A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (Do not use mixed numbers. Round your answers to three decimal places.)

(a) How fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall
_____ ft/sec

20 feet away from the wall
_____ ft/sec

24 feet away from the wall
_____ ft/sec

...?

Answers

Answer 1

last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez

x2+y2=25

calculus says

2xx′+2yy′=0

and you are told that

y′=2

so you know

2xx′+4y=0

or

x′=−2yx


Related Questions

Write the distribution of 7×6=

Answers

To figure this out you just have to add 7 6 times... if the problem was 2 x 4 than an easy way to do it is 2 + 2 + 2 + 2 = 8.

52.063 divided into 9.2 rounded to the nearest hundredth

Answers

The answer for this question is .18

Answer:

The answer is 5.66

Step-by-step explanation:

52.063 divided by 9.2 is 5.65902173913. Then you round of to the nearest hundredth which is two decimal places to the right (so it's 5). Then you round it off one value higher since 9 is above 5. Therefore the final answer is 5.66

Which statement best describes how to determine whether f(x) = 9 – 4x^2 is an odd function?

Determine whether 9 – 4(–x)^2 is equivalent to 9 – 4x^2.

Determine whether 9 – 4(–x^2) is equivalent to 9 + 4x^2.
Determine whether 9 – 4(–x)^2 is equivalent to –(9 – 4x^2).

Determine whether 9 – 4(–x^2) is equivalent to –(9 + 4x^2).

Answers

For odd functions there is a rule:
f(x) = -f(-x) or in other words
-f(x) = f(-x)

9 - 4x^2 = -(9-4(-x)^2) or in other words
-(9-4x^2) = 9 - 4(-x)^2

Answer is third option.

Answer:

Its CCCCCCCCCCCCCCC aka 3 aka third option

on dredful edge im going nuts

Step-by-step explanation:

From 2000-2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.

Answers

So you first need to find how much the population drops each year. For that you need to do 2.5%/10years which would be .25 then you would multiply by 8 to find for 2008 which you would get 2.Then you need to get 2% of 2950000. To do this you need to do 2,950,000*.02 which finally gives you 59,000 then you would subtract 2,950,000-59000 which the answer to this is 2,891,000! Hope it helps.

The population of the city in the year 2008 is 2409122.

Important information:

Initial population in 2000 is 2,950,000.Decreasing rate is 2.5%.Exponential formula:

According to the exponential decay formula:

[tex]f(t)=a(1-r)^t[/tex]

Where a is the initial value, r is the decay rate and t is the time period.

The difference between 2008 and 2000 is 8.

Substitute [tex]a=2950000, r=0.025, t=8[/tex] in the above formula.

[tex]f(8)=2950000(1-0.025)^8[/tex]

[tex]f(8)=2950000(0.975)^8[/tex]

[tex]f(8)=2409122.8208[/tex]

Round the value to the previous integer.

[tex]f(8)\approx 2409122[/tex]

Therefore, the population of the city in 2008 is 2409122.

Find out more about 'Exponential formula' here:

https://brainly.com/question/23942604

what is the value?
5x+3=4x ?? bit confused

Answers

minus 4x from both sides
x+3=0
minus 3 from both sides
x=-3

You drive your car for 3 hours at an average speed at 30 km per hour. how far did you go?

Answers

If you travel 30 km for every hour, then for 3 hours you drive 30 × 3 which is 90 km.

A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) ...?

Answers

The solution to the problem is as follows:


y' = 2y 

y'/y = 2 

dy/y = 2dx 

lny = 2x + k 

y = (e^k)(e^2x) 

5 = e^k 

y = 5e^(2x)


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Henry has 523 baseball cards. He buys 24 each month. What is a explicit rule for the number of baseball cards Henry has in n months?

Answers

To find your explicit rule, you would make your function (f(n)) equal to your change in cards per month (24) times your number of months (n) plus you initial number of cards (523). This creates the function f(n)=24n+523. What this is essentially doing is calculating the number of new cards bought in n months (24n) and adding it to your starting value (523) to get your new number of cards (f(n)).

Answer:

the answer is a_n= 24n+499 just took the test :)

Step-by-step explanation:


What is the area of ABC below? If necessary, round your answer to two decimal places.

Answers

Based on the given figure above, in order for us to find the area of the triangle, we need to find the value of the base first. So in finding the base, we are going to use the Pythagorean theorem. a2 + b2 = c2. Substitute the values.
(9.4)^2 + (23.2)^2 = c2
88.36 + 538.24 = c2
626.6 = c2
c= 25.03
Now that we have the base, let us proceed for the Area.
The formula for area would be A = 1/2 (b)(h)
Plug in the values.
A = 1/2(25.03)(7.9)
A= 1/2(197.74)
A= 98.87
Therefore, the area of figure ABC is 98.87.
Hope this answer helps.

The answer I got from apex was- 106.26


The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?

Answers

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola.  The first few steps are as follows.  Set the parabola equal to 0 so you can solve for the vertex.  Separate the x terms from the constant by moving the constant to the other side of the equals sign.  The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out).  Let's start there.  The first 2 steps result in this polynomial:

[tex]-2x^2+4x=-1[/tex].  Now we factor out the -2:

[tex]-2(x^2-2x)=-1[/tex].  Now we complete the square.  This process is to take half the linear term, square it, and add it to both sides.  Our linear term is 2x.  Half of 2 is 1, and 1 squared is 1.  We add 1 into the set of parenthesis.  But we actually added into the parenthesis is +1(-2).  The -2 out front is a multiplier and we cannot ignore it.  Adding in to both sides looks like this:

[tex]-2(x^2-2x+1)=-1-2[/tex].  Simplifying gives us this:

[tex]-2(x^2-2x+1)=-3[/tex]

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex.  Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

[tex]-2(x-1)^2+3=y[/tex]

From this form,

[tex]y=-a(x-h)^2+k[/tex]

you can determine the coordinates of the vertex to be (1, 3)

Answer:

(1,3)

Step-by-step explanation:

A writer charges $5 per word plus a start up fee of $50 per article.

Answers

There is no question here but im assuming its something along the lines of "if there were X words how much would it cost?" 

The equation would be Y=5x + 50
Y= answer
X= words

Just put the number of words as x and the solve the equation.

Add.
(5n^2+4n)+(3n^2+6n)

Answers

5n^2+4n+3n^2+6n=
5n^2+3n^2+4n+6n=
8n^2+10n

two consecutive odd negative integers have a product of 483, find the integers ...?

Answers

Negative 21 and Negative 23 are the two integers you are looking for. Two negatives make a positive and the are both consecutive odd integers that = 483 when multiplied.
In order to find this you need to assume that they are declared as X and as X + 2. This makes the formula for calculating it x (x+2)=483, and this, based on the formulas for calculation, equals

 x^2+2x-83=0

From this we can see that a negative X is -23, which when +2 is added results in -21.

Which of the following represents this function written in intercept form?

y=x^2-8x+12

a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6) Which of the following represents this function written in intercept form?

y=x^2-8x+12

a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6)

Answers

Answer:

B. y = (x-2)(x-6)

Step-by-step explanation:

The quadratic function y = x²- 8x + 12 can be factored into intercept form as y = (x - 2)(x - 6), which corresponds to option (b).

The function given is y = x² - 8x + 12. To write this function in intercept form, we need to factor it as the product of two binomials, each representing its intersections with the x-axis where y=0.

To do this, we look for two numbers that multiply to give the constant term (12) and add up to give the coefficient of the middle term (-8). These two numbers are -2 and -6.

Thus, the factored intercept form is y = (x - 2)(x - 6). This corresponds to answer choice (b).

Heather has $500 in her savings account. she withdraws $20 per week for gas. write an equation heather can use to see how many weeks it will take her to have a balance of $220.

Answers

220 = -20w + 500 <== ur equation
220 - 500 = -20w
- 280 = -20w
-280/-20 = w
14 = w.....it would take 14 weeks

A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a_______

.When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, _______vertex
of ∆A″B″C″ will have the same coordinates as B′.

Answers

Answer:The first one is a Reflection

The second one is B

Step-by-step explanation:

Use the function described below to answer questions 1 - 4.

Yvonne invested $4,000 in a savings account which pays 3.5% interest compounded annually. Use the formula A = P(1 + r)t, where P is the principal, r is the interest rate, and t is the time in years.
1. Approximately, how much money will Yvonne have in 4 years? Round to the nearest cent.
2. Approximately, how much money will Yvonne have in 8 years? Round to the nearest cent.
3. Approximately, how many years will it take for Yvonne to double her money? Write the number of years only.

4 Alex buys a top of the line computer. He did not realize that the computer would lose value so fast. If his computer cost $1800.00 and it depreciates at a rate of 45% each year, in how many years will it be worth less than 1/3 of what he paid for it?


Answers

1)4000(1+.035)^4=use the calculator,,2)4000(1+.035)^8=??,,,3)2p=p(1+.035)^t solve for t..

Estimate the tip on a $19.65 check using a tip rate of 15%

Answers

We can round the check up to $20
15% of 20
= 0.15 x 20 = $3
The tip is about $3 

music in 2001, full length cassettes represented 3.4% of total music sales. between 2001 and 2006, the present decreased by about 0.5% per year

Answers

i don get what you ask

Factor completely: 2x3 + 10x2 + 4x + 20

Prime

(2x + 10)(x2 + 2)

2[(x + 5)(x2 + 2)]

(x + 5)(2x2 + 4) ...?

Answers

Correct answer is D.

[tex]2x^3 + 10x^2 + 4x + 20 \\2x^2(x+5)+4(x+5) \\(x+5)(2x^2+4)[/tex]

Answer:

B) 2[(x + 5)(x2 + 2)]

Step-by-step explanation:

Given: 2x^3 + 10x^2 + 4x + 20

Here 2 is a common factor, so we take it out and write the remaining terms in the parenthesis.

2(x^3 + 5x^2 + 2x + 10)

Now let's take (X^3 + 5x^2 +2x + 10), we group and factor them as follows:

(x^3 + 5x^2 + 2x + 10) = x^2(x+5) + 2(x + 5) = (x+5)(x^2 +2)

When we combine them, we get

2x^3 + 10x^2 + 4x + 20 = 2(x+5)(x^2 +2)

Therefore, the answer is B) 2[(x + 5)(x2 + 2)]

Hope this will helpful.

Thank you.

Simplify the expression: √18x^4y^3

Answers

The answer is 3x^2y √2y.

Answer:

[tex]3x^2y\sqrt{2\cdot y}[/tex]

Step-by-step explanation:

We have been given an radical expression. We are asked to simplify our given expression.

[tex]\sqrt{18x^4y^3}[/tex]

We can rewrite terms of our given function as:

[tex]\sqrt{18\cdot x^4\cdot y^3}[/tex]

[tex]\sqrt{2\cdot 9\cdot x^4}\cdot y^2\cdot y}[/tex]

[tex]\sqrt{2\cdot 3^2\cdot (x^2)^2\cdot y^2\cdot y}[/tex]

Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:

[tex]3x^2y\sqrt{2\cdot y}[/tex]

Therefore, the simplified form of our given expression would be [tex]3x^2y\sqrt{2\cdot y}[/tex].

Justine enrolls in a music program. The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. If the average cost per music lesson is $12 and Justine has taken x classes, which equation represents this scenario?


A.12=54/x
B.12=45+9/x
C.12=45+9x/x
D.12=45x+9/x

Answers

If Justine has taken x classes of $9 per lesson, then the total fee for these lessons is $9x.

The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. This means that the total cost of the program in terms of x is

$45 + $9x = $(45 + 9x).

If the average cost per music lesson is $12 (includes a registration fee), then the cost of the program is $12x.

Therefore,

12x = 45 + 9x.

Divide this equation by x:

[tex]12=\dfrac{45+9x}{x}.[/tex]

Answer: correct option is C

The correct option is C) [tex]\[12 = \frac{45 + 9x}{x}\][/tex]. The equation that represents this scenario is [tex]\[12 = \frac{45 + 9x}{x}\][/tex].

To understand why option D is correct, let's break down the costs associated with Justine's music program.

1. The registration fee is a one-time cost of $45. This is a fixed amount and does not depend on the number of classes taken.

2. The cost per lesson is $9, and Justine has taken x classes. Therefore, the total cost for the lessons alone is 9x.

3. The average cost per music lesson, including the registration fee, is $12. This average cost is calculated by taking the total cost (registration fee plus the cost of x lessons) and dividing by the number of classes x.

4. The total cost for x classes, including the registration fee, is the sum of the registration fee and the cost of the lessons, which is [tex]\(45 + 9x\)[/tex].

5. To find the average cost per lesson, we divide the total cost by the number of classes x. This gives us the equation [tex]\(\frac{45 + 9x}{x}\)[/tex].

6. We know that the average cost per lesson is $12, so we set the equation equal to 12: [tex]\(12 = \frac{45 + 9x}{x}\).[/tex]

Therefore, the equation that correctly represents the scenario is: c)

[tex]\[12 = \frac{45 + 9x}{x}\][/tex].

if (3x^2)+7=0 then (x-1/3)^2

Answers

[tex]3x^2+7=0 \\x^2=- \frac{7}{3} \\x=\pm \sqrt{-\frac{7}{3} } \\x=\pm i \sqrt{\frac{7}{3} } \\ \\(x- \frac{1}{3} )^2=x^2- \frac{2}{3}x+ \frac{1}{9} =- \frac{7}{3} -\frac{2}{3}(\pm i \sqrt{\frac{7}{3} } )+ \frac{1}{9} = \\=- \frac{21}{9} -\frac{2}{3}(\pm i \sqrt{\frac{7}{3} } )+ \frac{1}{9} \\=- \frac{20}{9} \mp i\frac{2}{3} \sqrt{\frac{7}{3} } [/tex]

What is 35/10 convert into a decimal?

Answers

The answer to this is 3.5

A college writing seminar increased its size by 50% from the first to the second day. If the total number of students in the seminar on the second day was 15 how many students were in the class on the first day

Answers

10 students on the first day
20000 is the correct answer

What is the value of the expression below when r = 2?

9 – 3r


A.12


B.6


C.3

Answers

The answer is C. 3, because you're essentially saying 9 - (3 × 2) and that is 9 - 6, which equals 3. I hope this helps!

A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is



5 units

10 units

12.5 units

Answers

The diameter of the cylinder with a volume of 175 cubic units and a height of 7 units is 5 units.

To calculate the diameter of a cylinder, we first need to find the radius using the formula for the volume of a cylinder, V = πr²h. Given that the volume is 175 cubic units and the height is 7 units, the radius comes out to be 5 units. Since the diameter is twice the radius, the diameter of the cylinder is 5 units.

A student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d = days, r = raffle tickets, and h = hours, what function can he use to calculate his earnings?

Answers

answer is C

T = 15d +r/4 +2h

or

 you can write another way

T = 15d + 0.25r + 2h 

Answer: C. [tex]T=15d+\frac{r}{4}+2h[/tex]

Step-by-step explanation:

Let d = days, r = raffle tickets, and h = hours.

Given: A student earns in a day = $15

Then his earning in d days =$15d

Also, he earns for each riffle = $0.25

Then his earning in for r riffles =$0.25r

And , he earns for each hour he works at the game = $2

Then his earning for h hours = $2h

Then the function he can use to calculate his earnings is given by :_

[tex]T=15d+0.25r+2h\\\\\Rightarrow\ T=15d+\frac{1}{4}r+2h[/tex]

The price of a pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these shoes? A.) $2.84 B.) $3.16 C.) $4.50

Answers

A) I believe but you might not want to go with it cause I'm not good at math AT ALL:)
The equation you use to find the answer is...
tax=tax rate(change the % to a decimal)xprice of item
which in this case comes out to be $2.84

Subtract -34.7 from -7.85

Answers

i think it may be -42.55
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