Rewrite the function using the change-of-base identity as
[tex]e^{x^2} \log_{10}(2x) = e^{x^2} \dfrac{\ln(2x)}{\ln(10)}[/tex]
Apply the product rule:
[tex]\left(e^{x^2} \log_{10}(2x)\right)' = \left(e^{x^2}\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \left(\dfrac{\ln(2x)}{\ln(10)}\right)'[/tex]
Use the chain rule:
[tex]\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(x^2\right)' \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac{(2x)'}{2\ln(10)x}[/tex]
Compute the remaining derivatives:
[tex]\left(e^{x^2} \log_{10}(2x)\right)' = 2xe^{x^2} \dfrac{\ln(2x)}{\ln(10)} + e^{x^2} \dfrac2{2\ln(10)x} = e^{x^2}\left(\dfrac{2x\ln(2x)}{\ln(10)} + \dfrac1{\ln(10)x}\right)[/tex]
If you like, you can convert back to base-10 logarithms:
ln(2x) / ln(10) = log₁₀(2x)
1 / ln(10) = ln(e) / ln(10) = log₁₀(e)
Then
[tex]\left(e^{x^2} \log_{10}(2x)\right)' = e^{x^2}\left(2x\log_{10}(2x)+\frac{\log_{10}(e)}x\right)[/tex]
you decide to go to a star gazing event there are 12 people in the group
Answer:
whts the question??
Step-by-step explanation:
please help
- 3
- 1.5
- 6
- 4
Answer:
its -1.5
I got u trust me
aaaaaaaaa
Each side of the cube at the Discovery Science Center in Santa Ana is 64 feet long.
(a)
Find the volume (in cubic feet).
cu. ft
(b)
Find the surface area (in square feet).
Answer:
V = 262’144 ft^3, surface area = 24’576 ft^2
Step-by-step explanation:
The volume con be find with this formula =
V = side^3
V = 64^3 = 262’144 ft^3
For find the surface area we can proceed in this way: first of all we can find the area of a face.
A = side^2 = 4096 ft^2
a cube has 6 faces, so we have to the mutiply the value six times.
Surface area = 4096 x 6 = 24’576 ft^2
help me with this plzzzz
Answer:b c
Step-by-step explanation:
did it
Triangle ABC is transformed to obtain triangle A'B'C'. Identify the transformation.
Answer:
think it’s (-x,-y)
I’m not sure
Reflect B (6,5) across the X axis. What would the new coordinate be?
Answer:
(6,-5)
Step-by-step explanation:
Ben wants to buy a guitar. The regular price of the guitar is $364.00. The sale peke of the guitar is 20% off of the regular price. Ben must pay 8.75 sales tax in addition to the sale price of the guitar. What is
the total amount ben must pay for the guitar?
Answer:
299.95
Step-by-step explanation:
solve for x
3x + 7 = -2
Answer:
x = -3
Step-by-step explanation:
1. Write the equation
3x + 7 = -2
2. -7 from both sides
3x = -9
3. Divide 3 from both sides to get x alone
x = -3
Answer:
Hello There!!
Step-by-step explanation:
3x+7=-2 (-7 from both sides)
-7 -7
3x=-9 (divide by 3 from both sides)
÷3 ÷3
x=-3
hope this helps,have a great day!!
~Pinky~
You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning a 6 and flipping tails is
You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning a number less than 3 and flipping tails is
.
You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning a number less than 3 and flipping tails is
.
.
Answer:
The probability of spinning a 6 and flipping tails is 0
The probability of spinning a number less than 3 and flipping tails is 1/5
Step-by-step explanation:
There are 5 yellow pens 6 blue pens 9 green pens she picks 1 at random and does not replace it then she picks another pen
what number is the largest
15%
0.153
1/12
1/7
Answer:
0.153
Step-by-step explanation:
15% =0.15
0.153 = 0.153
1/12 =0.083
1/7=0.142
So the greatest one is 0.153
Question 7 of 19
A right cylinder has a radius of 4 and a height of 11. What is its surface area?
A. 1527 units2
B. 887 units2
C. 120 units2
D. 607 units2
SUBMIT
Find the equation of the line with slope =-4 and passing through (2,-10) Write your answer in the form y=mx+b
Answer:
y= -4x -2
Step-by-step explanation:
-10=-4(2) -2
y= -4x -2
what is the approximate length of hypotenuse with a 35 degree angle and one leg is 12
Answer:
37
Step-by-step explanation:
35^2+12^2=37
A random sample of students was surveyed on what they eat for lunch at school. The results are shown in the table
below.
Lunch Item
Number of Students
Pizza
52
Salad
26
Burger
30
Chicken Sandwich
48
Brought lunch from home
44
If the school has 1,000 students, about how many students can the cafeteria expect to buy pizza?
208
1,000
260
52
Answer:
260
Step-by-step explanation:
you would divide 52/200 because all the numbers added up is 200 and it comes out to 0.26 and the original number of students they wanted is 1,000 so look at those zeros and move the decimal 3 times and add the zero in the empty space to get 260.
A ratio shows us the number of times a number contains another number. The number of students the cafeteria should expect to buy pizza is 260.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the number of students to the number of total students can be written as,
Ratio = (Number of students)/(Number of total students)
Ratio = 52/(52+26+30+48+44) = 52/200
Now, the same ratio is applicable to 1000 students, therefore, the ratio will be,
Number of students who prefer pizza = 1000 × (52/200) = 260
Hence, the number of students the cafeteria should expect to buy pizza is 260.
Learn more about Ratios:
https://brainly.com/question/1504221
#SPJ2
a clothing distributor sold an $80 coat at a discount price of $73. what was the percentage of discount for the coat?
Answer:
91%
Step-by-step explanation:
The discount is $73 so we would get 73/80.
73/80 is also known as 73÷80
which would equal 0.9125
if we were to covert and round it to a percent, it would be 91%
A triangle is called
_____ if none of its sides are the same length. *
equilateral
isosceles
scalene
Answer:
scalene
Step-by-step explanation:
Answer:
Scalene
Step-by-step explanation:
Equilateral means all the sides are the same.
Isosceles means only two are the same.
Scalene means none are the same.
what is the slope of this graph?
Answer:
The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope.
Step-by-step explanation:
PLS ASAP!! Thank You
Answer:
[tex]y = \frac{1}{2}x - 4[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{1}{2}x[/tex]
Required
Shift [tex]3\ units[/tex] down and [tex]2\ units[/tex] right
[tex]y = \frac{1}{2}x[/tex]
Shift 3 units down
The rule is: (x,y)=> (x,y-a)
Where a is the number of units shifted down
In this case: [tex]a = 3[/tex]
So, we have:
[tex]y = \frac{1}{2}x[/tex] == > [tex]y = \frac{1}{2}x - 3[/tex]
Shift 2 units right
The rule is: (x,y)=>(x-b,y)
Where b is the number of units shifted right
In this case: [tex]b = 2[/tex]
So, we have:
[tex]y = \frac{1}{2}x - 3[/tex] ==> [tex]y = \frac{1}{2}(x - 2) - 3[/tex]
Open bracket:
[tex]y = \frac{1}{2}x - 1 - 3[/tex]
[tex]y = \frac{1}{2}x - 4[/tex]
Hence, the new equation after the transformation is:
[tex]y = \frac{1}{2}x - 4[/tex]
how many liters give u 3.1KL
Answer:
3100 liters
Step-by-step explanation:
multiply the value by 1000
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!! DUE TODAY I NEED HELP ASAP
A restaurant has a 15% mandatory tip rate.
(a) Complete the ratio table shown. Show your work.
Pre-Tax Bill ($): 10 __ 60 __
Tip ($) __ 12 __ 15
(b) Using the table, how can you find the total tip paid on $70?
Answer:
Subtotal 70.00
15% Tip 10.50
Total 80.50
Step-by-step explanation:
1% 0.70
2% 1.40
3% 2.10
4% 2.80
5% 3.50
6% 4.20
7% 4.90
8% 5.60
% Tip
9% 6.30
10% 7.00
11% 7.70
12% 8.40
13% 9.10
This dude above is trash and wrong, I got a 0 because of him
Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
y < -x +4
y > 3x – 8
Answer:
[tex](x,y) = (3,1)[/tex]
Step-by-step explanation:
Given
[tex]y < -x + 4[/tex]
[tex]y > 3x - 8[/tex]
Required
Solve graphically
See attachment for graph;
The blue shade represents [tex]y < -x + 4[/tex]
While the green, represents [tex]y > 3x - 8[/tex]
Next, determine the intersection points between the two lines
From the attached graph, we have:
[tex](x,y) = (3,1)[/tex]
Hence, the solution is: [tex](3,1)[/tex]
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling a number greater than 6.
Answer:
1/2
Step-by-step explanation:
There are 12 equally likely outcomes.
There are 6 numbers greater than 6 (7, 8, 9, 10, 11, 12)
Take the number of possible outcomes and divide it by the total number of outcomes. 6/12 is 1/2
PLEASE ANSWER ILL GIVE HOU BRAU=INLIEXST
Answer:
4775.22
Step-by-step explanation:
V= πr2h
Input your numbers into the equation, and it will give you this answer.
HELP ASAP I WILL MARK BRAINLEY
Explain how to solve the equation and how to check the solution. 40 = Sy
Answer:
y = 5
Step-by-step explanation:
40 = 8y
divide both sides by 8, isolating y by itself:
40/8 = 8y/8
5 = y
rearrange the equation so the y is on the left side
y = 5
The answer is y = 5
We can check by plugging in y = 5 into the original equation:
40 = 8y
40 = 8(5)
40 = 40
correct
Part 3: The Space Inside! 1. Find the volume of the shipping box using the two methods and show your work: A. Packing cubes B. Using the volume formula 2. Explain how both methods provide the same measurement of volume for the shipping Let's ship. You are done! Penny and her classmates thank you, i really need help with the volume formula and the packing cubes
Answer:
Don't click the site its a scam and will give your phone a virus
у = -x + 2
y = 2x + 5
Answer:
x= -1
Step-by-step explanation:
-x+2= y =2x+5
-x+2=2x+5 /+x
2=3x+5 /-5
-3=3x
x= -1
Find the area of the circle. Round to the nearest tenth. Use 3.14 forn.
24 m
select the best term from the box
________name same amount
(1) Equivalent fractions (2) common denominator
Solution:
1. Equivalent fractions name the same amount.
Equivalent fractions are the same value with different numerator and denominator.
Example:
These values are same.
2. A common denominator is a common multiple of two or more denominators.
Example:
Here 6 is a common multiple of 2 and 3.
Hence the answer is (1) Equivalent fractions (2) common denominator.
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What is the main problem with this introduction paragraph?
Games Games Games claims to have the best trade-in store.
Even though it was in great condition, I was given only $4 for it. Later, I
saw that you were selling used copies of the same game for $22. Is
this really fair to your customers?
A. The hook does not relate to the topic.
B. It includes opinions instead of just facts.
C. It does not restate the main points of the essay.
D. The thesis statement is unclear.
Answer:
The thesis statement is unclear.