We are given
equation of position
[tex]s(t)=(t)ln(3t)[/tex]
Calculation of velocity:
we can find derivative
[tex]s'(t)=1*ln(3t)+t*\frac{3}{3t}[/tex]
[tex]s'(t)=ln(3t)+1[/tex]
so, velocity is
[tex]v(t)=ln(3t)+1[/tex]
now, we can set it to 0
and then we can solve for t
[tex]v(t)=ln(3t)+1=0[/tex]
[tex]t=\frac{1}{3e}[/tex]
Calculation of acceleration:
we can find derivative again
[tex]v'(t)=\frac{3}{3t} +0[/tex]
[tex]v'(t)=\frac{1}{t} [/tex]
so, acceleration is
[tex]a(t)=\frac{1}{t} [/tex]
now, we can plug value of t
[tex]a(\frac{1}{3e})=\frac{1}{\frac{1}{3e}} [/tex]
[tex]a(\frac{1}{3e})=3e [/tex]..................Answer
An ice hockey rink is a rectangle with a perimeter of 174 meters. The length is 9 meters more than twice the width. Find the length and width.
let L be the length
let W be the width
L = 9 + 2W
since the perimeter = 2L + 2W
Perimeter = 2 x (9 + 2W) + 2W
174 m = 18 + 4W + 2W
174 m = 18 + 6W
6W = 174 - 18
6W = 156
W = 156/6
W = 26
L = 9 + 2W
L = 9 + 2 x 26
L = 9 + 52
L = 61
Therefore, length = 61 m and width = 26 m.
The cost (in dollars) of making N birthday cakes is represented by C= 24n + 35. How many birthday cakes are made when the cost is $395? Show your work and include units in your Answer.
The cost is $395. You are trying to find n in 24n + 35.
Set C = 395.
You get 395 = 24n + 35.
Solve for n by first subtracting 35 from both sides of the equation:
395 - 35 = 360.
24n + 35 - 35 = 24n.
Now you have 360 = 24n. Divide both sides by 24 to get:
15 = n.
So, 15 birthday cakes are made when the cost is $395.
The Number of cakes that can be made with $395 is 15.
The cost function :
C(n) = 24n + 35
The number of cakes, n that can be made with $395:
Substitute, C(n) = 395 into the equation :
395 = 24n + 35
24n = 395 - 35
24n = 360
Divide both sides by 24
n = 360 / 24
n = 15
Therefore, 15 cakes can be made with $395
Learn more : https://brainly.com/question/18796573
23 - 4 - 6 + 7 + 5 - 1 x 0 + 1 = x
Solve the equation.
Sushirama sells rolls for 12$ each. For 20$ per month, you can purchase a discount card which makes the rolls 9$ each. Which inequality below couod be used to find how many rolls of sushi(r) you would need to eat in month to make the discount card a good deal? (A) 12r > 20 + 9r (B) 12r > 20r + 9 (C) 12r < 20 + 9r (D) 12r < 20r + 9
3.44444444444 in simplest form
What is 7 3/8 of 1600
What is [tex]7\dfrac{3}{8}[/tex] of [tex]1600[/tex] ?
You must multiply [tex]1600[/tex] by [tex]7\dfrac{3}{8}=\dfrac{7\cdot8+3}{8}=\dfrac{59}{8}[/tex].
[tex]1600\cdot\dfrac{59}{8}=200\cdot\dfrac{59}{1}=200\cdot59=11800[/tex]
If f(x)=5x^2 and g(x)=x^2-4x-8, find (f-g)(x)
Important!!!
Answer:
Option B.
Step-by-step explanation:
(f-g)(x) = f(x)-g(x)
= (5x²-3) - (x²-4x-8)
=5x²-3 -x² +4x +8 ( - sign outside will multiply each sign inside)
=4x² +4x + 5
After 10 months the simple interest earned annually on an investment of $6000 was $769. Find the interest rate to the nearest tenth of a percent.
t-shirts are on sale for $4 ofc the regular price. Jeb buys 5 t-shirts for a total of $45.05, including a 6% sales tax. Which equation can Jeb use to find the regular price, r, of 1 t-shirt?
a)0.06(5r-4)=45.05
b)5(r-4)=1.06×(45.05)
c)1.06×5(r-4)=45.05
d)5(r-4)+0.06r=45.05
Alexandra has 78 emails in her inbox. She deletes 47 emails. How many emails are left in her inbox? Draw jumps and label the numbers line to show your thinking
Bea bakery bakes 215 cookies and 45 muffins every hour how May baked goods are baked in 4 hours.
Solve for x. −5x−4(x−6)=−3 Enter your answer in the box. x =
-5x -4(x-6) = -3
distribute
-5x -4x+24 = -3
combine like terms
-9x +24 = -3
subtract 24 from each side
-9x = -27
divide by -9
x = 3
Answer:
x=3
Step-by-step explanation:
−5x−4(x−6)=−3
To solve for x:
for this we have to make the equation in such a way that the variable x lies on the left side and constant terms on the right side.
First distribute -4 over x and -6
We get -4x+24.
Substitute in the equation.
-5x-4x+24 =-3
Subtract 24 from both the sides
-5x-4x = -3-24
Or =9x = -27
Divide by -9
X = 3
What is 7 * 3? this is very important so plz help
The answer to your question is 21.
7 * 3 = 21
7 x 3 = 21
(you can learn your multiplications, or get a calculator)
hope that helps anyway :)
List the key words in the equation twice the sum of a number and three is seven and than write the equation
3.4 divided by 55.318
3.4/55.318= 0.06146281499
There isn't much of a way to explain this just divide it as it is stated.
Here is a square..
Inside the square is an equilateral triangle.
The perimiter of the triangle is 54cm.
Find the perimiter of the square.
Show your working out.
Please help!! Thanks!
[tex]f(x)=2x^2+5\sqrt{x-2}\\\\f(3)\to\text{put the value of x = 3 to the equation of the function}\\\\f(3)=2(3^2)+5\sqrt{3-2}=2(9)+5\sqrt1=18+5(1)=18+5=23[/tex]
AHHHHHH NEED HALP C AND B
Answer: science
Step-by-step explanation:
original price $45.00; markdown 22%
The sale price of the item is $35.10.
To find the sale price of an item with a markdown, you can follow these steps:
1. Convert the markdown percentage to a decimal. In this case, the markdown is 22%, so convert it to 0.22.
2. Subtract the decimal equivalent of the markdown from 1. This will give you the "discount factor." In this case, 1 - 0.22 = 0.78.
3. Multiply the original price by the discount factor to find the sale price.
Let's calculate it:
1. Markdown as a decimal: 22% = 0.22.
2. Discount factor: 1 - 0.22 = 0.78.
3. Sale price = Original price * Discount factor
Sale price = $45.00 * 0.78
Sale price = $35.10.
So, the sale price of the item is $35.10.
Explanation: The markdown percentage of 22% represents the reduction in price from the original price. By subtracting this percentage from 100% (or 1 in decimal form), we find the discount factor, which tells us how much of the original price remains. Multiplying the original price by the discount factor gives us the sale price. In this case, the sale price is $35.10, reflecting a 22% reduction from the original price of $45.00.
For more such questions on sale price:
https://brainly.com/question/7459025
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The probable question may be:
Find the sale price of the following item. Round to two decimal places when necessary: Original price: $45.00; Markdown : 22%.
Multi-step: This week, Maddie worked 2 1/2 hours on Monday, 2 2/3 hours on Tuesday, and 3 1/4 hours on Wednesday. How many more hours will Madie need to work this week to make her goal of 10 1/2 hours a week? ( show steps please)
Answer:
2 1/12
Step-by-step explanation:
Maddie wants her total hours to be 10 1/2. That is, she want the sum of the daily hours to be that value:
... 10 1/2 = 2 1/2 + 2 2/3 + 3 1/4 + (more hours)
Subtracting the contant terms on the right, we can find the value of (more hours).
... 10 1/2 - 2 1/2 - 2 2/3 - 3 1/4 = (more hours)
Doing the subtraction left to right, we have
... 8 - 2 2/3 - 3 1/4 = (more hours)
... 5 1/3 - 3 1/4 = (more hours)
... 2 1/12 = (more hours)
The only subtraction that may require any extra effort is subtracting 1/4 from 1/3.
... (1/3) - (1/4) = (4/12) - (3/12) = (4 -3)/12 = 1/12
_____
If you play with fractions very much, this is a number fact you will have run across before.
solve the equation x/4+5/8=3/8
X/4 +5/8 = 3/8
X/4 = 3/8-5/8
X/4 = (3-5)/8
X/4 = -2/8
Multiply both sides by 4 we get
4x/4 = -8/8
X = -1
after 3/4 of a minute a sloth has moved just 3/8 of a foot. what is the sliths speed in feet per minute?
This is a tricky question but my best guess is .5 or 1/2 a foot per minute. I divided 3-8 as a decimal and added one/4th part to it to be a full minute.
Which of the following statements is correct?
• 15 > 700
• 15 = 700
• 15 < 700
• 700 = 700
The last two ones
< Less than
> Greater than
= Equal to
The correct statements are '15 < 700' and '700 = 700'.
In mathematics, we use comparison operators to establish relationships between numbers.
By comparing the given numbers, we see that 15 is less than 700, which makes the correct statement: '15 < 700'. Additionally, the statement '700 = 700' is also correct, as these values are identical and other statements are incorrect.
What’s 1 1/3 as an improper fraction?
*(Answer)*= [tex]4/3[/tex]
*(Explanation)*= You multiply 3 (denominator) to 1 (whole number) then you add 1 (numerator)
how to convert 0.61 km into meters
Which number line represents all of the values of x for the equation x2 = 16?
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 4 and is labeled as p.
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 8 and is labeled as p.
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 4, another dot is shown on negative 4, and are labeled as p and q, respectively.
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 8, another dot is shown on negative 8, and are labeled as p and q, respectively.
i think it is the third one
hope it helps
Answer:
The given equation is
→x²=16
→x²-16=0
→(x-4)(x+4)=0
x=4, -4
p=4
q=-4
Option C
A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on the number line, and all these are increments are labeled. A dot is shown on positive 4, another dot is shown on negative 4, and are labeled as p and q, respectively.
What’s is the standard form of the equation of the given circle with center A(4,8)
The X. axis is you final answer!
Will mark brainliest if you could explain this to me??
Your answer would be 4379 members because at the very beginning you had started off with 4372 members, however as the months go by changes happen. On october, it changed by -10, meaning that 10 students left the school meaning 4372-10=4362 members remaining. Then there's november with -8, so you subtract 8 from your new total 4362-8=4354. Then december comes, and this time it's a positive number, so you have to add 23 to 4354, giving you a new total of 4377. Then there's january, and its back to a negative number so you subtract 12 from 4377, 4377-12=4365. Then february comes and it's a change of a positive number, so you add 3 to the 4365, giving you 4368. And then finally by march, it's another positive number so you add 11 to your total, giving you 4379 students which are now at school. So basically if it's a negative change, subtract from the total, and if it is a positive, add to it. And you have to continue with the total that you got from the previous change that you did. Hope this was helpful
basically you start with 4372 the table shows what happens during the school so after September you go to October which is -10 so you end up with 4362 then, November which is -8 so you get 4354 then in December you have +23 which makes 4377 then in January you have -12 which makes 4365 then in Feburary you have +3 which makes 4368 then in march you have +11 so 4379 so
1rst one
-hope this helps
solve y=x^2+23 for x
For this case we must clear x from the given equation:
[tex]y = x ^ 2 + 23[/tex]
We passed 23 subtracting the other side of equality:
[tex]y-23 = x ^ 2[/tex]
By definition, [tex]a ^ 2 = b[/tex]is written as [tex]a = +/-\sqrt{b}[/tex]
So, we have:
[tex]x = + / -\sqrt{(y-23)[/tex]
So, the solution of [tex]y = x ^ 2 + 23[/tex] for x is:
[tex]x = + / -\sqrt{(y-23)[/tex]
Answer:
[tex]x = + / -\sqrt{(y-23)[/tex]
[tex]x1=+\sqrt{(y-23)[/tex]
[tex]x2=-\sqrt{(y-23)[/tex]
Answer:
x = +/- (square root) y-23
Step-by-step explanation:
A P E X
please help!!! 50 pts to accurate solver!!!! no work needed. just answers
Because G is a 90 degree angle ( right angle) the 2 angles given when added together also need to equal 90 degrees:
4x + 5x = 90
Combine like terms:
9x = 90
Divide both sides by 9:
X = 90/9
X = 10
2x and 8X are supplementary angles and need to equal 180 degrees when added together:
2x + 8x = 180
Combine like terms:
10x = 180
Divide both sides by 10:
X = 180 /10
X = 18
The inside angle where they have 32 is a vertical angle to 32 so it is also 32.
The four inside angles need to equal 360 degrees.
Subtract the 3 known angles from 360 to find x:
X = 360 - 158 - 148 - 32 = 22 degree.