geometry please help

Answer:

Step-by-step explanation:

To find the values of the angle which makes maximum r you use the derivative of r

[tex]\frac{dr}{d\theta}=\frac{1}{3}sin(3\theta)[/tex]

If you equals this derivative to zero you obtain the value of the angle:

[tex]\frac{dr}{d\theta}=0\\\\cos3\theta=0\\\\3\theta=\frac{\pi}{2}\\\\\theta=\frac{\pi}{6}[/tex]

However, the values of 5π/6 and 9π/6 are also available, because makes the sinusoidal function equal  to 1.

hence, the answer is:

[tex]\theta_1=\frac{\pi}{6} \\\\\theta_2=\frac{5\pi}{6}\\\\\theta_3=\frac{9\pi}{6}=\frac{3\pi}{2}[/tex]

answer b

The maximum values of r for the polar equation r=4+3 sin 3θ occur at the angles where sin 3θ = 1, within the range of 0 to 2π. Solving the equation 3θ = nπ/2 for odd integers n gives the values of θ where r is maximum, which must be checked against the range [0, 2π].

We can find the maximum values of r for the polar equation r=4+3 sin 3θ by looking for the values of θ that give the maximum value for the sinusoidal function sin 3θ.

Since we know that the sine function reaches its maximum value of 1, we can find the values of θ that satisfy the condition sin 3θ = 1 within the given range of θ from 0 to 2π.

Thus, the equation becomes r = 4 + 3(1), which simplifies to r = 7.
Now, we seek to solve 3θ = nπ/2 where n is an odd integer since the sine function is maximum at π/2, 3π/2, 5π/2, and so on. Therefore, we obtain θ values of π/6, π/2, 5π/6, etc., until we reach the limit of 2π.

We must also consider the range of the function which brings us to the fact that θ must lie within [0, 2π].
Thus, we have to evaluate this for values such as θ = π/6, 5π/6, 3π/2, and so on, checking which of these are within the specified range and hence can be considered valid solutions where maximum r values occur.

Answer:

Part a) [tex]-2x(2x-5)[/tex]

Part b) [tex]3x+6[/tex]

Step-by-step explanation:

Part a)

I first determined what each piece in the rectangular array meant.

Then I wanted to figure out the height and the base length.

I know [tex]-x(x)=-x^2[/tex] so that is why I put those purple [tex]x[/tex]'s on top and purple [tex]-x[/tex]'s down alongside for the [tex]-x^2[/tex] pieces. To get [tex]x[/tex] when I already had [tex]-x[/tex], I needed to multiply by -1 which is why there is a -1 along the top where those [tex]x[/tex] pieces are.

So in the first question down the side of the box, we have [tex]-x+-x=-2x/tex].

Along the the top we have [tex]x+x-1-1-1-1-1=2x-5[/tex].

To find the area of the rectangle, you multiply height by base.

[tex]-2x(2x-5)[/tex].

Part b)We have six [tex]x^2[/tex]'s and twelve [tex]x[/tex]'s. So that means the polynomial represented here is [tex]6x^2+12x[/tex].

What happens if we divide that by [tex]2x[/tex].

Let's see:

[tex]\frac{6x^2+12x}{2x}[/tex]

[tex]\frac{6x^2}{2x}+\frac{12x}{2x}[/tex]

[tex]3x+6[/tex]

Answer:

A) 2x(2x - 5)

B) -(3x + 6)

Step-by-step explanation:

Each empty square represents: x²

Each filled rectangle represents: -x

Area is 4x² - 10x

There are two rows:

Each row is: 2x² - 5x = x(2x - 5)

Statement:

2x(2x - 5)

In b, there are 6 tiles of -x², and 12 tiles of -x, which makes it:

-6x² - 12x

-(6x² + 12x)

-(6x² + 12x)/2x

-[(6x²/2x) + (12x/2x)0

-(3x + 6)

-3x - 6

Answer:

May 4th, 2012.

Step-by-step explanation:

The highest level can be found with the help of the First Derivative and Second Derivative Tests. First and second derivatives of the function are, respectively:

[tex]l'(t) = 0.04323\cdot t^{2}-0.8354\cdot t +2.703[/tex]

[tex]l''(t) = 0.08646\cdot t - 0.8354[/tex]

The First Derivative Tests consists on equalizing the first derivative to zero and finding the critical points.

[tex]0.04323\cdot t^{2}-0.8354\cdot t +2.703 = 0[/tex]

Roots are [tex]t_{1} \approx 15.672[/tex] and [tex]t_{2} \approx 4.077[/tex]. just the second root offer a realistic solution and is test by the second derivative.

[tex]l''(4.077) = -0.482[/tex] (which leads to a maximum).

Given that a year has 365 days or 12 months, the highest water level occurs at day:

[tex]n = \frac{4.077}{12} \cdot (365\,days)[/tex]

[tex]n \approx 124[/tex] (May 4th).

Answer: A − 9/7

Step-by-step explanation:

Hi, to answer this question we have to convert all the numbers into decimal form.

-3 1/3 = - (3x3+1)/3 =-10/3 = - 3.3334

-4/5 = -0.8

Since he number must greater than −3 1/3 but less than − 4/5.

−3 1/3 < x < − 4/5.

- 3.3334 < x < -0.8

The correct option is A = -9/7 , because in decimal form is equal to -1.28-

- 3.3334 < -1.28 < -0.8

here u go:

BC = 18 × 1.96

    = 35.28 ft

Therefore the distance between the pole and the tree is 35.28 ft .

Answer:

19 !

Step-by-step explanation: make me brainlist

So we go up in 10's. It simply goes like this, 10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,200... etc.

Answer:

   1 x 10 = 10

   2 x 10 = 20

   3 x 10 = 30

   4 x 10 = 40

   5 x 10 = 50

   6 x 10 = 60

   7 x 10 = 70

   8 x 10 = 80

   9 x 10 = 90

   10 x 10 = 100

   11 x 10 = 110

   12 x 10 = 120

Step-by-step explanation:

Answer:

81,3 ft to the nearest tenth.

Step-by-step explanation:

Tan 19 = 28 / h  where h = the horizontal distance.

h = 28 / tan 19

h = 81.3 ft.

Final answer:

To calculate the horizontal distance between the boat and the shark, the tangent of the angle of depression (19 degrees) is set equal to the vertical depth (28 ft) divided by the horizontal distance. The horizontal distance is found to be approximately 81.32 ft.

Explanation:

To determine the horizontal distance between the boat and the shark when the shark is swimming 28 ft below sea level and the angle of depression from the boat to the shark is 19 degrees, we can use trigonometry, specifically the tangent function. The angle of depression corresponds to the angle between the horizontal sightline from the boat and the line of sight to the shark.

In the right-angled triangle formed by the vertical depth of the shark, the horizontal distance to the shark, and the line of sight from the boat, the angle at the boat's position is 19 degrees and the opposite side (depth) is 28 ft. Using the formula tangent of an angle equals the opposite side divided by the adjacent side (tan(θ) = opposite/adjacent), we get:

tan(19°) = 28/horizontal distance

Therefore, the horizontal distance = 28 / tan(19°) = 28/0.3443

Calculating this, we get the horizontal distance to be approximately 81.32 ft.

Answer:

y = x + 2, assuming you need it in slope-intercept form.

Step-by-step explanation:

Isolate the y-value by dividing 2 from both sides of the equation.

Answer:I have no idea I just need points sorry lol :(

Step-by-step explanation:

Answer: Alex earned $87.5 more than Ben

Step-by-step explanation:

Last year,Alex earned a monthly salary of $250. This year, he received a pay increase of 25%. It means that the amount by which his pay was increased is

25/100 × 250 = 62.5

His new monthly salary would be

250 + 62.5 = $312.5

Last yearBen earned a monthly salary of $180. This year, he also received a pay increase of 25%. It means that the amount by which his pay was increased is

25/100 × 1800 = 45

His new monthly salary would be

180 + 45 = $225

The difference between the amount earned by Alex and Ben monthly is

312.5 - 225 = $87.5

Answer:

u=10

Step-by-step explanation:

Answer

u = 10

Step-by-step explanation:

For now we do not know what u equals, but we do know that 20/5 = 4, because 20/5 simplified is just 4 since the fraction means 20 ÷ 4. Now that we are back to the question, with 2/5; if you multiply by 10 the numerator will then be 20. And now the equation is true! Hope this helps!

Answer:

(a)Sample 1

The Mean = 20

The median = 25

Sample 2

The Mean = 31

The median = 60

(b) Sample 1 has the least spread

Sample 1 has the least deviations from the mean

(c) Sample 1 align with the third sample

The least representative of the population is sample 1

Step-by-step explanation:

The mean is ∑fx/∑f

∑fx = 30 + 25 + 10 + 25 + 10 = 100

∑f = 5

Mean = 100/5 = 20

For the median, we arrange the data in increasing order;

10, 10, 25, 25, 30

The median = the middle number = 25

Sample 2

The mean is ∑fx/∑f

∑fx = 5 + 60 + 10 + 30 + 50 = 155

∑f = 5

Mean = 155/5 = 31

For the median, we arrange the data in increasing order;

5, 10, 30, 50, 60

The median = the middle number = 30

(b) Sample 1 range =$30 -$10 = $20

Sample 2 range =$65 -$5 = $60

Sample 1 has the least spread

Sample 1 standard deviation = 9.354

Sample 2 standard deviation =24.083

Sample 1 has the least deviations from the mean

(c) $30, $25, $20, $20, $25

Mean = 24

$20, $20, $25, $25, $30

Median = $25

∑fx = 120

Therefore sample 1 align with the third sample

The least representative of the population is sample 1 with ∑fx = 100.

Answer:

290=(20+c)+(40+g)

Step-by-step explanation:

c=Gabe's children's age

g=Laura's grandchildren's age

all add up to 290

To find the value of 6 units when 32 units are worth $2,080, calculate the per unit value by dividing $2,080 by 32 to get $65 per unit, then multiply by 6 to obtain the value of 6 units, which is $390.

The question asks to find the value of 6 units given that 32 units represent $2,080. To solve this, we first find the value of one unit by dividing the total amount of money by the number of units. So, $2,080 divided by 32 units gives us the value per unit.

Next, we multiply the value of one unit by the number of units we want to find the value for, which is 6 units. This will give us the value for 6 units. Let's go through the steps:

Therefore, the value of 6 units is $390.

Answer:

3/5

Step-by-step explanation:

Answer:

Your answer should be 3/5

Answer:

I don’t see photo

Step-by-step explanation:

I

Don’t

See

The

Photo

Answer:

C =12.56 inches

Step-by-step explanation:

The circumference is given by

C = 2*pi*r  where r is the radius

C = 2* 3.14 * 2

C =12.56 inches

Answer:

4π

Step-by-step explanation:

The equation for circumference is 2πr

In order to find the circumference here, plug in the given radius

2π(2) = 4π

Answer:

The amount the $20.000 will be worth in 17  years at compound interest is $65068.443

Step-by-step explanation:

Here we have the Principal, P = $20,000.00

The annual interest rate, r = 7% = 0.07

Time , t = 17 years

Number of compounding period per year, m = quarterly = 4

The compound interest can be found from the following formula;

[tex]Amount, \ A = P \left (1 + \frac{1}{r} \right )^{mt}[/tex]

Therefore, by plugging the values of the equation parameters, we have;

[tex]Amount, \ A = 20000 \left (1 + \frac{0.07}{4} \right )^{4 \times 17} = \$ 65068.443[/tex]

Therefore, the amount the $20.000 will be worth in 17  years at compound interest = $65068.443.

So, the amount of $20,000 be worth in 17 years if it is invested at 7% and compounded quarterly is $65068.443 and this can be determined by using the compound interest formula.

Given :

A newborn child receives a $20,000 gift toward college education from her grandparents.

The formula of compound interest is given by:

[tex]\rm A= P(1+\dfrac{r}{n})^{nt}[/tex]

where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest applied per time period and t is the number of periods elapsed.

Substitute the known terms in the above formula:

[tex]\rm A = 20000(1+\dfrac{0.07}{4})^{4\times 17}[/tex]

[tex]\rm A = 20000(1.0175)^{68}[/tex]

A = $65068.443

So, the amount of $20,000 be worth in 17 years if it is invested at 7% and compounded quarterly is $65068.443.

For more information, refer to the link given below:

https://brainly.com/question/22803385

Answer:

In accounting, residual value is another name for salvage value, the remaining value of an asset after it has been fully depreciated. The residual value derives its calculation from a base price, calculated after depreciation.

Steph's parents need to buy 1654 meters more of fencing.

To find out how many more meters of fencing Steph's parents need to buy, let's first calculate the perimeter of the square fence.

Since all sides of a square are equal, if each side measures 666 meters, then the perimeter of the square is:

[tex]Perimeter = 4 * Side[/tex]

Given that each side measures 666 meters:

[tex]Perimeter = 4 * 666[/tex]

Now, let's calculate the total perimeter:

[tex]Perimeter = 4 * 666[/tex]

[tex]Perimeter = 2664 meters[/tex]

Now, let's see how much fencing they already have and how much more they need to buy:

[tex]Fencing already obtained = 1010 meters[/tex]

[tex]Fencing needed = Perimeter - Fencing already obtained[/tex]

[tex]Fencing needed = 2664 meters - 1010 meters[/tex]

[tex]Fencing needed = 1654 meters[/tex]

Complete correct question:

Steph needs to help her parents put a fence around their pool. They want the fence to be square and want each side to measure 666 meters. They already have 101010 meters of fencing. How many more meters of fencing should they buy?

Answer: [tex]10m+3[/tex]

Combine Like Terms

[tex]4m+6m+3\\(4m+6m)+(3)\\10m+3[/tex]

Answer:

10m + 3

Step-by-step explanation:

You are supposed to add the like terms which are 4m and 6m to equal 10m

4m + 6m + 3

=

10m + 3

please give me brainliest

Answer:

x=17

Step-by-step explanation:

To solve this, we can add 9 to each side of the equation. This will cancel out the 9 to only leave x by itself on one side

Once we add 9 to each side, we will be left with x=17

Answer:

  4m+3

Step-by-step explanation:

Helena had ...

  m +m +m +m +3

marbles. This is more easily written as ...

  4m +3 . . . . the number of Helena's marbles

Answer:

70

Step-by-step explanation:

In this problem, 27 adults conduct a survey.

In the results of the survey, it is found that 35% of the adults are concerned with poverty.

If we call:

x = number of adults surveyed

y = adults concerned with poverty

This means that we can write the following relationship:

[tex]y=0.35x[/tex] (1)

where [tex]0.35[/tex] represents the percentage of adults concerned with poverty, rewritten in decimal form ([tex]0.35=\frac{35}{100}[/tex])

Later, we are told that 200 adults are surveyed, so now we have

x = 200

So substituting into eq(1) we can find how many of these adults are concerned with poverty:

[tex]y=0.35\cdot 200 =70[/tex]

Answer:

5/2= 2 1/2 miles 2 1/2 mi x 4= 10 MPH

Step-by-step explanation:

Answer:

9.6 in an hr

Step-by-step explanation:

24 divided by 2.5

Answer:

[tex]z(1910)=1.3429\\\\z(1230)=-0.9006\\\\z(2190)=2.2404\\\\z(1380)=-0.3558[/tex]

Step-by-step explanation:

-Given the population mean is [tex]\mu=1491[/tex]and  the standard deviation is [tex]\sigma=312[/tex], we calculate the z-scores using the formula:

[tex]z=\frac{\bar x-\mu}{\sigma}[/tex]

#The z-score for 1910 can be calculated as:

[tex]z(1910)=\frac{x-\mu}{\sigma}\\\\=\frac{1910-1491}{312}\\\\=\frac{419}{312}\\\\=1.3429[/tex]

#The z-score for 1230can be calculated as:

[tex]z(1230)=\frac{x-\mu}{\sigma}\\\\=\frac{1230-1491}{312}\\\\=\frac{-281}{312}\\\\=-0.9006[/tex]

#The z-score for 2190 is calculated as follows:

[tex]z(2190)=\frac{x-\mu}{\sigma}\\\\=\frac{2190-1491}{312}\\\\=\frac{699}{312}\\\\=2.2404[/tex]

#The z-score for 1380 is calculated as:

[tex]z(1380)=\frac{x-\mu}{\sigma}\\\\=\frac{1380-1491}{312}\\\\=\frac{-111}{312}\\\\=-0.3558[/tex]

Answer:

2 km

Step-by-step explanation:

4π = π × r²

r² = 4

r = 2

Answer:

See attachment

Step-by-step explanation:

A) We draw the number line as shown in the attachment with intervals of 0.2 from 0 to 2.

B) Observe that, from 0 to 0.2 you move one units to get to 0.2.

From 0 to 2, on the number line with intervals of 0.2, you move 10 units from 0.

This means that:

[tex]2 = 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2[/tex]

This gives us:

[tex]2 = 0.2(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1)[/tex]

Then finally we have:

[tex]2 = 0.2(10)[/tex]

By the commutative property of multiplication:

[tex]2 = 10 \times 0.2[/tex]