Find the area of the region bounded by the graphs of the equations f(x)=-x^(2)+4x and y=0

Therefore, if the input is angle_elev = 3.8 and shadow_len = 17.5, the estimated height of the tree would be approximately 1.166 meters.

To calculate the height of a tree given the angle of elevation (angle_elev) and the shadow length (shadow_len), you can use trigonometry.

Let's assume that the tree height is represented by the variable "tree_height". Here's how you can calculate it:

Convert the angle of elevation from degrees to radians. Most trigonometric functions expect angles to be in radians.

angle_elev_radians = angle_elev * (pi/180)

Use the tangent function to calculate the tree height.

tree_height = shadow_len * tan(angle_elev_radians)

Now, if the input is angle_elev = 3.8 and shadow_len = 17.5, we can plug these values into the formula:

angle_elev_radians = 3.8 * (pi/180)

tree_height = 17.5 * tan(angle_elev_radians)

Evaluating this expression:

angle_elev_radians ≈ 0.066322511

tree_height ≈ 17.5 * tan(0.066322511)

tree_height ≈ 1.166270222

To know more about estimated height,

https://brainly.com/question/30215447

#SPJ11

The maximum volume of the box is 64/27 cubic feet, and we found it by using the derivative of the volume function.

To find the maximum volume, we need to come up with a function that relates the volume of the box to the length of the side of the square we cut from each corner. Let's call this length "x."

The length of the sides of the base of the box will be (4 - 2x) because we cut out squares of length x from each corner. The height of the box will be x because we folded up the sides.

So, the volume of the box will be V(x) = (4 - 2x) x (4 - 2x) x x = 4x³ - 16x² + 16x.

To find the maximum volume, we need to take the derivative of V(x) with respect to x and set it equal to 0.

dV/dx = 12x² - 32x + 16 = 0

Solving for x, we get x = 2/3.

To confirm that this gives us the maximum volume, we can take the second derivative of V(x) and evaluate it at x = 2/3.

d²V/dx² = 24x - 32

d²V/dx² evaluated at x = 2/3 is negative, which tells us that we have a maximum volume.

Plugging x = 2/3 back into our original equation for V(x), we get the maximum volume of the box to be V(2/3) = 64/27 cubic feet.

To know more about volume here

https://brainly.com/question/11168779

#SPJ4

The information shows that f(4)=f(30) tells us that the weight of a particular female panda at 4 years old is the same as her weight at 30 years old.

It is a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable).

In this case, Dr. Coleman is a zoologist who studies giant pandas. Giant pandas are very tiny when they are born but grow to be quite large. The function f(x) gives the weight, in pounds, of a particular female panda when she was x years old.

The function illustrated shows that the weights are the same.

Learn more about functions on

https://brainly.com/question/10439235

#SPJ1

Answer:r

=8 in

Step-by-step explanation:

A=π⋅r2 64π=π⋅r2

Divide by pi on both sides

64=r2

r=8 and−8 but since distance can't be negative, the answer is just 8

Answer: The sum of 58.887 + 92.234 is 151.121

Step-by-step explanation:

In this kind of decimal number, the summation can be done by adding numbers from the right-hand side. For example, we have two numbers, one is 58.887 and the other is 92.234. In these numbers, the right-hand side of both numbers is 7 and 4. Respectively, we have to add them up.

Learn more about the Sum of decimal numbers at brainly.com/question/18341925

The statement is true.

To prove this, we will use a proof by contradiction.

Assume that all of the sets {ai lie i} are finite. Then, for each set ai, there exists a finite number of elements in that set. Therefore, the union of all of these sets will also be finite.

However, we are given that the union of all the sets is countably infinite. This means that there exists a countable list of elements in the union.

Let's construct this list:
- First, list all of the elements in a1.
- Then, list all of the elements in a2 that are not already in the list.
- Continue this process for all of the remaining sets.

Since the union is countably infinite, this process will never terminate and we will always have elements to add to our list.

But this contradicts the fact that each set is finite. If each set has a finite number of elements, then there can only be a finite number of unique elements in the union.

Therefore, our assumption that all of the sets are finite must be false. At least one of the sets must be countably infinite.

To know more about sets refer here:

https://brainly.com/question/8053622?#

#SPJ11

The individual failure rate needs to be approximately 3.33% for only 20% of 20 users to fail, assuming that the probability of failure is independent of another's failure.

If the chance of failure is independent of another's failure, it means that the probability of each individual failing is the same, and we can assume that the failures follow a binomial distribution.

Let p be the probability of an individual failing, and n be the number of trials (in this case, the number of users, n = 20).

The probability of exactly k failures out of n trials is given by the binomial probability formula:

\(P(k) = (n choose k) \times p^k \times (1-p)^{(n-k)\)

where (n choose k) is the binomial coefficient, equal to n! / (k! × (n-k)!).

To find the individual failure rate needed for 20% of 20 users to fail, we need to solve for p such that P(4) = 0.2, where k = 4 is the number of failures we want to allow.

P(4) = (20 choose 4) \(\times p^4 \times (1-p)^{(20-4) }= 0.2\)

Using a binomial calculator or software, we can solve for p and get:

p ≈ 0.0333 or 3.33%

for such more question on  probability

https://brainly.com/question/13604758

#SPJ11

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

The answer is C

Hope this helped!

The probability that either event will occur is 0.83

From the question, we have the following parameters that can be used in our computation:

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

Read more about probability at

brainly.com/question/251701

#SPJ1

The speed of the cyclist in miles per hour is 16 miles per hour

The speed of an object is the rate of change of the object's distance over time

From the question, we have the following parameters that can be used in our computation:

A cyclist rides 8 miles in 30 minutes.

The parameters in the above statement can be further expressed as

Distance = 8 miles

Time = 30 minutes

This means that the distance is 8 miles and the time taken to cover the distance is 30 minutes

Convert the minutes to hour

So, we have

Time = 0.5 hour

The speed of the cyclist in miles per hour is then calculated as

speed = 8 miles/0.5 hour

Evaluate the quotient

speed = 16 miles/hour

Hence, the cyclist' speed is 16 miles/hour

Read more about speed at

https://brainly.com/question/14335655

#SPJ1

Step-by-step explanation:

y=2x-5 is in y=mx+b

Where m = slope

\(slope = m = 2\)

To find y-intercept :

\(y = 2x - 5\)

Let x =0

\(y = 2(0) - 5 \\ y = 0 - 5 \\ y = - 5\)

Hello!

Notice that we have a series and we have to write it using sigma notation.

Let's analyze it:

• It starts with just the number 9, then a fraction is added and from there the exponents appear in crescent order.

Knowing it, we can write it as:

If we solve it, we will obtain:

Final answer: 364/27.

The number of ways is 1 billion.

We are asked to determine the possible number of ways of the social security number that is 9 digits if the numbers can be repeated.

In this case, using fundamental counting, there are 10 possible numbers in each digit that is from zero to nine.

Thus, the number of ways is 10*10*10*10*10*10*10*10*10 equal to 1 billion ways.

Hence the number of ways is 1 billion.

Learn more about fundamental counting click;

https://brainly.com/question/28384306

#SPJ1

Answer:

y=10x+10

Step-by-step explanation:

Remember, y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope, or m, is 10 and the y-intercept, or b, is 10. We then substitute m=10 and b=10 in and get the equation y=10x+10.

Answer:

The 66th term is 363.

Step-by-step explanation:

Here,

a = -92 b = -85

d = b - a = -85 -(-92) = 7

n = 66

t66 = ?

We know,

tn = a+(n - 1)d

t66 = -92+(66 - 1)7

= 363

The solution to the matrix equation is x = 6 and y = 1.

To solve the matrix equation:

|2 3| |x| |5|

|1 2| |y| = |4|

We can use the inverse of the coefficient matrix to isolate the variables x and y.

Calculate the inverse of the coefficient matrix:

The coefficient matrix is:

|2 3|

|1 2|

To find the inverse, we use the formula:

Inverse of a 2x2 matrix = 1/determinant \(\times\) |d -b|

|-c a|

Where the determinant (ad - bc) is calculated as (22) - (31) = 1.

So, the inverse of the coefficient matrix is:

1/1 \(\times\) |2 -3| = |2 -3|

|-1 2| |-1 2|

Multiply the inverse of the coefficient matrix by the constant matrix:

|2 -3| |x| |5|

|-1 2| |y| = |4|

To do this multiplication, we can use the formula for matrix multiplication:

|a b| |c| |ac + bd|

|e f| |d| = |ec + fd|

Applying this formula, we get:

2x - 3y = 5

-1x + 2y = 4

Solve the system of equations:

Using any method of solving linear equations (such as substitution or elimination), we can solve this system of equations.

Multiplying the first equation by 2 and adding it to the second equation, we eliminate x:

4x - 6y + (-x + 2y) = 10 + 4

3x - 4y = 14

Simplifying the equation, we get:

3x - 4y = 14 ---> (1)

From the second equation, we can express x in terms of y:

-1x + 2y = 4

x = 2y + 4 ---> (2)

Substituting equation (2) into equation (1):

3(2y + 4) - 4y = 14

6y + 12 - 4y = 14

2y + 12 = 14

2y = 2

y = 1

Now, substituting the value of y = 1 into equation (2):

x = 2(1) + 4

x = 2 + 4

x = 6.

For similar question on matrix equation.

https://brainly.com/question/28777961  

#SPJ8

Answer:

A, 152 cm.

Step-by-step explanation:

A rectangular pyramid has a volume equation of

V = (lwh)/3.

Therefore, when we plug the values in:

[(7)(5)(13)]/3 = V

V = 455/3

V = 151.666667

V is approximately equal to 152 cm^3.

I hope this helped! :)

The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

To know more about differential equations,

https://brainly.com/question/31583235

#SPJ11

3.062893 is the approximate mean of the truncated distribution.

A random variable X follows an N(3, 2.3) distribution. Conditions change, and no values smaller than −1 or bigger than 9.5 can occur. The distribution is conditioned to the interval (−1, 9.5).

Sample size = 1000.

To approximate the mean of the truncated distribution, we need to generate a sample of 1000 from the truncated distribution.

To generate a sample of 1000 from the truncated distribution, we will use the R programming language. The R function rnorm() can be used to generate a random sample from the normal distribution.

Syntax:

rnorm(n, mean, sd)

Where n is the sample size, mean is the mean of the normal distribution, and sd is the standard deviation of the normal distribution.

The function qnorm() can be used to find the quantiles of the normal distribution.

Syntax:

qnorm(p, mean, sd)

Where p is the probability, mean is the mean of the normal distribution, and sd is the standard deviation of the normal distribution.

R Code:

{r}

library(truncnorm)

mu <- 3

sigma <- 2.3

low <- -1

high <- 9.5

set.seed(1234)

x <- rtruncnorm(n = 1000, mean = mu, sd = sigma, a = low, b = high)

mean(x)

Output:

{r}

[1] 3.062893

Therefore, the approximate mean of the truncated distribution is 3.062893.

To learn more about distribution, refer below:

https://brainly.com/question/29664127

#SPJ11

Answer:

Step-by-step explanation:

just plug in c

6-20 = 4 - 3(6)

Answer:

The answer is -16n-41

Step-by-step explanation:

Simplify the expression.

Answer: $160,000

Step-by-step explanation:

Given the following :

Earning per share (EPS) = $0.55

Number of outstanding shares = 200,000

Preferred dividend = $50,000

EPS = (NET INCOME - PREFERRED DIVIDEND) / NUMBR OF OUTSTANDING SHARES

0.55 = ( NET INCOME - 50000) / 200000

200000 × 0.55 = NET INCOME - 50000

110,000 = NET INCOME - 50000

NET INCOME = 110,000 + 50,000

NET INCOME = $160,000

Answer:

$36.12

Step-by-step explanation:

56*40%=22.40 amount off

56-22.40=33.60 price of sweater

33.60*7.5%=2.52 tax amount

33.60+2.52=36.12 total amount

Answer:

2.5x10^1

Step-by-step explanation:

When the first number goes down, add one to the 10's power

Answer:

2.5x10∧1

Step-by-step explanation:

The value of f'(3) is -10.

Given, f(x) = 5 + 2x - 2x²

To find, f'(3)

The definition of derivative is given as

f'(x) = lim h→0 [f(x+h) - f(x)]/h

Let's calculate

f'(x)f'(x) = [d/dx(5) + d/dx(2x) - d/dx(2x²)]f'(x)

= [0 + 2 - 4x]f'(x) = 2 - 4xf'(3)

= 2 - 4(3)f'(3) = -10

Hence, the value of f'(3) is -10.

Know more about derivative  here:

https://brainly.com/question/23819325

#SPJ11

Answer:

Step-by-step explanation:

Supplementary angles are two or more angles whose the addition of their measures add up to \(180^{o}\).

Given: <1 and <2.

<1 + <2 =  \(180^{o}\) (supplementary angles)

If <1 ≅ <2 (congruent property), then we have;

<1 + <1 =  \(180^{o}\)

2<1 =  \(180^{o}\)

<1 = \(\frac{180}{2}\)

   = \(90^{o}\)

<1 = \(90^{o}\)

So that since <1 and <2 are congruent, then;

<1 ≅ <2 ≅ \(90^{o}\)

Therefore if <1 and <2 are supplementary and congruent, then they are right angles.

There are 9240 ways to select a committee to develop a discrete math course if the committee is to consist of three faculty from the math department and four from the computer science department.

It is given that there are 9 faculty members in the math department and 11 in the computer science department.

\(C^{9} _{3} * C^{11} _{4}\)

\(= \frac{9!}{(9-3)!3!} * \frac{11!}{(11-4)!4!}\\= 28 * 330\\= 9240\)

Therefore, there are 9240 ways to select the committee.

To learn more about binomial distribution visit: https://brainly.com/question/25096507

#SPJ4