Hello! :)
[tex]\large\boxed{\frac{dy}{dx} = 3^{(2x^{2} - 1)} (4x^{2}ln3 + 1)}[/tex]
Use the Product Rule to solve for the derivative:
[tex]\frac{dy}{dx}= f(x) * g'(x) + g(x) * f'(x)[/tex]
We can divide the expression into two different functions:
[tex]f(x) = x\\\\g(x) = 3^{2x^{2} -1}[/tex]
Use the Product Rule equation and the following rules to solve for the derivative:
Derivative of an exponential function with base other than e:
[tex]\frac{dy}{dx} a^{u} = a^{u} * u' * lna[/tex]
Power rule:
[tex]\frac{dy}{dx} x^{n} = nx^{(n-1)}[/tex]
Find the derivatives using the power rule and derivative of an exponential function. Plug these into the product rule equation:
[tex]\frac{dy}{dx} = x(3^{(2x^{2} -1)} * 4x* ln3) + (1)3^{(2x^{2} - 1)}[/tex]
Simplify by factoring out a common factor: [tex]3^{(2x^{2} - 1)}[/tex]
[tex]\frac{dy}{dx} = 3^{(2x^{2} - 1)}( x* 4x * ln3) + (1)[/tex]
Simplify further:
[tex]\frac{dy}{dx} = 3^{(2x^{2} - 1)} (4x^{2}ln3 + 1)[/tex]
This is the final derivative.
Answer:
[tex]3^{2x^2-1}+4ln(3)*3^{2x^2-1}x^2[/tex]
Step-by-step explanation:
[tex]x3^{(2x^2-1)}[/tex]
~Apply product rules
[tex]\frac{d}{dx}(x)3^{2x^2-1}+\frac{d}{dx}(3x^{2x^2-1})x\\\frac{d}{dx}=1\\(3^{2x^2-1})=4ln(3)*3x^{2x^2-1}x\\1*3^{2x^2-1}+4ln(3)*3^{2x^2-1}xx[/tex]
~Simplify
[tex]3^{2x^2-1}+4ln(3)*3^{2x^2-1}x^2[/tex]
Best of Luck!
80 divided by (6 + (3 - 5) X 2)
Answer:
40
Step-by-step explanation:
remember PEMDAS
our equation looks like tihs: [tex]\frac{80}{(6+(3-5)*2)}[/tex]
1. parentheses: in the denominator we have a parentese inside of another parenthese, so start with the inside first: (3-5) = -2.
so now our equation looks liek this [tex]\frac{80}{(6-2 *2)}[/tex]
now we have a mini PEMDAS situation within the parentheses: multiplication comes before addition/subtraction, so multiply -2*2 = -4, so now your equation looks like this: [tex]\frac{80}{(6-4)}[/tex]
6-4 =2: so now we're done with parentheses part of PEMDAS, the only thing left is dividing 80/2 which equals 40.
I need help with step by step : (−4x to the power of -5 y)(x to the power of -7 y)
Answer:
(−4x to the power of -5 y) = 20xy
(x to the power of -7 y) = -7xy
Step-by-step explanation:
Hope this helped!
Triangle LMN is plotted on a coordinate plane. It is then dilated by a factor of 2 using the origin as the center of dilation, and translated 5 units left and 3 units up.
How is this sequence of transformations written in coordinate notation to correctly map triangle LMN to its image, triangle L'M'N' ?
A. ( x , y )→(2 x + 3, 2 y - 5)
B. ( x , y )→(2 x - 5, 2 y + 3)
C. ( x , y )→(2 x + 5, 2 y + 3)
D. ( x , y )→(2 x + 3, 2 y + 5)
Answer:
B. ( x , y )→(2 x - 5, 2 y + 3)
Step-by-step explanation:
when x goes to the left it is negative and when y goes up it is positive, making B the only possible answer choice.
13 m
12 m
wall
ladder
The ladder, the ground, and the wall form a right triangle.
ground
How far away from the wall does the ladder need to be placed so that it reaches 12 meters up the wall? If needed, ROUND TO THE NEAREST TENTH.
A
17.7 meters
B.
25 meters
С
5 meters
D
313 meters
Answer:
The ladder needs to be placed at 5 m from the wall.
Step-by-step explanation:
Pythagoras's Theorem
Being a and b the legs of a right triangle and c its hypotenuse, then
[tex]c^2=a^2+b^2[/tex]
The image shows a ladder of length c=13 m as the hypotenuse of the right triangle formed by the height, the ladder, and the ground.
We are given the height up the wall as a=12 m.
We calculate the distance b solving it from the equation above:
[tex]b^2=c^2-a^2[/tex]
Substituting:
[tex]b^2=13^2-12^2[/tex]
Operating:
[tex]b^2=169-144[/tex]
[tex]b^2=25[/tex]
Taking the square root:
[tex]b=\sqrt{25}[/tex]
b = 5 m
The ladder needs to be placed at 5 m from the wall.
Heather purchased a prepaid phone card for $30 . Long distance calls cost 14 cents a minute using this card. Heather used her card only once to make a long distance call. If the remaining credit on her card is $28.18 , how many minutes did her call last?
Answer:
13 Minutes
Step-by-step explanation:
30-28.18=1.82
1.82 devided by 0.14= 13 minutes
answer 13 minutes
What is $2.75 in cents
To convert dollar into cents, we need to multiply by 100. Thus, the total amount is equivalent to 275 cents.
Given:
Given amount is $ 2.75.
According to question, we have to convert currency of dollar into cents.
Conversion of amount from dollar to cent can be done as,
[tex]1\;\$=100\;\rm{cents}\\ \$\;2.75=\$\;\frac{275}{100}\\=\frac{275}{100}\times 100\;\rm{cents}\\=275\;\rm{cents}[/tex]
Therefore, the total amount in cents is 275 cents.
Learn more about dollar to cent conversion here:
https://brainly.com/question/14790293
I need help with this question!
Answer:
Meg needs the part.
Steve needs the percent.
Step-by-step explanation:
This is a weird question that I've never seen before. But, anyway....
Meg is given the percentage (50%) and the total (16 dogs). Steve has the total (35) and the part (7) but not the percentage.
PROBLEM: Juan hires an electrician. Juan pays a one-time fee of $30. Juan also pays $45 for each hour the electrician works. A. Write a function that can be used to find the total charge, c, Juan will pay when the electrician works, h, hours. Y=mx+b B. How much will Juan pay if it takes the electrician 6 1/2 hours to complete the job? (Vou should have 9 answers in question 2
Answer: a. c = 30 + 45h
b. $322.50
Step-by-step explanation:
A. Write a function that can be used to find the total charge, c, Juan will pay when the electrician works, h, hours.
This will be calculated as:
c = 30 + 45h
B. How much will Juan pay if it takes the electrician 6 1/2 hours to complete the job?
Using the expression,
c = 30 + 45h
c = 30 + 45(6 1/2)
c = 30 + 292 1/2
c = 322.50
Therefore, Juan will pay $322.50
what is m?
please help
Given:
[tex]\Delta ABC\sim \Delta QRS[/tex]
To find:
The missing value of m.
Solution:
We have,
[tex]\Delta ABC\sim \Delta QRS[/tex]
Corresponding parts of similar triangles are proportional.
[tex]\dfrac{AB}{QR}=\dfrac{AC}{QS}[/tex]
Putting the given values, we get
[tex]\dfrac{m}{10}=\dfrac{2}{4}[/tex]
[tex]\dfrac{m}{10}=\dfrac{1}{2}[/tex]
Multiply both sides by 10.
[tex]\dfrac{m}{10}\times 10=\dfrac{1}{2}\times 10[/tex]
[tex]m=5[/tex]
Therefore, the value of m is 5.
pahelp badly needed!!!!
Answer:
Step-by-step explanation:
1. 2x - 28
2. 6x3 - 4x2 + 2x
3. x2 + 7x + 12
4. m2 - 4mn + 21n2
5. x2 - 9x + 18
i don't understand how to solve it
Step-by-step explanation:
f(-4) = 5x
f(-4) = 5 . -4
f( -4) = -20
same for the
f(1)
What is the equation of the line that has a slope of 3/10 and goes through (-10, -17)?
Which input value produces the same output value for
the two functions?
O x= -12
O x= -9
O x= -6
O X=-3
HELP PLEASE
Answer
-6
Step-by-step explanation:
Took test
A set of average city temperatures in December are normally distributed with a mean of 16.3 degrees C and a standard deviation of 2 degrees C.
∘What proportion of temperatures are between 12.9 degrees C and 14.9 degrees C?
you may round your answer four decimal places.
Answer: 0.1974
Step-by-step explanation:
z1 = (12.9 - 16.3)/2 = (-3.4)/2 = -1.7
Z2 = (14.9 - 16.3)/2 = (-1.4/2) = -0.7
“Z table”
Z1= -1.7 ~ 0.0446
Z2 = -0.7 ~ 0.242
0.2420 - 0.0446= 0.1974
Solve for y.
3x + 4y = z
-----------------
Answer:
y= z-3x/4
Step-by-step explanation:
4y=z-3x
y=z-3x/4
Answer:
[tex]y=\frac{z-3x}{4}[/tex]
Step-by-step explanation:
[tex]3x+4y=z[/tex]
Subtract 3x from both sides:-
[tex]3x+4y-3x=z-3x[/tex]
[tex]4y=z-3x[/tex]
Divide both sides by 4:-
[tex]\frac{4y}{4}=\frac{z}{4}-\frac{3x}{4}[/tex]
[tex]y=\frac{z-3x}{4}[/tex]
OAmalOHopeO
convert the expression [tex]\sort[4]{3}[/tex] into exponential form
Answer:
what is this ?
Step-by-step explanation:
PLS HELP !! I WILL GIVE BRAINLIEST !!! I JUST NEED THE ANSWER WITH A SENTENCE EXPLANATION !!!
Answer:
Blue
Step-by-step explanation:
Hard to explain just trust.
Answer:
Blue
Step-by-step explanation:
because A has a right angle so it's
Help me I neeeeeeede itttt
Answer:
True
Step-by-step explanation:
7.613 rounded to the nearest tenth is 7.6
Which expression finds the length of side y of this right triangle? Math item stem image
Answer: X
Step-by-step explanation:
Y intercept
Answer:
x=the square root of 5 squared + 8.5 squared which is the top right one
Step-by-step explanation:
What is the difference between an expression and an equation? Use complete sentences and math vocabulary to explain!
Answer:
An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.
Step-by-step explanation:
john wants to earn money over the summer mowing lawns to buy several CD's which will cost $59. He earns $14 for each lawn he mows. How many days will john have to mow to earn enough money?
Answer:
5 days if he only does one lawn every day
Step-by-step explanation:
A supermarket purchases chickens wholesale from a farm for $4 each. The store then marks up the chickens 50%. After 10:00 p.m., the supermarket marks down the price of the chickens by 50% to make sure they all sell before the store closes. Which statements are true about the price of a chicken? Check all that apply.
O) The marked up price of a chicken is $6 before 10:00 p.m.
O) The 50% markdown is taken off the marked-up price.
O) The chickens sell for $4 after 10:00 p.m., because the 50% markup and 50%
O) markdown cancel each other out.
O) The 50% markdown is taken off the $4 wholesale price.
Answer:
a- the marked up price of a chicken is $6 before 10pm
b- the 50% markdown is taken off the marked up price
Answer:
A and B
Step-by-step explanation:
I need help! Please! 30 points!
I'm sorry and I feel that your probably going to get mad, but we can't answer this question without knowing what those drag-and-drop options are! I hope that you can quickly re-post this, and then I will be able to help you! Sorry!
Miri
A model car is built to a scale of 1 in. : 2.5 ft. If the model is 5.8 in. Long how long is the car in real life?
Answer:
14.5 ft
Step-by-step explanation:
We are told that the model car is built to a scale of 1 in. : 2.5 ft.
That means 1 inches represents 2.5 ft in actual measurement.
Thus, for a 5.8 inch long model, the real life measurement is;
(5.8 inch × 2.5 ft)/1 inch = 14.5 ft
These equations represent the number of bacteria in four different dishes as a function of time, t,
in days. Which equation represents the population with the greatest growth factor?
A
a(t) = 1000
(65)
t
B
b(t) = 800
50
t
Ос
c(t) = 600 o
5
2
D
d(t) = 400 • 3+
Answer:
D i believe.
Step-by-step explanation:
Hope this helps :)
The equation with the greatest growth factor is d(t) = 400 . 3^t
Correct option is D.
As per the given data:
Equations representing the number of bacteria in four different dishes as a function of time, t in days, are given.
To find out the equation with the greatest growth factor:
Growth Factor = Term whose power is raised to t.
For option (A), Growth Factor = (5/6) = 0.834
For option (B), Growth Factor = (1/50) = 0.02
For option (C), Growth Factor = (5/2) = 2.5
For option (D), Growth Factor = (3) = 3
Hence, the equation with the greatest growth factor is d(t) = 400 . 3^t
To learn more about equation, click:
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What is the slope of this line?
Answer:
zero
Step-by-step explanation:
there is no slope because the line is horizontal
help plzzz ill give extra points dawg
Answer:
The answer is z= 7.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
56
Help Help Help Help please
Brainliest if correct
Answer:
least to greatest
|y-z|
|x-y|
|x-z|
z
Step-by-step explanation:
write an equivalent expression by combining like terms (3/5y+4)+(1/5y-1)
If a line goes through the following two points: (0,-2) and (3,4), the slope of the line is:
Answer:
y = 2x – 2
Step-by-step explanation:
