Find the area of the figure. Round to the nearest hundredth.

The top of the ladder will be falling down the side of the house at a rate of approximately 0.1005 feet per second after 1 second, 0.3145 feet per second after 3 seconds, and 1.3333 feet per second after 8 seconds.

These rates can be calculated using the Pythagorean theorem and differentiation to find the rate of change of the hypotenuse with respect to time. Specifically, if x represents the distance of the base of the ladder from the house and y represents the height of the ladder on the side of the house, then we have

x^2 + y^2 = 10^2

and we can differentiate both sides with respect to time to obtain

2x(dx/dt) + 2y(dy/dt) = 0

Solving for dy/dt, we get

dy/dt = -(x/y)(dx/dt)

Substituting dx/dt = 1 ft/s, x = t and y = √(10^2 - x^2) = √(10^2 - t^2), we can then evaluate dy/dt at t = 1, 3, and 8 to obtain the desired rates.

dy/dt = -t/ √(10^2 - t^2)

t = 1 : dy/dt = -1/ √(10^2 - 1^2) = -0.1005ft/s

t = 3: dy/dt = -3/ √(10^2 - 3^2) = -0.3145ft/s

t = 8: dy/dt = -8/ √(10^2 - 8^2) = -1.3333ft/s

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Step-by-step explanation:

we have 11k + 4k.

this is like saying "I have 11 apples and then get 4 more apples - how many apples do I have ?"

in other words, how many "k" do I have ?

11 + 4 = 15.

we have 15k.

and then there is -3 + 8 = 5

so, the answer is

15k + 5

Answer:

15k + 5

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 11k - 3 + 4k + 8

Let's simplify the expression,

→ 11k - 3 + 4k + 8

→ 11k + 4k - 3 + 8

→ (11k + 4k) + (-3 + 8)

→ (15k) + (5)

→ 15k + 5

Hence, the answer is 15k + 5.

The account would be worth approximately $62,420.80, which includes both the initial investment of $36,000 and the accumulated interest.

Assuming that the $200 has been added each month for the past 15 years, the total amount of money invested would be $200 x 12 months x 15 years = $36,000.
To calculate the amount of money earned from the 4% interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (the initial investment), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values, we get:
A = $36,000(1 + 0.04/12)^(12*15)
Simplifying, we get:
A = $36,000(1.0033)^180
A = $36,000(1.7328)
A = $62,420.80
Therefore, after 15 years, the account would be worth approximately $62,420.80, which includes both the initial investment of $36,000 and the accumulated interest.

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The balance of the account after 15 years is given as follows:

$49,218.

The balance of an account, considering periodic deposits, is given as follows:

\(B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}\)

The meaning of each parameter is given as follows:

The parameter values for this problem are given as follows:

P = 200, r = 0.04, n = 12, t = 15.

Hence the balance of the account after 15 years is given as follows:

\(B = \frac{P\left(\left(1 + \frac{r}{n}\right)^{nt}-1\right)}{\frac{r}{n}}\)

\(B = \frac{200\left(\left(1 + \frac{0.04}{12}\right)^{12 \times 15}-1\right)}{\frac{0.04}{12}}\)

B = 49,218.

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Therefore, the iterated integral ∫2,0∫4,1 sqrt(x+4y)dxdy is equal to -4/3.

We can evaluate the given iterated integral ∫2,0∫4,1 sqrt(x+4y)dx dy by first integrating with respect to x and then integrating with respect to y.

∫2,0∫4,1 sqrt(x+4y)dxdy = ∫2,0 [∫4,1 sqrt(x+4y) dx] dy

Let's evaluate the inner integral first.

∫4,1 sqrt(x+4y) dx = (2/3) * (x+4y)^(3/2) | from x=4 to x=1

= (2/3) * [(1+4y)^(3/2) - (4+4y)^(3/2)]

Now we can substitute this result into the outer integral and evaluate it with respect to y.

∫2,0 [∫4,1 sqrt(x+4y) dx] dy

= ∫2,0 [(2/3) * [(1+4y)^(3/2) - (4+4y)^(3/2)]] dy

= [-(2/15) * (1+4y)^(5/2) + (2/15) * (4+4y)^(5/2)] | from y=4 to y=1

= [-(2/15) * (1+41)^(5/2) + (2/15) * (4+41)^(5/2)] - [-(2/15) * (1+42)^(5/2) + (2/15) * (4+42)^(5/2)]

= [-(2/15) * 25^(1/2) + (2/15) * 36^(1/2)] - [-(2/15) * 81^(1/2) + (2/15) * 100^(1/2)]

= 16/15 - 8/5

= -4/3

Therefore, the iterated integral ∫2,0∫4,1 sqrt(x+4y)dxdy is equal to -4/3.

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An equilibrium phase diagram can be used to determine phase transitions, phase presence, and phase compositions at different conditions.

An equilibrium phase diagram can be used to determine the below mentioned parameters:

A) It can determine where phase transitions will occur. Phase transitions refer to changes in the state or phase of a substance, such as solid to liquid (melting) or liquid to gas (vaporization). The phase diagram provides information about the conditions at which these transitions take place, such as temperature and pressure.

B) It can determine what phases will be present for each condition of chemistry and temperature. The phase diagram shows the different phases or states of a substance (such as solid, liquid, or gas) under different combinations of temperature and pressure. It provides a visual representation of the stability regions for each phase, indicating which phase(s) will be present at a given temperature and pressure.

C) It can determine the chemistry and amount of each phase present at any condition. The phase diagram gives information about the composition (chemistry) and proportions (amount) of different phases present under specific conditions. It helps identify the coexistence regions of multiple phases and provides insight into the equilibrium compositions of each phase at various temperature and pressure conditions.

In summary, an equilibrium phase diagram is a valuable tool in understanding the behavior of substances and can provide information about phase transitions, phase stability, and the chemistry and amounts of phases present at different conditions.

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Answer:

a.

inverse

of

(0,1)=(1,0)

(1,0)=(0,1)

(2,-1)=(-1,2)

(3,0)=(0,3)

(4,1)=(1,4)

Step-by-step explanation:

b.

yes the function are inverse

as

(-1,2)=(2,-1)

(0,1)=(1,0)

Take any one point .

For inverse

(x,y) should be (y,-x)

Apply

Yes the functions are inverses of each other

The fourth vertex of the rectangle is obtained as (-5, 4).

A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.

To find the fourth vertex of the rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length.

The given vertices are (1, 4), (1, -4), and (-5, -4).

Apply the midpoint theorem of diagonals of a rectangle -

Midpoint of BD = Midpoint of AC

(x,y) =  , [(1 - 5)/2 , (4 - 4)/2)

(x,y) = (-2, 0)

Now, the fourth vertex of the rectangle is -

(-2,0) = [(x + 1)/2 , (y - 4)/2)

-2 = (x + 1)/2

-4 = x + 1

x = -5

0 = (y - 4)/2

y = 4

So, the fourth vertex of the rectangle is (-5, 4).

Therefore, the points are is (-5, 4).

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Answer:

It’s equivalent.

Step-by-step explanation:

Collect like terms: 4x+12 = 4(3+x)

Expand brackets: 4x+12 = 12+4x

Rearrange: 4x+12 = 4x+12

The x coordinate of the critical point of the function is x = 0.

Given a function.

We have to find the x coordinate of the critical point of the function.

Given function is,

f(x) = log₅ (eˣ - x)

We have to first find the derivative of the function and then we have to set the derivative equal to 0.

First find the derivative of f(x).

f'(x) = d/dx [log₅ (eˣ - x)]

We know that,

logₐ (x) = ln (x) / ln (a) [ By the change of base formula]

d/dx [logₐ (x)] = d/dx [ln (x) / ln (a)]

                      = 1/ln(a) . 1/x

Using this,

f'(x) = d/dx [log₅ (eˣ - x)]

      = 1/ln(5) × 1 / (eˣ - x) × (eˣ - 1)

      = (eˣ - 1) / [ln(5) × (eˣ - x)]

Let f'(x) = 0.

(eˣ - 1) / [ln(5) × (eˣ - x)] = 0

⇒ (eˣ - 1) = 0

⇒ eˣ = 1

⇒ x = 0 [ since e⁰ = 1]

Hence the x coordinate is x = 0.

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\(\huge\sf\red{Answer}\)

=>yx + yz + zx + zy

=> yx +zx +yz + zy

=> yz² + zx + zy

_______________

Hence solved ✓

\(\Huge \red{An} \green{s} \pink{we} \purple{r:-}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{=2zy+xy+zx}\)

__________________________________________

\(\large\bf{\underline{Here,}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟼y(x+z)+z(x+y)}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟼(xy+zy)+ (zx + zy) }\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟼zy+zy+xy+zx}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(\large\bf{⟼2zy+xy+zx}\)

Answer:

x = 11 \(\frac{4}{23}\)

Step-by-step explanation:

23x + 56 = 313

23x = 257

x = 11 \(\frac{4}{23}\)

Answer:

11 4/23

Step-by-step explanation:

\(23x+56=313\\\\23x +56 -56 = 313-56\\\\23x = 257\\\\23x \div 23 = 257 \div 23\\\\x = \dfrac{257}{23} = 11 \dfrac{4}{23}\)

Answer:

Your correct answer is 14t - 40

Step-by-step explanation:

Combine like terms:

10t + 3t + t = 14t

Since there are no other integers, just tag on the -40:

14t - 40

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The population at the onset as 250,000. There has been a 3.5% decrease every year.

The exponential decay function therefore is;

Hence, to approximate what the population would be 7 years from now;

The population after 7 years shall be 194,819 people (rounded to the nearest whole number).

Answer:

1080 times

Step-by-step explanation:

72*15=1080

It will beat 1080 times

Answer:

1080

Step-by-step explanation:

72 beats per minute times 15 minutes = 1,080 beats in 15 minutes.

The derivative of \(r\) with respect to \(\theta\) can be found using the chain rule. Let's proceed with the differentiation:

\frac{dr}{d\theta} = \frac{d}{d\theta}\left(\cos\left(\frac{\theta}{3}\right)\right)

To differentiate \(\cos\left(\frac{\theta}{3}\right)\), we treat \(\frac{\theta}{3}\) as the inner function and differentiate it using the chain rule. The derivative of \(\cos(u)\) with respect to \(u\) is \(-\sin(u)\), and the derivative of \(\frac{\theta}{3}\) with respect to \(\theta\) is \(\frac{1}{3}\). Applying the chain rule, we have:

\frac{dr}{d\theta} = -\sin\left(\frac{\theta}{3}\right) \cdot \frac{1}{3}

Now, let's evaluate this derivative at \(\theta = \pi\):

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\sin\left(\frac{\pi}{3}\right) \cdot \frac{1}{3}

The value of \(\sin\left(\frac{\pi}{3}\right)\) is \(\frac{\sqrt{3}}{2}\), so substituting this value, we have:

\frac{dr}{d\theta} \bigg|_{\theta=\pi} = -\frac{\sqrt{3}}{2} \cdot \frac{1}{3} = -\frac{\sqrt{3}}{6}

Therefore, the slope of the tangent line to the polar curve \(r = \cos(\theta / 3)\) at the point specified by \(\theta = \pi\) is \(-\frac{\sqrt{3}}{6}.

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The choice that  most effectively sets up the examples at the end of the sentence is given by:  During periods of economic recession (option B).

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

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So, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate

To find out how many days it takes for all 24 gallons of water to leak out of the pool, we need to determine the rate at which the water is leaking and use that to calculate the total time it takes for the pool to empty.

We know that the pool initially has 24 gallons of water and that it is leaking out at a rate of 2 gallons every 3 days. This means that the pool loses 2/3 of a gallon of water per day.

To find out how many days it will take for the pool to empty, we can divide the total amount of water in the pool by the rate at which it's leaking out.

24 gallons / (2/3 gallons/day) = 24*3/2 = 36 days

Therefore, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate.

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Answer:

3 = 14 and 4 = 8

Step-by-step explanation:

The reason as to why this is, is because of the line going down the middle. If you were to open one of the lengths as a door starting from the middle line it would fit perfectly with the top one.

the probability that a student scored greater than 65 is 0.2389.

The probability that a student scored greater than 65 can be calculated using the standard normal distribution and the z-score. The z-score represents the number of standard deviations a value is from the mean, and can be calculated as follows:

z = (x - mean) / standard deviation

Where x is the score of interest (65)

Mean is the average score of the students (70)

Standard deviation is the standard deviation of the scores (7).

Plugging in the values, we get

z = (65 - 70) / 7 = -0.714.

Using a standard normal distribution table, we can find the probability that a student scored greater than 65 by finding the area to the right of the z-score. The probability of a student scoring greater than 65 is approximately 0.2389, or 23.89%.

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Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

Answer:

Rule is add 5

Step-by-step explanation:

Therefore, 85 is the input and 90 is the output

Answer:

{x,y} ={0,-7}

Step-by-step explanation:

[1]  3 x - 2 y = 14

[2] 5 x 6 y =42

Answer:

13.6%

Step-by-step explanation:

Step 1

Find the actual volume of the box

Volume = Length × Width × Height

You measure the box and find that it has a length of 10 inches, a width of 9 inches, and a helght of 4.5 inches.

Volume = 10 inches × 9 inches × 4.5 inches

Volume of the box = 405 cubic inches

Step 2

Calculate the percent error

|Estimated value - Actual value|/Actual value ×100

Estimated value= 350 cubic inches

Actual value = 405 cubic inches

= |350 - 405|/405 × 100

= |-55|/405 × 100

= 55/405 × 100

= 13.580246914%

Approximately = 13.6%

The Percent error is 13.6%

Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

Answer:

(14, - 3 )

Step-by-step explanation:

Under the translation < 6, 0 >

Add 6 to the x- coordinate and 0 to the y- coordinate, that is

B(8, - 3 ) → B'(8 + 6, - 3 + 0 ) → B'(14, - 3 )

Answer:

168

Step-by-step explanation:

24cm by 7

= L x W

= 24 x 7

A = 168

Answer:

84 cm²

Step-by-step explanation:

The fromula for the area of a triangle is:

\(A=\frac{hb}{2}\)

h - height

b - base

We are given the measurements of 24cm and 7 cm.

\(A=\frac{7*24}{2}\\\\A=\frac{168}{2}\\\\\boxed{A=84}\)

The area of the triangle should be 84 cm².

Hope this helps.

Answer:

-1/2y+1/2x

Step-by-step explanation:

when you times -1/2 times you get -1/2 but when you get -1/2y- -1/2x

but when your working with integers if there is two negetive signs together than you will add