What is the explicit formula for this geometric sequence?
64, 16, 4, 1,

The value of a using integration is 2, such that the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units

The given parameters are:

Curve, y² = 4ax

Line, x = 4a

Substitute x = 4a in y² = 4ax

y² = 4a * 4a

Take the square root of both sides

y = ±4a

This means that the point of intersection between the line and the curve is (4a, -4a) and (4a, 4a)

Remove the negative interval

So, we have: (4a, 0) and (4a, 4a)

The area is then calculated as

[tex]A =2 \int\limits^{4a}_0 {\sqrt y} \, dx[/tex]

This gives

[tex]A =2 \int\limits^{4a}_0 {\sqrt {4ax}} \, dx[/tex]

Remove the constant

[tex]A = 2\sqrt{4a}\int\limits^{4a}_0 {\sqrt {x}} \, dx[/tex]

Integrate

[tex]A = 2\sqrt{4a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]

Evaluate the exponent

[tex]A = 4\sqrt{a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]

Expand

[tex]A = 4\sqrt{a} * \frac 23 (4a)^\frac32[/tex]

Rewrite as:

[tex]A = 4 * a^\frac12 * \frac 23 * 4^\frac32 * a^\frac32[/tex]

Evaluate the exponents by the laws of indices

[tex]A = 4 * \frac 23 * 8 * a^2[/tex]

Recall that the area is:

A = 256/3

So, we have:

[tex]\frac{256}3 = 4 * \frac 23 * 8 * a^2[/tex]

Evaluate the quotients

[tex]256 = 4 * 2 * 8 * a^2[/tex]

Divide both sides by 64

4 = a²

Take the square root of both sides

2 = a

Rewrite as:

a = 2

Hence, the value of a is 2

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Reason:

There are 7 outcomes we don't want vs 1 outcome we do want

outcomes we don't want = rolling one of the following {1,2,3,4,5,6,7}

outcome we want = rolling an 8

The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.

Saving is the method of saving your money for the future. We can not predict the future if anything bad happens and we need a large amount of money these savings will help us.

The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.

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Answer:

For the answer to the question above, the numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30 pages, you can conclude that about 16% of the books have fewer than 150 pages.

In the given diagram, the length of the side marked x is 21.34

From the question, we are to determine the value of the side marked x

In the given diagram,

Hypotenuse = x

Adjacent = 15

Included angle = 49°

Using SOH CAH TOA

We can write that,

cos 49° = 14 / x

∴ x = 14 / cos 49°

x = 21.34

Hence, the length of the side marked x is 21.34.

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Answer:

Hoang has been at the hospital for 12 years while Bill has worked for 7 years.

Step-by-step explanation:

Let the years Hoang has worked as a nurse equal h and let the years Bill has worked as a nurse equal b.

Since Hoang has worked 5 years longer, h is five more than b:

h = b + 5

Now we move onto the situation 2 years ago. 2 years ago, Hoang had worked at the hospital two less than h or h-2 years while Bill has worked for b-2 which is two years less than b. We are also told that at the time, Hoang worked twice as longs, so

h - 2 = 2(b - 2)

This can be simplified:

h - 2 = 2b - 4

h = 2b - 2

We can use substitution. Since h = b + 5 and h = 2b - 2,

b + 5 = 2b - 2

b = 7

Therefore, since Hoang has worked five more years, h = 12. So, Hoang has been at the hospital for 12 years while Bill has worked for 7 years.

Answer:

1) 0.25%

Step-by-step explanation:

Ratio= weight in g/ volume in ml

1. percent strength = 12.5× 10-³g /5ml × 100%

=0.25%

Answer:

0.25%

Step-by-step explanation: Convert mg to g (1g = 1000mg)

12.5mg/1000mg = 0.0125g/5ml ( 0.0025) x 100 = 0.25%

Answer:

(5 • x) - 9 = 2x + 23

Answer:

X * H

-----------

  2

Step-by-step explanation:

Base of the triangle (X) times height of triangle, divided by 2

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

The area of the isosceles triangle will be A(x) = √15(x² / 4).

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.

The base of an isosceles triangle is half as long as each of the two equal sides.

Let the base length be x. Then the length of each other legs will be 2x.

A(x) = √[s(s - x)(s - 2x)(s - 2x)]

The value of s is half of the perimeter.

s = (x + 2x + 2x) / 2

s = 5x / 2

Then the area of the isosceles triangle will be

A(x) = √[5x / 2(5x / 2 - x)(5x / 2 - 2x)(5x / 2 - 2x)]

A(x) = √[5x / 2(3x / 2)(x / 2)(x / 2 )]

A(x) = √(15x⁴ / 16)

A(x) = (x² / 4)√15

The area of the isosceles triangle will be A(x) = √15(x² / 4).

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Answer:

=4m^2−11m+6

Step-by-step explanation:

Given algebraic expression:

(m-2)(m•2+2m-3)

To:

Simplify

Solution:

(m−2)(m(2)+2m−3)

=(m)(m(2))+(m)(2m)+(m)(−3)+(−2)(m(2))+(−2)(2m)+(−2(−3)

=2m^2+2m^2−3m−4m−4m+6

=4m^2−11m+6

Answer:

Answer: {b,d,e,f,g,h,i,l,m,n,q,r,s,u,v,w,x,y,z}

Step-by-step explanation:

A' = U-A

={b,d,e,f,g,h,i,l,m,n,q,r,s,u,v,w,x,y,z}

Answer:

  57 feet

Step-by-step explanation:

A formula is given for the height of the ball, and all of the values necessary to evaluate the formula are also given. The height of the ball after 4 seconds is found by substituting the given values into the formula and doing the arithmetic.

__

  height = -16t² +vt +h . . . . . for t=4, v=72, h=25

  height = -16(4²) +72(4) +25 = -256 +288 +25 = 57

The height of the ball is 57 feet above the bottom of the hill 4 seconds after it was kicked.

_____

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Answer:

[tex]2y(x-1)(x^2+x+1)[/tex]

Step-by-step explanation:

[tex]~~~2x^3y-2y\\\\=2y(x^3-1)\\\\=2y(x-1)(x^2+x+1)~~~~~~~~~~;[a^3-b^3 = (a-b)(a^2 +ab+b^2)][/tex]

The graph of the dilated absolute value function can be seen below.

We know that h(x) = (1/4)*f(x), where f(x) is the parent absolute value function.

Then we have a vertical dilation of scale factor k = 1/4. Then the graph of h(x) wil be four times wider than the parent absolute value function.

The graph of h(x) is the one you can see below. Where there is also the graph of f(x) so you can compare them.

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Answer: if you multiply decimals , the estimate value is necessary !

it could be understood easily, if at any place the number exceeds 4 , then the value in front is raised by one !

as;

2.234 = 2.23 , it will remain same but,

2.235 = 2.24 the 3 raised to 5 !!

Step-by-step explanation:

The total weight of the 100 cantaloupe is 324 pounds

The given parameters are:

Since the number of zeros in 100 is 2;

All Evans needs to do is to move the decimal point in 3.24 two places forward.

i.e. 3.24 becomes 324 when the decimal point is moved

Hence, the total weight of the 100 cantaloupe is 324 pounds

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Answer:

A. Three

explanation :

In Spherical Geometry, a triangle can have three right angles!

Answer: [tex]\angle A+\angle D=180^{\circ}[/tex]

Step-by-step explanation:

Adjacent angles of a parallelogram are always supplementary.

Answer:

5L/2 < 100

Step-by-step explanation:

Let's get started!

Let :

⇒ Length = L

⇒ Width = L/4

It mentions the perimeter must be less than 100 inches.

Perimeter Formula :

Perimeter (Rectangle) = 2(Length + Width)

Then, the inequality formed will be :

⇒ 2 (L + L/4) < 100

⇒ 2 (5L/4) < 100

⇒ 10L/4 < 100

⇒ 5L/2 < 100

Length be L

width be L/4

Now

Perimeter=2(Length+Breadth)

There were 2350 people supporting the home team

The given parameters are:

Total = 2500

Proportion that supports the visiting team= 6%

Let the number of people that supports the team be x.

So, we have:

x = (1 - Proportion that supports the visiting team) * Total

This gives

x = (1 - 6%) * 2500

Evaluate

x = 2350

Hence, there were 2350 people supporting the home team

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Answer:

Its 43.2

I hope this helps ^^

Answer:

43.2

Step-by-step explanation:

kilometers, hectometers, decameters, meters, decimeters, centimeters, millimeters

To go right once multiply be ten

To go left once divide by ten

4.32 • 10 = 43.2

The correct answer is option D. Which is the even function is f (x) = x⁴.

The function in which when the sign of the input variable is changed the output remains the same is called the even function. Mathematically we can write it as f(x) = f(-x ).

let us check the given four options:-

A f(x) = √x ;  f(-x) = √-x  here f(x) ≠ f(-x)

B f(x) = x ;  f(-x) = -x    here f(x) ≠ f(-x)

C f(x)  = x³ + 1 ; f(-x) = -x³ + 1  here f(x) ≠ f(-x)

D f(x)  = x⁴  ;  f(-x) = (-x)⁴ = x⁴  here f(x) = f(-x)

We can see that in the option D the f(x) = x⁴ is an even function because f(x) = f(-x).

Therefore the correct answer is option D. Which is the even function is f (x) = x⁴.

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Answer: D

Step-by-step explanation:

Answer: Choice D

Plot the points given for choice D. See below.

It is impossible to draw a single straight line through all of the points.

Therefore, this set of points do not represent a linear function.

The correct answer is option D which is the difference between the mean times is about 16 times the mean absolute deviation of the data sets.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The difference between the mean times is about 16 times the mean absolute deviation of the data set.

127.9-127.4=0.5

0.26-0.23=0.03

0.5/0.03=16.6666

We can see that the ratio of the mean times difference is 16 times the mean deviation by solving the above.

Therefore the correct answer is option D which is the difference between the mean times is about 16 times the mean absolute deviation of the data sets.

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Answer: D

Step-by-step explanation:

Answer:[tex]x^{2}+\frac{11x}{5}-\frac{12}{5}[/tex]

Step-by-step explanation:

The roots are really just what x is when the equation is equal to zero. So, an equation with these roots would look like this:

(x+3)(x-4/5)=y

however, this is not standard form. To get standard form we will need to expand the equation using FOIL.

x^2+3x-4x/5-12/5=

x^2+11x/5-12/5

and that would be your answer.

This stuff is a bit tricky and it get annoying with those pesky fractions. If you have any questions just comment.

Answer:

x = 14 units

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Lets put the 3/4 at the beginning and expand this bracket :

3/4(x-4) = 27

3/4x - 3 = 27

Now we add 3 to both sides :

3/4x = 30

Now we times both sides by 4 :

3x = 120

Now we divide both sides by 3:

x = 40

Hope this helped and brainliest please

Answer:

175 ft^2

Step-by-step explanation:

split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2

then the pentagon has an area 35*5 = 175 ft^2

sin 30 = x/4

sin 30 = 0.5

0.5 = x/4

x = 2