Help pls! A room is 12 feet long and 10.5 feet wide. A scale model of the room is 3.5 feet wide. What is the area of the scale model?


A. 10.3 square feet

B. 14 square feet

C. 122.5 square feet

The critical points of the function f(x) = 4sin(x)cos(x) in the interval (0,2π) are {π/6, π/4, 5π/6, 5π/4}.

Given a function f(x) = 4sin(x)cos(x), we are supposed to find the critical points of the function in the interval (0,2π).

Let's get started with the solution.

Step 1: To find the critical points, we need to find the first derivative of the given function.  

So, f(x) = 4sin(x)cos(x)

Let's use the product rule:

f(x) = u(x)v'(x) + v(x)u'(x)where u(x)

= 4sin(x) and v(x) = cos(x

)Thus, u'(x) = 4cos(x)and v'(x)

= -sin(x)

Now, f'(x) = (4sin(x))(-sin(x)) + (cos(x))(4cos(x))

= -4sin^2(x) + 4cos^2(x)

= 4cos^2(x) - 4sin^2(x)= 4(cos^2(x) - sin^2(x))

= 4cos(2x)So, f'(x) = 4cos(2x)

Step 2: Now, we need to solve for the critical points by setting f'(x) = 0.  

That is, 4cos(2x) = 0cos(2x)

= 0, when x = π/4 and

5π/4(cos(2x) = 1/2,

when x = π/6 and 5π/6)

Thus, the critical points of the function f(x) = 4sin(x)cos(x) in the interval (0,2π) are {π/6, π/4, 5π/6, 5π/4}.

Know more about the critical points here:

https://brainly.com/question/30459381

#SPJ11

The direction angle of the vector v = 2i -6j is approximately 288.43 degrees.

What is a vector ?

In mathematics, a vector is a mathematical object that has both magnitude (length) and direction. Vectors are commonly used to represent physical quantities such as displacement, velocity, and force in physics and engineering, but they are also used in many other fields such as computer graphics, machine learning, and economics.

The direction angle of a vector is the angle it makes with the positive x-axis in the counterclockwise direction.

To find the direction angle, we first need to calculate the angle that the vector makes with the positive x-axis.

Using trigonometry, we can see that:

tan θ = (opposite side) / (adjacent side)

     = (-6) / 2

     = -3

Taking the inverse tangent of both sides, we get:

θ = tan⁻¹(-3)

Using a calculator, we find that:

θ ≈ -71.57°

However, since we are looking for the direction angle in the counterclockwise direction, we need to add 360 degrees to get the final answer:

θ = -71.57° + 360°

Thus, the direction angle of the vector v is approximately:

θ ≈ 288.43°

Therefore, the direction angle of the vector v = 2i -6j is approximately 288.43 degrees.

To learn more about Vector from given link.

https://brainly.com/question/29740341

#SPJ1

In this case, 5 percent - 3 percent = 2 percent. However, since we are interested in per capita output,the growth relative to the population size. Dividing the 2 percent growth by the population growth rate of 3 percent and multiplying by 100 gives us approximately 1.94 percent.

To provide a more detailed explanation, per capita output refers to the average output per person in a population. It is calculated by dividing the total output by the population size. When output increases, it can be due to factors such as technological advancements, increased productivity, or expanded production capacity. Population growth, on the other hand, refers to the increase in the number of individuals in a population over time.

When output increases by 5 percent, it indicates that the total output has grown. However, to determine the per capita output, we need to account for the population growth as well. If the population is growing at a rate of 3 percent, it means that the number of individuals in the population is increasing. This increase in population should be considered when calculating the per capita output.

By subtracting the population growth rate of 3 percent from the output growth rate of 5 percent, we obtain the net growth in per capita output, which is approximately 2 percent. This means that on average, each person in the population experiences a growth in output of approximately 1.94 percent after accounting for population growth.

It's important to note that these calculations assume that the output growth and population growth rates are constant and apply uniformly across the entire population. In reality, variations in growth rates and population dynamics can lead to different outcomes.

know more about population growth :brainly.com/question/12739583

#SPJ11

Answer:Sin

Step-by-step explanation:

right angled triangle special trig functions can be applied

Answer:

9)  3.7 in

10) 12 in²

11) 18 in³

12) V=432π cm³

   TSA= 216π cm²

13)V=448π ft³

   TSA=240π ft²

Step-by-step explanation:

9) Since all side of the trapezium are the same the height = perpendicular line which is 3.7 in

10) 3×4 (the quadrilateral at the bottom)

11)∵ A= Cross-sectional area× height

  ⇒A= Area of the trapezium × 4

  ∴ A=\(\frac{1}{2} \\\) (sum of the parallel sides) × 4

  A=\(\frac{1}{2} \\\) (3+6) × 4

  A= 18 in²

12) V=πr²h

    V=π(6)²(12)

⇒V=432 cm³

   TSA=2(πr²)+2πrh

  TSA=2(π(6)²)+2π(6)(12)

 ⇒TSA=240π cm²

13. V=πr²h

    V=π(8)²(7)

   V=448π ft³

TSA=2(πr²)+2πrh

TSA=2(π(8)²)+2π(8)(7)

TSA=240π ft²

9)  3.7 in

10) 12 in²

11) 18 in³

12) V=432π cm³

   TSA= 216π cm²

13)V=448π ft³

   TSA=240π ft²

Answer:

x is 1,800 kw energy used and y is $162 so a equation you can use

for every 1,800 kw of energy used you need to spend $162 so the equation would be

f(n)= 1,800 x 162^2

Answer:

(-5.5, -4.5)

Step-by-step explanation:

Answer:

il faut diviser chaque nombre par 7/3

donc 2 divisé par 7/3

-5 divisé par 7/3 etc

Answer:

  (a)  8 : 3

  (b)  1 7/8 cups

Step-by-step explanation:

Given a recipe that calls for 2 cups of flour and 3/4 cup of water, you want to know the ratio in simplest terms, and the amount of water for 5 cups of flour.

The ratio can be written and simplified as a fraction. Fractions are divided in the usual way.

  2/(3/4) = 2 ÷ 3/4 = 2 × 4/3 = 8/3 = 8 : 3

If we multiply each term in this ratio by 5/8, we can find the recipe that uses 5 cups of flour:

  (5/8)·8 : (5/8)·3 = 5 : 15/8 = 5 : 1 7/8

Naomi uses 1 7/8 cups of water with 5 cups of flour.

Answer:

Step-by-step explanation:

\((a)\)

\(2:\frac{3}{4}\)

Multiply both sides by 4 to remove fraction:

\(2\times4:\frac{3}{4} \times 4\)

\(8:3\)     (this is simplest form because no number goes into both 8 and 3)

\((b)\)

5 cups of flower:

\(8 \times \frac{5}{8} : 3 \times \frac{5}{8}\)   (I chose \(\frac{5}{8}\) to turn the 8 into 5)

\(5:\frac{15}{8}\)

5 cups flour needs \(\frac{15}{8}\) (\(=1\frac{7}{8}\)) cups water

A The histogram is the best graph showing the average scores of 5 UCI volleyball teams in UCI history. Because it allows us to divide the data into as many or as few groups as we want and clarify the comparison between them.

We would like to view the average points data of the top 5 UCI basketball players in UCI history. There are two types of charts used to present data. The first is a histogram and the second is a scatterplot. We have to decide which picture is the best. Now, as we know, scatter charts are used to plot observations based on points to show the relationship between two data sets. A histogram is a type of bar chart in which all values are divided. Divides the range of results in the data into classes or groups. It can help identify outliers or gaps in the data. After discussing the features of the two graphs, shows the average score of 5 UCI basketball players in UCI history, the histogram is the best choice here because it allows us to divide and share the difference between clearly.

For more information about Histogram, visit :

https://brainly.com/question/28164315

#SPJ4

complete question:

The above figure complete the question..

you want to display data on average number of points scored by the top 5 uci basketball players in the history of uci. which type of graph would be best?

z_1 and z_2 are complex number;

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

To calculate z₁z₂ and z₁/z₂, we need to perform the complex number operations on z₁ and z₂. Let's break down the calculations step by step:

i) To find z₁z₂, we multiply the magnitudes and add the angles:

z₁z₂ = 4cos(cos(π/4) + isin(π/4)) * 2cos(2π/3) + isin(2π/3))

= 8cos((cos(π/4) + 2π/3) + isin((π/4) + 2π/3))

= 8cos(7π/12) + isin(7π/12)

ii) To find z₁/z₂, we divide the magnitudes and subtract the angles:

z₁/z₂ = (4cos(cos(π/4) + isin(π/4))) / (2cos(2π/3) + isin(2π/3))

= (4cos((cos(π/4) - 2π/3) + isin((π/4) - 2π/3))) / 2

= 2cos(π/12) + isin(π/12)

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

Please note that the given calculations are based on the provided complex numbers and their angles.

To know more about complex number visit:

https://brainly.com/question/1245664

#SPJ11

Answer:

5. ∠1.

6. ∠3.

7. ∠1.

8. 180°.

note: wherever there is a ∠ symbol, it means "angle".

Step-by-step explanation:

5. An exterior angle of the triangle is ∠1.

6. The remote interior angles of the triangle to the exterior angle 1 are ∠2 and ∠3.

7. The sum of the measure of angles 2 and 3 is equal to the measure of ∠1.

8. The sum of the measure of angles 1 and 4 is 180°.

note: wherever there is a ∠ symbol, it means "angle".

Answer: 30/52 or 58%

Step-by-step explanation:

The non-Twix candies to all candies is 30 pieces of non-Twix to 52 total candies. This is a ratio of 30:52 or 58%. I hope this helps you. <3

Answer: 15 non-twix to 26 total candy

Step-by-step explanation:

non twix: 14+16=30

all candy: 22+14+16=52

30:52

simplify

15:26

If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

Learn more about total obligation here:https://brainly.com/question/15893784

#SPJ1

==============================================

Work Shown:

L = theta*r

12 = theta*4

12/4 = theta

3 = theta

theta = 3 radians, choice C is the answer.

--------

Side note: The formula L = theta*r only works if theta is in radians.

If theta is in degrees, then use L = (theta/360)*2pi*r. So you can see that radian mode is much easier in this case.

Answer:

a. -2

b. s = 2 and y = -5

c. (2.5, -9)

d. -7x - 2

Step-by-step explanation:

a. In the image, I have used rise over run, which is -8/4 or -2.

b. slope formula is mx + b = y, where m is slope and b is the y-intercept. In the equation 2x - 5y = -10, 2 is the slope and -5 is the y-intercept.

c. Plug in all given numbers into an equation and the ones you do not have will be in the points you need it to be. Once you graph the equation you will receive (2.5, -9).

d. y = mx + b

   5 = (-7)(-1) + b

   5 = 7 + b

   -2 = b

y = -7x - 2  

Answer:

less than tell me if i'm wrong

Answer: 12ft^2

Step-by-step explanation:

how many more do you have. can’t you do it by now? And the least you could do is give me brainiest.

According to the question, the probability that a new oil filter is needed given that the automobile's oil is being changed is 0.20.

To find the probability that a new oil filter is needed given that the automobile's oil is being changed, we can use conditional probability.

Let's define the events:

A: The car needs an oil change.

B: Both the oil and the filter need changing.

We are given:

\(P(A) = 0.30\) (probability that a car needs an oil change)

\(P(B) = 0.20\) (probability that both the oil and the filter need changing)

We need to find P(B|A), which represents the probability that both the oil and the filter need changing given that the car needs an oil change.

The conditional probability formula is given by:

\(\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]\)

In this case, P(A ∩ B) represents the probability that both events A and B occur.

Since we know that P(B) = 0.20, we can rewrite P(A ∩ B) as:

P(A ∩ B) = P(B) * P(A|B)

P(A|B) represents the probability that a car needs an oil change given that both the oil and the filter need changing.

We can rearrange the conditional probability formula as follows:

P(A ∩ B) = P(A|B) * P(B)

Substituting the given values:

P(A ∩ B) = P(A|B) * 0.20

Now we can solve for P(A|B):

\(\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]\)

\(\[ P(A|B) = \frac{P(A|B) \times 0.20}{0.20} \]\)

Simplifying, we can cancel out the 0.20:

P(A|B) = P(A|B)

This means that the probability of needing a new oil filter given that the oil is being changed is equal to the conditional probability of needing an oil change given that both the oil and the filter need changing.

Therefore, the probability that a new oil filter is needed given that the automobile's oil is being changed is equal to the conditional probability of needing an oil change given that both the oil and the filter need changing, which is 0.20.

Hence, the probability that a new oil filter is needed given that the automobile's oil is being changed is 0.20.

To know more about Formula visit-

brainly.com/question/31062578

#SPJ11

Answer: rectangleular pyramid

Step-by-step explanation:

Answer:

i try my best to find the answer if i can

Step-by-step explanation:

Answer:

  6 m

Step-by-step explanation:

The missing dimension can be found using the volume formula with the known values filled in. This gives an equation that can be solved for z.

The volume of a cylinder is given by the formula ...

  V = πr²h

__

Using the given values, we have ...

  1696.5 m³ = 3.14(z²)(15 m)

  z² = (1696.5 m³)/(47.1 m) ≈ 36.0191 m² . . . . divide by 47.1 m

Taking the square root, we find z to be ...

  z ≈ √(36.0191 m²) ≈ 6.00 m

The value of z is about 6 m.

Answer:

2) -3x+10

4) -4x+10+x

Step-by-step explanation:

Use the distributive property to get rid of the parentheses.

(2 × -2x) + (2 × 5) + x

-4x + 10 +x is correct, but the x's can be combined.

(-4x + x) + 10 = -3x + 10

According to the weather forecasting website, the probability of rain in a certain region is 0.95. 95% becomes 0.95 when expressed as a decimal.

The statement "A weather forecasting website indicated that there was a 95% chance of rain in a certain region" can be rewritten to express the likelihood of rain as a value between 0 and 1.

Probability is a measure of the likelihood of an event occurring, and it is typically represented as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

In this case, the statement states that there is a 95% chance of rain. To convert this into a probability value, we divide the percentage by 100. Therefore, 95% becomes 0.95 when expressed as a decimal.

By stating that the probability of rain in the region is 0.95, we convey that there is a high likelihood of rain occurring. The value 0.95 indicates that, out of 100 instances or trials, rain is expected to occur approximately 95 times.

It provides a clear and standardized representation of the likelihood, allowing for easier comparison and interpretation of the forecasted chances of rain.

#Rewrite the following statement so that the likelihood of rain is expressed as a value between 0 and 1. A weather forecasting website indicated that there was a 95% chance of rain in a certain region.

Learn more about probability here:
brainly.com/question/31828911

#SPJ11

-3/2

slope = rise/run

We can use the two points to calculate rise (y value change) and run (x value change)

slope = (-6)/4 = -3/2

Answer:what do you need help with

Step-by-step explanation:

I will help