Can you help me with this question? Complete the proof and show your work.

Answer:

look in picture below :)

Answer:

D

Step-by-step explanation:

maximum at 12am which is time, t = 0 and 12pm which is time, t = 12

so we’ll use a cosine function since no phase shift is given.

period, T: 1 cycle = 2π and time taken to complete one cycle is 12hrs

T = 2π/(12) = ⅙π

med-line = ½(1 + 2.2) = 1.6

and thus amplitude = 1.6 - 1 = 0.6 or 2.2 - 1.6 = 0.6

h(t) = 0.6 cos(⅙πt ) + 1.6

ANS: D  Can I get brainliest on this please because I only need two more until virtuoso

The function h(t) = 0.6 cos (πt/6) + 1.6 models the height of the tide at Dolphin Beach.

1. To model the height of the tide at Dolphin Beach, we need to consider the given tide heights and times. High tide occurs at 12 a.m. and 12 p.m. with a height of 2.2 meters, and low tide occurs at 6 a.m. and 6 p.m. with a height of 1 meter. This suggests a periodic function with a 12-hour period.

2. The general form for such a function can be a sine or cosine function. Based on the information, we can match the function's characteristics with the function options provided:

3. The cosine function, which starts at its maximum value, would be appropriate, and since the low tide occurs 6 hours later, the function should resemble a cosine function shifted by 6 hours:

Among the options provided h(t) = 0.6 cos (πt/6) + 1.6, perfectly alligns :

Thus, the function h(t) = 0.6 cos (πt/6) + 1.6 models the height of the tide at Dolphin Beach.

Final answer:

To compare Plan A's increase of 200 homes per year and Plan B's 10% increase per year for a town's housing development, Plan A adds homes linearly, while Plan B's growth is exponential, potentially leading to a larger increase and more significant infrastructure needs over time.

Explanation:

To compare the two growth plans for the town's development—which are Plan A, an increase of 200 homes per year, and Plan B, a 10% increase each year—we need to analyze the two scenarios mathematically.

Under Plan A, the town will add a fixed number of homes each year, that is, 200 homes. After one year, the total will be 1200 homes, after two years 1400 homes, and this pattern will continue linearly.

Plan B's 10% annual increase results in exponential growth. Starting with 1000 homes, in the first year, there will be 1000 + (10% of 1000) = 1100 homes. The second year, the growth will be based on the new total, so it will be 1100 + (10% of 1100) = 1210 homes, and this pattern will continue to result in an increasingly larger number of homes added each year.

In terms of the community's development, Plan A adds homes predictably and steadily, while Plan B accelerates growth over time. This could lead to a boom in construction and investment depending on the current needs and infrastructure of the town.

Plan B's compound growth could lead to a much larger number of homes in the long run, but might require more significant investment in infrastructure and services as the growth compounds.

Answer:

m = 15.

Step-by-step explanation:

∛(3375) =  15.

You can use a calculator to do this. Some calculators have a direct key giving you a cube root or  you can use the power key + 1/3 .

Note:   ∛(3375) = 3375^(1/3).

Answer:

-5

Step-by-step explanation:

Edge 2020

Answer:

2/3

Step-by-step explanation:

5 black

3 green (not black)

3 blue (not black)

4 yellow (not black)

there are 5 black and 10 not black out of a total of 15 marbles.

there are 10/15 that are not black.  Reduced 2/3.

The probability of not drawing a black marble is 2/3, calculated by subtracting the number of black marbles from the total number of marbles in the bag and dividing the result by the total number of marbles.

The question asks to find the probability of not drawing a black marble. To solve this, we first determine the total number of marbles and then subtract the number of black marbles to find the number of marbles that are not black. In this case:

Next, we calculate the probability using the formula:

Probability (not black) = Number of marbles that are not black / Total number of marbles

Plugging in the numbers:

Probability (not black) = 10 / 15 = 2/3

Therefore, the probability of not drawing a black marble is 2/3.

Answer:

Similarity means that two figures are the same shape, but not necessarily the same size, color or orientation, congruent means two figures are the same in every form.

Step-by-step explanation:

In my understanding, The Property of Rigid motion holds two points:

- The relative distance between two points stays the same,

- The relative position of the points stays the same

This includes, translations, reflections, and rotation but not to dilutions since it breaks these rules. The relative distance between points gets smaller after dilution.

False. That does not satify the equation

Answer:

False

Step-by-step explanation:

The given inequality  is [tex]-3 \:<\:x\:<\:14[/tex].

Since both boundaries of the inequalities are not inclusive , we use the parenthesis for open interval."()".

We write the given inequality in interval notation as;

[tex](-3,14)[/tex].

The correct choice is false

Answer:

Option b

Step-by-step explanation:

To solve this problem use the law of the sines.

We have 2 angles of the triangle and one of the sides.

[tex]a = 4.6\\B = 19\°\\A = 92\°\\C = 180 -A - B\\C = 180 - 92 - 19\\C = 69\°[/tex]

The law of the sines is:

[tex]\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}[/tex]

Then:

[tex]\frac{sin(92)}{4.6} = \frac{sin(19)}{b}\\\\b = \frac{sin(19)}{\frac{sin(92)}{4.6}}\\\\b = 1.5[/tex]

[tex]\frac{sin(B)}{b} = \frac{sin(C)}{c}\\\\\frac{sin(19)}{1.5} = \frac{sin(69)}{c}\\\\c = \frac{sin(69)}{\frac{sin(19)}{1.5}}\\\\c = 4.30[/tex]

Answer:

x = 15.

Step-by-step explanation:

Given : Two similar triangle .

To find : What is the value of x in the diagram.

Solution : We have given that

Two triangle with corresponding sides .

By the similar triangle property

The ratio of the two corresponding sides  are equal.

[tex]\frac{x}{25} = \frac{9}{15}[/tex].

On cross multiplication

x = [tex]\frac{9* 25}{15}[/tex].

x =  [tex]\frac{225}{15}[/tex].

x =  [tex]\frac{45}{3}[/tex].

x = 15.

Therefore,  x = 15.

The value of x in the diagram is 15. Option A

Similar triangles have the same shape but different sizes. In similar triangles, corresponding angles are equal.

Corresponding sides of similar triangles are in the same ratio.

The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides.

Then, we have that;

x/25 = 9/15

cross multiply the  values, we have;

x = 9(25)/15

Multiply the values

x = 225/15

Divide the values

x = 15

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Answer:

Step-by-step explanation:

Use the cosine law:

[tex]BC^2=AB^2+AC^2-2(AB)(AC)\cos(\angle A)[/tex]

We have:

[tex]BC=a\\\\AB=4\\\\AC=3\\\\m\angle A=32^o\to\cos32^o\approx0.848[/tex]

Substitute:

[tex]a^2=4^2+3^2-2(4)(3)(0.848)\\\\a^2=16+9-20.352\\\\a^2=4.648\to a=\sqrt{4.648}\\\\a\approx2.2[/tex]

Answer:

  tn = 243·(1/3)^(n-1)

Step-by-step explanation:

The recursive formula tells you the first term (243) and the common ratio (1/3). You can put these numbers into the general formula for the n-th term of a geometric sequence:

  an = a1·r^(n-1) . . . . . where a1 is the first term and r is the common ratio

You want the n-th term of your sequence to be called tn, so ...

  tn = 243·(1/3)^(n-1)

First, lets start with the formula for the volume of a cone

[tex] \frac{1}{3} (\pi \times {r}^{2})h [/tex]

Then lets find the diameter so we can get the radius...

Since we have circumference, all we need to do is use this formula-

[tex] c \div \pi[/tex]

C being circumference, the PI being the 3.14, we plug it in to the formula as the number we have to get the diameter...

[tex]{75.36} \div 3.14[/tex]

And it comes out to...

24.

Now we need to divide it by two to get the radius, and we come up with 12.

Now that we have our radius, we can finally plug in all of the numbers into our original formula...

[tex] \frac{1}{3} (3.14 \times \: {12}^{2} ) \times 18[/tex]

The answer of the entire problem turns out to be... Drum roll please...

2712.96 cubic centimeters.

Answer:

$14.21

Step-by-step explanation:

Hello, I think I can help yo with this

if the lamp is on sale for 25% it means you have to pay the 75% of the original cost, you can find that 75% or to find the 25 % and the subtract that value from the original cost, it is the same anyway

Step 1

if

$18.95 ⇔100%

x$?       ⇔75%

[tex]\frac{18.95}{100}=\frac{x}{75}[/tex]

Step 2

solve for x

[tex]\frac{75*18.95}{100}=x\\x=\frac{1421.51}{100}\\ x=14.21\\\\[/tex]

the new price is $14.21

have a great day.

Answer:12 yards

Step-by-step explanation: 22-10=12

Answer:

[tex]y = 2 - \frac{1}{32}x\text{ or } y=2-0.03125x[/tex]

Step-by-step explanation:

Here x represents the number of student and y represents the amount of juice remain after x students are served,

Given,

The total number of cup = 32,

And, the amount of juice in 32 cups = 2 gallon,

⇒ The amount in 1 cup = [tex]\frac{2}{32}[/tex] = [tex]\frac{1}{16}[/tex] gallons,

Number of cups served to a student = [tex]\frac{1}{2}[/tex] cup.

⇒ The amount of juice served to a student = [tex]\frac{1}{32}[/tex] gallon.

⇒ The amount of juice served to x students = [tex]\frac{x}{32}[/tex] gallon

Thus, the remaining amount of juice = The amount of juice in 32 cups - served amount

⇒ [tex]y = 2 - \frac{1}{32}x\text{ or } y=2-0.03125x[/tex]

Which is the required equation.

Hello!

The answer is:

B. [tex]9x^{2}-16y^{2}[/tex]

To find the equivalent expression we need to apply the distributive property, so:

[tex](3x-4y)(3x+4y)=9x^{2}+12xy-12yx-16y^{2}\\\\9x^{2}+12xy-12yx-16y^{2}=9x^{2}+12xy-12xy-16y^{2}=9x^{2}-16y^{2}[/tex]

So, the correct option will be B. [tex]9x^{2}-16y^{2}[/tex]

Have a nice day!

Answer:

Step-by-step explanation:

[tex]3\sqrt2\cos\theta+2=-1\\\\\text{Method 1}\\\\\text{Put}\ \theta=\dfrac{\pi}{4}\ \text{to the equation and check the equality:}\\\\\cos\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\L_s=3\sqrt2\cos\dfrac{\pi}{4}+2=3\sqrt2\left(\dfrac{\sqrt2}{2}\right)+2=\dfrac{(3\sqrt2)(\sqrt2)}{2}+2\\\\=\dfrac{(3)(2)}{2}+2=3+2=5\\\\R_s=-1\\\\L_s\neq R_s\\\\\boxed{FALSE}[/tex]

[tex]\text{Method 2}\\\\\text{Solve the equation:}\\\\3\sqrt2\cos\theta+2=-1\qquad\text{subtract 2 from both sides}\\\\3\sqrt2\cos\theta=-3\qquad\text{divide both sides by}\ 3\sqrt2\\\\\cos\theta=-\dfrac{3}{3\sqrt2}\\\\\cos\theta=-\dfrac{1}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\\\\\cos\theta=-\dfrac{\sqrt2}{2}\to\theta=\dfrac{3\pi}{4}+2k\pi\ \vee\ \theta=-\dfrac{3\pi}{4}+2k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\text{It's not equal to}\ \dfrac{\pi}{4}\ \text{for any value of }\ k.[/tex]

Answer:

the mean (average) will change

Step-by-step explanation:

Answer:

the rangue

Step-by-step explanation:

Assume the car starts at the origin, so that its initial position is [tex]x(0)=0[/tex]. The car's displacement at any time [tex]t[/tex] over the 20 second interval is

[tex]\displaystyle x(0)+\int_0^t(44+2.2u)\,\mathrm du=0+\left(44u+1.1u^2\right)\bigg|_{u=0}^{u=t}=44t+1.1t^2[/tex]

so that after 20 seconds the car has moved 1320 ft.

###

Without using calculus, recall that under constant acceleration, the average velocity of the car over the 20 second interval satisfies

[tex]v_{\rm avg}=\dfrac{v_f+v_i}2[/tex]

and that, by definition, we have

[tex]v_{\rm avg}=\dfrac{\Delta x}{\Delta t}[/tex]

where [tex]v_f[/tex] and [tex]v_i[/tex] are the final/initial speeds of the car and [tex]\Delta x[/tex] is the displacement it undergoes. It starts with a speed of 44 ft/s and ends with a speed of 88 ft/s, so we have

[tex]\dfrac{88\frac{\rm ft}{\rm s}+44\frac{\rm ft}{\rm s}}2=\dfrac{\Delta x}{20\,\rm s}\implies\Delta x=1320\,\mathrm{ft}[/tex]

same as before.

To find the distance traveled by the car during the 20 seconds, we integrate the velocity function and solve for the distance using the given values. The car travels a distance of 1320 feet.

To find the distance traveled by the car during the 20 seconds, we need to calculate the area under the velocity-time graph. The velocity function given is v(t)=44+2.2t. To find the distance, we integrate the velocity function from 0 to 20 seconds:

d = ∫(44+2.2t) dt

Applying integration, we get: d = 44t + 1.1t^2

Substituting the values t=0 and t=20 into the equation, we can find the distance traveled by the car:

d = 44(20) + 1.1(20)^2

Solving this equation, we get d = 880 + 440

So, the car has traveled a distance of 1320 feet during the 20 seconds.

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Answer:

C

Step-by-step explanation:

We will graph [tex]3^{-x}[/tex]  and  [tex]6^{-x}[/tex]  and find WHERE in the x-axis,  [tex]3^{-x}[/tex]  is greater than  [tex]6^{-x}[/tex].

Attached is the graph of both the functions. RED color graph is of  [tex]3^{-x}[/tex]  and BLUE color graph is of  [tex]6^{-x}[/tex].

So, WHICH WHERE IN X-AXIS IS THE RED GRAPH "ABOVE" THE BLUE GRAPH?

We can clearly see that this occurs when x > 0.

Hence, C is the correct answer.

Answer:

C edge

Step-by-step explanation:

The y coordinate of the point which lies on the circle is y = 2√5

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r = 6 units

The point on the circle is P ( x , y )

where the x coordinate is x = 4

So , the point is P ( 4 , y )

And , the equation of circle is given as

x² + y² = r²

On simplifying , we get

x² + y² = ( 6 )²

The point will lies on the circle , so

when x = 4

( 4 )² + y² = ( 6 )²

Subtracting ( 4 )² on both sides , we get

y² = 36 - 16

y² = 20

Taking square roots on both sides , we get

y = ±2√5

The point P lies in the first quadrant , so

y = 2√5

Hence , the y coordinate of the circle is y = 2√5

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Final answer:

Without a specific circle equation, it's impossible to definitively determine the correct y-coordinate for point Q on the circle with an x-coordinate of 4. Additional information such as the circle's center and radius is needed.

Explanation:

The question asks us to identify a possible y-coordinate value for a point Q that lies on a circle with an x-coordinate of 4. Using the information on parametric equations, Pythagorean theorem, and circle equations provided, we can infer that the circle equation might typically be in the form of (x - h)² + (y - k)² = r², where h and k are the coordinates of the center of the circle and r is the radius. However, without a specific equation for the circle in question, we cannot conclusively determine the y-coordinate that corresponds to an x-coordinate of 4 on this circle. Therefore, additional information is required to answer this question correctly.

The difference between the greatest and least areas is 72 square inches.

What is perimeter of a rectangle?

Let L be the length and w be the width of the rectangle.

Perimeter = 2l + 2w = 48

Since each side is a whole number, list pairs of whole numbers that satisfy the equation.

Potential pairs (length, width) are:

(23, 1)

(22, 2)

(21, 3)

(20, 4)

(19, 5)

Let's calculate the areas for the pairs mentioned:

Area = l*w

(23, 1)) A = 23* 1 = 23

(22, 2) A = 22 *2 = 44

(21, 3) A = 21 *3 = 63

(20, 4) A = 20 *4 = 80

(19, 5) A = 19 *5 = 95

The greatest area is 95 square inches, and the least area is 23 square inches.

The difference between the greatest and least areas is 95 - 23 = 72 square inches. Therefore, the answer is 72.

angle GAL would be the same as MLA

Answer:

[tex]\large\boxed{1.\ f(1)=135}\\\boxed{2.\ f(6)=115}\\\boxed{3.\ f(26)=25}\\\boxed{4.\ f(n)=139-4n}[/tex]

Step-by-step explanation:

[tex]f(1)=135\\f(2)=135-4=131\\f(3)=131-4=127\\f(4)=127-4=123\\f(5)=123-4=119\\\vdots\\\\\text{It's an arithmetic sequence with firs term = 135 and the common}\\\text{difference d = -4.}\\\text{The formula of arithmetic sequence: }\\\\f(n)=f(1)+(n-1)d\\\\\text{We have}\ f(1)=135\ \text{and}\ =-4.\ \text{Substitute:}\\\\f(n)=135+(n-1)(-4)=135+(n)(-4)+(-1)(-4)\\=135-4n+4=139-4n\\\\\boxed{f(n)=139-4n}[/tex]

[tex]\text{Put n = 6, n=26 to the formula:}\\\\f(6)=139-4(6)=139-24=115\\\\f(26)=139-4(26)=139-104=25[/tex]

Answer:

[tex]x=20.6\ in[/tex]

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

[tex]41.2^{2} =35.7^{2} +x^{2}[/tex]

solver for x

[tex]x^{2}=41.2^{2}-35.7^{2}[/tex]

[tex]x^{2}=422.95[/tex]

[tex]x=20.6\ in[/tex]

It would be 30.8 hope this helps

Answer:

Step-by-step explanation:

10x10 squared

=10x100

=1000

Answer 10000

Step-by-step explanation:

10x10=100

100x100=10000

Here is your answer

[tex]<b>always</b>[/tex]

REASON :

Integers are all natural numbers their negative including 0.

Rational numbers are the numbers of the form p/q where p and q are integers and q is not equal to 0.

So, the definition itself defines that every integer is a rational number.

Exa- Integers

1, -2 , 3, 90, -6

These are rational numbers as

1=1/1 (p/q form)

-2=-2/1 (p/q form)

3= 3/1 (p/q form)

90= 90/1 (p/q form)

-6= -6/1 (p/q form)

HOPE IT IS USEFUL

the answer is always :)))))

Answer:

im pretty sure its d) 0.25

Step-by-step explanation:

To find the experimental probability of each, divide the number for each color by 500. Then, multiply it by 20, to find the amount expected out of 20.