the initial capital
P = $2,560
R = 7.25% = 0.0725
T = 1
I = $2,560 × 0.0725 × 1
I = $185.60
Let the amount Invested in the account that paid 6% interest = x
Let the amount Invested in the account that paid 8% interest = y
Hence:
$185.60 = x × 6% + y × 8%
$185.60 = 0.06x + 0.08y......Equation 1
$2560 = x + y........ Equation.2
x = $2560 - y
$185.60 = 0.06x + 0.08y......Equation 1
185.60 = 0.06(2560 - y) + 0.08y
185.60 = 153.6 - 0.06y + 0.08y
185.60 - 153.60 = 0.02y
y = 32/0.02
y = $1600
x = $2560 - y
x = $2560 - $1600
x = $960
The amount she put in the account that paid 6% interest = x = $960
The amount she put in the account that paid 8% interest = y = $1600
A dock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. How much has the polygon rotated after 7 minutes? O 14 O 21 O 35 O 42
Answer: 42
Step-by-step explanation:
Did the test
Solve for b : 1/2b+G=D
Answer:
I believe the answer is b=1/2(d-g)
Step-by-step explanation:
multiply to remove the variable from the denominator.
is this a function or not?
Answer: yes
Step-by-step explanation:
The x value does not repeat itself
Which of the following numbers would be an outlier if added to the data set below?
234, 187, 201, 199, 217, 200, 201, 193
A: 111
B: 201
C: 235
D: 204
Answer:
111
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
Find the angle BCD.PLZ!!!!!!!
Answer:
19
Step-by-step explanation:
Firstly find BCE then divide by 2.
Answer this is your dont like the Teletubbies. Literally there your sleep paralysis!
Search them up if your dont know them!!!!
10 points!
Answer:
I am terrified of the Teletubbies. I always have been, I even hated it as a young child. (I'm 15 now) I still love Blues Clues though. Still slaps.
Step-by-step explanation:
Answer:
tramuatized
Step-by-step explanation:
teletubies are h e l l a wierd
Arron can join a gym for $19.99 per month plus an annual fee of $12.80 or he can pay $21.59 per month. He thinks the second option is better because he plans to use the gym for 10 months. Is Aaron correct ? Set up an equation (with variables on both sides) to describe the situation.
Answer: Aaron is wrong. The first option is better as it costs less than the second option.
Step-by-step explanation:
Arron can join a gym for $19.99 per month plus an annual fee of $12.80.
Since Aaron wants to spend 10 months at the gym, this will cost him:
= $12.80 + ($19.99 × 10)
= $12.80 + $199.9
= $212.7
Paying $21.59 for 10 months will be:
= $21.59 × 10
= $215.9
The first option is better as it costs less than the second option.
Help I’m so confused
Answer:
its a
Step-by-step explanation:
Multiply. Write each product in simplest form, 1 4/5 x 1/2
8/9
9/8
1 1/8
1/8
9/10 or 0.9
mark me brainliest if you feel like mine was helpful!! I hope that helped!
The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time.
A'(t) =???
MARK AS BRAINLIST
Step-by-step explanation:
L = 6t+5
H = √t
A = L*H
= (6t+5) *√t = 6t√t + 5√t
A'(t) = 6t * 1/2*√t + √t * 6 + 5/2*√t
= 6t/2√t + 6√t + 5/2√t
Expression for the rate of change of the area with respect to time will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex] cm per second
It's given in the question,
Length of a rectangle is given by the expression(6t + 5) cm
Width or height of the rectangle is given by the expression,[tex]\sqrt{t}[/tex] cm
Area of the rectangle is given by,
Area = Length × Height
A = (6t + 5)(√t)
A = [tex]6t^{\frac{3}{2}}+5t^\frac{1}{2}[/tex]
Now find the derivative of area (A) with respect to time (t).
[tex]\frac{dA}{dt}=\frac{d}{dt}(6t^{\frac{3}{2}}+5t^\frac{1}{2})[/tex]
A' = [tex](6\times \frac{3}{2})t^\frac{1}{2}+\frac{5}{2} t^{-\frac{1}{2}}[/tex]
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
Therefore, expression for the rate of change of the area will be,
A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]
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Write in slope-intercept form with the given information. Show all work. Passes through (-8,3) with a slope of -2
Answer:
y=-2x-13
Step-by-step explanation:
y=mx+b
3=-2(-8)+b
3=16+b
3-16=b
-13=b
ok there’s the science slides , and i think they are quite easy i just need some help bc im lazy . ik this is the math thing but
Answer:
just look up the answers on google
Step-by-step explanation:
What is the solution to 8x - 3(2x - 4) = 3x - 18?
Answer:
X=30
Step-by-step explanation:
The answer is X=30
What is .24 written as a percent?
Answer:
24%
Step-by-step explanation:
Step 1: Shift the decimal point two places to the right: 0.24 → 2.4→ 24.
Step 2: Add a percent sign: 24%
and that's how you get your answer
The .24 written as a percent is 24%.
To convert .24 to a percent, multiply it by 100.
.24 ×100 = 24
When we express a number as a percent, it represents a proportion out of 100. In this case, .24 as a percent means that .24 is equivalent to 24 out of 100 or 24%. The percent symbol (%) indicates that the number is being represented as a fraction of 100. This can be interpreted as .24 representing 24 parts out of 100, or 24 hundredths.
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If you could travel back in time one year, what advice would you give yourself?
10 sentence required for the brainlleist if 2 people answer
1
Answer:
To keep my head up and focus on the good instead of the bad. To understand that life gets hard. I would remind myself that I'm worth it and I am a strong person. I would tell myself that whatever bad happens, something good will come out of it. To remind myself that all the bad I've been through is only making me a stronger person. And I would remind myself that everything happens for a reason, whether I see it now or I see it later on down the road. I would remind myself that it's never too late to change for the better. I would tell my self "you made it this far, your strong". And I would tell myself that I can do whatever I put my mind to. And that nothing is impossible.
Hope this helps :)
Step-by-step explanation:
If someone could travel back in time one year, the advice I would give myself would be to embrace change and adaptability. The world is constantly evolving, and it is important to stay open-minded and flexible in order to thrive.
I would encourage myself to be proactive in seeking opportunities for growth and learning, even if they seem daunting or unfamiliar at first. Additionally, I would remind myself to prioritize self-care and mental well-being. It is easy to get caught up in the hustle and bustle of daily life, but taking time for oneself is crucial.
Whether it be spending time in nature, practicing mindfulness, or pursuing hobbies and interests, nurturing my own happiness should be a priority. Lastly, I would advise myself not to dwell on past mistakes or missed opportunities.
Every setback is an opportunity for growth, and it is important to learn from these experiences rather than letting them define me. By adopting a positive mindset and focusing on the present moment, I can ensure that I make the most of every opportunity that comes my way.
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The polynomial p(x)=x^3+7x^2-36p(x)=x 3 +7x 2 −36p, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 7, x, squared, minus, 36 has a known factor of (x+3)(x+3)left parenthesis, x, plus, 3, right parenthesis. Rewrite p(x)p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p(x)=
Answer:
(x-2)(x+3)(x+6)
Step-by-step explanation:
Given the polynomial function p(x)=x^3+7x^2-36
We are to write it as a product of its linear factor
Assuming the value of x that will make the polynomial p(x) to be zero
Let x = 2
P(2) = 2³+7(2)²-36
P(2) = 8+7(4)-36
P(2) = 8+28-36
P(2) = 0
Since p(2) = 0 hence x-2 is one of the linear factors
Also assume x = -3
P(-3) = (-3)³+7(-3)²-36
P(-3) = -27+7(9)-36
P(-3) = -27+63-36
P(-3) = 36-36
P(-3) = 0
Since p(-3) = 0, hence x+3 is also a factor
The two linear pair are (x-2)(x+3)
(x-2)(x+3) = x²+3x-2x-6
(x-2)(x+3) = x²+x-6
To get the third linear function, we will divide x^3+7x^2-36 by x²+x-6 as shown in the attachment.
x^3+7x^2-36/x²+x-6 = x+6
Hence the third linear factor is x+6
x^3+7x^2-36 = (x-2)(x+3)(x+6)
Answer:
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
Step-by-step explanation:
Here we want to rewrite the polynomial
P(x) = x^3 + 7x^2 - 36
As a product of linear factors given that we have one of the roots already as (x + 3)
What we shall do here is to divide the polynomial by x + 3
Please check attachment for long polynomial division
From the division, the other factor is x^2 + 4x -12
So we can rewrite the polynomial as;
x^3 + 7x^2 -36 = (x + 3)(x^2 + 4x -12)
So let’s now write x^2 + 4x -12 as a product of its linear factors
x^2 + 4x -12 = x^2 + 6x -2x -12
= x(x + 6)-2(x + 6)
so we have;
(x -2)(x + 6)
Therefore;
x^3 + 7x^2 -36 = (x + 3)(x-2)(x + 6)
Help!! !!!!! What’s the answer?
Answer:
1296m^2
Step-by-step explanation:
12m = 1cm per square
3 squares • 3 squares = 36 • 36 = 1296
Hope this helps! :)
I need help answer this Question!
-6+3(-4-2x)>=-16-6x
There is no solution for that problem....
Solve the equation 5x+9=4.
Answer: x=−1
Step-by-step explanation: hope this helps!
can someone please solve −5 − y = −3x
Answer:
Slope = 3
x-intercept = 5/3 = 1.66667
y-intercept = 5/-1 = -5.00000
Step-by-step explanation: Notice that when x = 0 the value of y is 5/-1 so this line "cuts" the y axis at y=-5.00000
y-intercept = 5/-1 = -5.00000
When y = 0 the value of x is 5/3 Our line therefore "cuts" the x axis at x= 1.66667
x-intercept = 5/3 = 1.66667
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -y+3x-5 = 0 and calculate its properties
Carina spent a total of $5.27 buying a pineapple for $3.40 and some tomatoes that were on sale for $0.85 per pound. To determine the number of pounds of tomatoes that she bought, x, Carina wrote and solved the equation as shown below.
3.40 + 0.85 x = 5.27. 0.85 x = 8.67. x = 10.2 pounds.
Where, if anywhere, did Carina make an error?
HELP PLS!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Carina make an error because her solving problem, Carina should have subtracted 3.40 from 5.27.
Answer:
Carina should have subtracted 3.40 from 5.27
Step-by-step explanation:
i took the quiz, hope this helps<3
Find the Value of 2a2+5b2
Answer:
I get 92 but not really sire
A line passes through the HELP ME PLEASE
point (4, -6) and has a slope of -3/4. Which is the equation of the line?
O y=-x-3
O y=-x-6
O y=-3x-
3
4
3
O y=-6x-
Answer:
i hope this helps
Step-by-step explanation:
ggbsus dvrjsjagaubs don't mind this
Algebra Test Question! Please answer correctly!! :)
Please answer the following questions with this format
A:
B:
C:
You are 9 miles away from home. You start biking home at a speed of 6 miles per hour.
a. write an equation that represents your distance from home ( y ) after ( x ) hours
b. find the y-intercept of the graph
c. find the x- intercept of the graph
Answer:
A: y=9-6x
B: y=6x+9
C: y=9-6x
Step-by-step explanation:
a) y=9-6x, standard form is ax+by=c so add 6x to both sides
b) from the first, we had it in slope intercept form, mx+b where b is the y-intercept. y=-6x+9
c) The x intercept occurs when y=0 so: y=9-6x
x=1.5
Mr. Cooper is baking chocolate chip cookies using his grandma's recipe. The number of cups of chocolate chips needed to the number of dozens of cookies made can be represented by the ratio 4 : 5. Using the same recipe, what is the amount of chocolate chips needed for 1 dozen?
Answer:
0.8 cups
Step-by-step explanation:
Given that:
Numbe of cups of chocolate chips needed to the Number of dozens of cookies made can be represented using the ratio 4:5
Hence,
The proportion of cups of chocolate chips to the number of dozens of cookies = 4 / 5
4 cups of chocolate chips to 5 dozens of cookies ;
For 1 dozen of cookies, number of chocolate chips will be (x)
4 / 5 = x / 1
Cross multiply
4 * 1 = 5 * x
4 = 5x
x = 4/5 = 0.8
Hence, for 1 dozen of cookies, 0.8 cups of chocolate chips is required
Does the following equation have one or no solution?
4 – (2x + 5) = 1/2(–4x – 2)
Answer:
4-(2x+5) = 1/2(-4x-2)
4-2x-5=-2x-1
-1-2x-=-2x-1
Infinite solution
Step-by-step explanation:
Branliest pls
Question 3 50 points
Part A
Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship.
Answer:
Part A-
Answer- f(x) is the profit made from selling 'x' number of salads.
Part B-
Question- Identify and interpret the key features of the function in the context of the situation you described in part A.
Answer-
End behavior- As 'x' approaches 25, f(x) approaches 20. As 'x' approaches 1, f(x) approaches 4.
Domain- 1, 4, 9, 16, 25
Range- 4, 8, 12, 16, 20
x and y- intercepts- None
Maximum- 20
Minimum- 4
Step-by-step explanation:
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Picture provided
Please solve.
Step-by-step explanation:
hope this helps, good night!!!!
What is 125 x 64 in expanded form