[tex]\text{Given that,}\\\\\\f(x) = \ln(x^4 +e^{2x})\\\\\\f'(x) = \dfrac{1}{x^4 + e^{2x}} \left(4x^3+2e^{2x}\right) = \dfrac{2(2x^3+e^{2x})}{x^4 + e^{2x}}~~~~;[\text{Chain rule}]\\\\\\\text{Note:}\\\\\dfrac{d}{dx} \ln x = \dfrac 1x\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} e^{mx} = m e^{mx}[/tex]
After solving the given equation, the value obtained is equal to [tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex].
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.
As per the given data in the question,
f(x) = ln (x⁴ + e²ˣ)
[tex]f'(x)=\frac{1}{x^4+e^2^x}(4x^3+2e^2^x)[/tex]
Now, use the chain rule,
[tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex]
Also, note some points,
d/dx ln (x) = 1/x
[tex]\frac{d}{dx}x^n=nx^n^-^1[/tex]
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An angle of 90° measures (___) Pi radians.
An angle of -pi/5 radians measures ____?
°.
[tex]\huge \bf༆ Answer ༄[/tex]
Conversion from degree to radian ~
[tex] \boxed{ \sf{ \frac{\pi}{180} \times \theta }}[/tex][tex] \sf \dfrac{\pi}{180 } \times 90[/tex][tex] \sf \dfrac{\pi}{2} \: \: rad[/tex]Conversion from radians to degree ~
[tex] \boxed{ \sf{ \frac{180}{\pi} \times \theta}}[/tex][tex] \sf \dfrac{180}{\pi} \times - \dfrac{ \pi}{5} [/tex][tex] \sf - 36 \degree[/tex]The required measures of the angles in radians and degree are given as π/2 radians and -36° respectively.
What are the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
An angle of 90° measures
in radians,
angle = π/180 × Ф
angle = π/180 × 90 = π/2 radians
Similarly,
An angle of -pi/5 radians
in degrees,
angle = 180 / π × -π/5
angle = -36°
Thus, the required measures of the angles in radians and degree are given as π/2 radians and -36° respectively.
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The triangle and rectangle have the same perimeter.find the value of x.
Answer:
[tex]x + 5 \: + \: x \: + 6 \: + x + 7 = 2x - 1 + x + 7 + x + 7 + 2x - 1[/tex]
[tex]3x + 18 = 6x + 12[/tex]
[tex]18 = 3x + 12[/tex]
[tex]6 = 3x[/tex]
[tex]x = 6 \div 3 = 2[/tex]
[tex]x = 2[/tex]
I hope this helps you !!help me please please
Answer:
11/14
Step-by-step explanation:
Have a nice day !!!
Answer:
its B, its 11/14
Step-by-step explanation:
How are the two triangles congruent? If not congruent, select not
congruent.
1 point
SSS
SAS
ASA
AAS
ОО
Not congruent
Answer:
SAS
Step-by-step explanation:
there are vertical angles in the middle and the sides are already marked
(2 pts.) 9.) Find two equivalent expressions to tan 20° using the cotangent function in degrees.
tan (u) = a/b = cot (90° – u)
Let u = 20°
Take it from here.
The equivalent value of the expression is tan20 is a cot(70).
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
The area of mathematics is concerned with how triangles' sides and angles relate to one another as well as with the pertinent uses of any angle.
Given that the trigonometric expression is tan30. The equivalent expression will be written as,
tan (u) = a/b = cot (90° – u)
tan (20) = cot ( 90 - 20 )
tan 20 = cot 70
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Though it just opened last month, the Mash Mobile food truck has been doing well; they're now serving an average of 200 mashed potato creations every day. If there are 8 ounces of potatoes in each dish, how many 50-pound bags of potatoes does the food truck use every day?
Answer:
2 50-pound bags
Step-by-step explanation:
[Conversions] 50-pound bags -> 800-ounce bags
[Total potatoes used] 200 mashed potato creations * 8 ounces of potatoes in each dish = 1,600 ounces of potatoes
[Bags used] 1,600 / 800 = 2 bags
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
David plays baseball 18 times each month for 3 months. He also plays soccer 15 times each month for 3 months. How many more times does he play baseball than soccer each month?
Plzz help asp
Answer:
3
Step-by-step explanation:
3 months baseball = 18 x 3 = 54
3 months soccer = 15 x 3 = 45
54-45 = 9
9 / 3 = 3
David plays baseball 3 more times than soccer each month.
David plays 3 more times baseball than soccer each month.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
David plays baseball for 3 months, and each month he plays 18 times.
Also, David plays soccer for 3 months, and each month he plays 15 times.
In 3 months, David plays baseball = 18 x 3 = 54
Also, in 3 months, David plays soccer = 15 x 3 = 45
The more number of times David plays baseball than soccer
= 54 - 45
= 9
In 3 months, David plays 9 more times baseball than soccer.
In one month, David plays 9/3 = 3 more times baseball than soccer.
3 more times David plays baseball than soccer each month.
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Please help derivitive
Please dont comment if you dont know …
[tex]\lim \limits_{x \to 0^{+}} \left( \csc x + \dfrac 1x \right)\\=\lim \limits_{x \to 0^{+}} \csc x + \lim \limits_{x \to 0^{+}} \dfrac 1x\\\\=\infty[/tex]
PLEASE HELP!!
Solve by completing the square 2x^2+x-4=0
Answer:
image attached with answer
Step-by-step explanation:
Help help help math math
Answer:
yes
Step-by-step explanation:
x increases by 2, and y increases by 3 consistently
Answer:
No
Step-by-step explanation:
please mark me brainliest
find the quotient 3^1^5/3^3 3^5 3^18 3^12 3^45
Answer:
It's about drive its about power put in the work put in the hours and take what's ours
Step-by-step explanation:
It's about drive its about power put in the work put in the hours and take what's ours It's about drive its about power put in the work put in the hours and take what's ours It's about drive its about power put in the work put in the hours and take what's ours It's about drive its about power put in the work put in the hours and take what's ours It's about drive its about power put in the work put in the hours and take what's ours
Hey mathematicians ! Can anyone help me with these problems please ! Will give brainly !
27) 115=5(5a-2)
115= 25a-10
125=25a
a=5
28) -72=-x-6(x+5)
-72=-7x-30
-42=-7x
x=6
i did two of them. now i gtg so won't do the rest
if the poins A(-6,-5),B(-3,-2) and C(3,k) is on the same straight line, find the value of k.
Answer:
4
Step-by-step explanation:
y = x + 1
yeah-ya.... right?
Answer:
4 is the answer i believe
Step-by-step explanation:
C skips 2 dots, Hope this helps:)
which is bigger 0.5 or 9%
this answer is 9% it is bigger than 0.5
The password must consist of a vowel followed by 3 letter and 2 odd digits. How many passwords are possible if repetition is allowed?
2. Dominique baked 4 dozen muffins. She wants to put the muffins in packages of 6.
How many packages will she have?
A 6
(B 8
© 10
0 24
E 288
Answer:
24 packages
Step-by-step explanation:
One dozen is 12, so 4 x 12 = 24
Trey wants to earn more than $89 trimming trees. He charges $8 per hour and pays S7 in equipment fees. What are the possible numbers of hours Trey could
trim trees?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answer:
11 hours
Step-by-step explanation:
8t + 7 > 89
8t > 81 : subtract 7 from both sides
t > 10.125 : divide by 8 for both sides
t = 11 : estimate
Trey has to work 11 hours because 10 hours would only give him $87.
Given that f(x) = ax – 5 and f(4) = 15, determine the value of a.
Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5
The given function is:
f(x) = ax - 5
If f(4) = 15, then x = 4
Substitute x = 4 into f(x) = ax - 5
f(4) = a(4) - 5
15 = 4a - 5
Solve for a by adding 5 to both sides
15 + 5 = 4a - 5 + 5
20 = 4a
Divide both sides by 4
4a/4 = 20/4
a = 5
Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5
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2.03 of 0.045 is what number?
Answer:
2.03% of 0.045=0.0009135
Step-by-step explanation:
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 0.045 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 0.045 is 100%, so we can write it down as 0.045=100%.
4. We know, that x is 2.03% of the output value, so we can write it down as x=2.03%.
5. Now we have two simple equations:
1) 0.045=100%
2) x=2.03%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
0.045/x=100%/2.03%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 2.03% of 0.045
0.045/x=100/2.03
(0.045/x)*x=(100/2.03)*x - we multiply both sides of the equation by x
0.045=49.261083743842*x - we divide both sides of the equation by (49.261083743842) to get x
0.045/49.261083743842=x
0.0009135=x
x=0.0009135
Answer:
0.09135
Step-by-step explanation:
when it says "of" a number, you simply multiply them
Sara says, "If you subtract 17 from my number and multiply the difference by - 4, the result is
- 60." What is Sara's number?
Answer:
32
Step-by-step explanation:
ok to the result is - 60 she said. So then we know that in order to get -60, you had to subtract 17 from the original number and multiply by -4.
equation is this: (x-17)×-4= -60
Next, we solve using pemdas!
x-17=[tex]\frac{-60}{-4}[/tex] (keep in mind that a negative cancels out a negative!)
add 17 to both sides
x= [tex]\frac{-60}{-4}[/tex]+17
So then now that you have the new equation you simplify!
x= 32
You are training for the upcoming bike and hike race. On the days you bike, you will ride 8 miles. On the days you hike, you will walk 3 miles. By the end of the training you want to have covered at least 200 miles. Write a linear inequality to represent this situation. Let x represent days biked and y represent days hiked.
Answer:
8x + 3y [tex]\geq[/tex] 200
Step-by-step explanation:
List the first 5 multiples and find ALL the factors of 16.
Multiples:
Factors:
Answer:
Multiples: 16, 32, 48, 64, 80 Factors: 1, 2, 4, 8 and 16
Step-by-step explanation:
hope this helped :3
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answer:
Step-by-step explanation:
Determine the period of the function g(x) = (cos ;)
Answer:
6[tex]\pi[/tex]
Step-by-step explanation:
The period of a sinusoidal function in the form a * cos (b (x + h)) + m is [tex]\frac{2\pi }{|b|}[/tex]. Therefore, we can see that "b" in g(x) is 1/3 and 1/3 substituted into [tex]\frac{2\pi }{|b|}[/tex] is 2[tex]\pi[/tex]/1/3 which is 6[tex]\pi[/tex].
Listen
If you draw a triangle with these measurements, which kind of triangle would it be?
Angles Sides
400
4 cm
50
7 cm
90°
8 cm
O acute scalene triangle
O acute isosceles triangle
O right equilateral triangle
Oright scalene triangle
Step-by-step explanation:
An acute triangle is a triangle whose angles are all acute (i.e. less than 90°). In the acute triangle shown below, ∠a, ∠b and ∠c are all acute angles. Example 1: A triangle has angles 46°, 63° and 71°.
Getting trained and licensed as a truck driver involves a one-time cost of $450. Gas and insurance end up costing about $2 per mile. For the first delivery, you will get paid $350 plus $6 per mile that you drive. Write 2 equations and solve this system.
The question is an illustration of a system of linear equations.
The system of linear equations is: [tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]The solution to the equation is (25,500)Let the number of miles be x.
Getting trained and licensed
One time cost: $450Gas and Insurance: $2 per mileSo, the equation is:
[tex]y=450 + 2x[/tex]
Delivery
First delivery: $350Rate: $6 per mileSo, the equation is:
[tex]y = 350 + 6x[/tex]
Hence, the system of linear equations is:
[tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]
To solve the equation, we equate both, as follows:
[tex]450 + 2x = 350 + 6x[/tex]
Collect like terms
[tex]6x - 2x = 450 - 350[/tex]
[tex]4x = 100[/tex]
Divide both sides by 4
[tex]x = 25[/tex]
Substitute 25 for x in [tex]y=450 + 2x[/tex]
[tex]y = 450 + 2 \times 25[/tex]
[tex]y = 450 + 50[/tex]
[tex]y = 500[/tex]
Hence, the solution to the equation is (25,500)
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Triangles ABC and EDC are similar.
ACE and BCD are straight lines.
Angle BAC = angle DEC
Angle CBA= angle CDE
AB = = 6 cm, BC = 2.5 cm, CD = 7.5 cm and CE = 10.5 cm.
Answer:
18cm
Step-by-step explanation:
The ratio is given by: 7.5/2.5=3
DE = 6 × 3 = 18 cm
or
DC/CB = x/AB
7.5/2.5 = x/6
3=x/6
x=6×3=18 cm
Use the Fundamental Theorem of Calculus to find y′ pls help me
Answer:
Convert to the form of fundamental theorem
[tex]y = \int_{1-6x}^1 \frac{u^3}{1+u^2}du= -\int\limits^{1-6x}_1 {\frac{u^3}{1+u^2} } \, du[/tex]
Step-by-step explanation:
Now, you can apply the theorem, that is [tex]y'= f(1-6x) \times (1-6x)' = -6 \frac{(1-6x)^3}{(1+(1-6x))}[/tex]
Simplify!!
A coin weighs 3/4 ounces. Laura picked up 6 of these coins. What is the total weight of the coins she picked up? In simplest form.
Answer:
1 1/2 pound
Step-by-step explanation:
If each coin weighs 3/4 ounces and she picked up 6 then you do 3/4 x 6/1 which equals 18/4 and since there is 16 ounces in a pound it simplifies to 1 2/4 or 1 1/2 pounds
= Homework: Mo...
Ben bowled 122 and 188 in his first two games. What must he bowl in his third game to have an average of at least 160?
HOM
Answer:
i think its 195 but i am not for sure correct me if i am wrong
Step-by-step explanation: