What is the 101st term in the sequence 876, 869, 862, ...?

1583

176

1576

169

The solution to this problem involves using calculus to model the total area as a function of the lengths of the wire used for the square and the circle. However, without further context or information, a concrete answer cannot be provided.

In this given case, you have a wire of length 24m that needs to be bent into two shapes - a square and a circle - and we need to know how much wire should be used for the square to maximize or minimize total area. The problem involves concept of both geometry and calculus.

To find the solution we must determine the lengths for the square and the circle that will maximize or minimize the total area. But the concept of area maximization and minimization comes from calculus, especially derivative application. Specifically, to find the maximum or minimum area, we would model the total area as a function of lengths and use first derivative to find where the area is maximized and minimized. Unfortunately, without more context or information, we cannot provide an accurate answer to this question.

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To maximize the total area, use 192 / (2π + 8) units of wire for the square and 24 - 192 / (2π + 8) units of wire for the circle. To minimize the total area, follow the same wire lengths.

To maximize the total area, we need to find the lengths of the wire that will create squares and circles with the largest possible areas. Let's start with part (a).

Part (a)

Let the length of the wire used for the square be x. Then the length of the wire used for the circle would be 24 - x. The perimeter of the square is 4x, so the side length of the square is x/4. The circumference of the circle is 2πr, where r is the radius. Since the wire used for the circle is 24 - x, we have 2πr = 24 - x. Solving for r, we get r = (24 - x) / (2π).

The area of the square is (x/4)^2 = x^2/16. The area of the circle is πr^2 = π((24 - x) / (2π))^2 = (24 - x)^2 / (4π). The total area is the sum of the areas of the square and the circle, so we need to maximize (x^2/16) + (24 - x)^2 / (4π).

Let's find the derivative of this expression with respect to x, set it equal to 0, and solve for x:

(1/8)x - (24 - x) / (2π) = 0

Simplifying, we get (1/8)x = (24 - x) / (2π)

Multiplying both sides by 8 and 2π, we have 2πx = 8(24 - x)

Expanding, we get 2πx = 192 - 8x

Bringing like terms to one side, we have 2πx + 8x = 192

Combining like terms, we get (2π + 8)x = 192

Dividing both sides by (2π + 8), we have x = 192 / (2π + 8)

Now that we have the value of x, we can calculate the lengths of the wire used for the square and the circle. The length of the wire used for the square is x, which is equal to 192 / (2π + 8). The length of the wire used for the circle is 24 - x, which is equal to 24 - 192 / (2π + 8).

So, the solution for part (a) is to use 192 / (2π + 8) units of wire for the square and 24 - 192 / (2π + 8) units of wire for the circle in order to maximize the total area.

Part (b)

To minimize the total area, we follow a similar approach. The area of the square is x^2/16 and the area of the circle is (24 - x)^2 / (4π). We want to minimize (x^2/16) + (24 - x)^2 / (4π).

Again, let's find the derivative of this expression with respect to x, set it equal to 0, and solve for x:

(1/8)x - (24 - x) / (2π) = 0

Expanding and rearranging, we get (2π + 8)x = 192

Dividing both sides by (2π + 8), we have x = 192 / (2π + 8)

As in part (a), the length of the wire used for the square is x, which is equal to 192 / (2π + 8), and the length of the wire used for the circle is 24 - x, which is equal to 24 - 192 / (2π + 8).

Therefore, the solution for part (b) is to use 192 / (2π + 8) units of wire for the square and 24 - 192 / (2π + 8) units of wire for the circle in order to minimize the total area.

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Answer:

C

Step-by-step explanation:

Use the Heron's formula for the area of the triangle:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where a, b, c are lengths of triangle's sides and [tex]p=\dfrac{a+b+c}{2}.[/tex]

Since [tex]a=2,\ b=7,\ c=8,[/tex] then

[tex]p=\dfrac{2+7+8}{2}=8.5.[/tex]

Hence,

[tex]A=\sqrt{8.5(8.5-2)(8.5-7)(8.5-8)}=\sqrt{8.5\cdot 6.5\cdot 1.5\cdot 0.5}=\\ \\=\sqrt{41.4375}\approx 6.4\ un^2.[/tex]

Answer:

Area Δ = 6.4 units² ⇒ the answer is (c)

Step-by-step explanation:

* Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 2 , b = 7 , c = 8

∴ cos(C) = (2² + 7² - 8²)/2(2)(7) = 4 + 49 - 64/28 = -11/28

∴ m∠C = 113.1°

∴ Area Δ = (1/2)(2)(7)sin(113.1) = 6.4 units²

D) 408 in^2 is your answer.

The surface area of the pyramid is approximately 345 square inches.

The base of the pyramid is a polygon, and in this case, it is a square since it has 12-inch sides. The formula to find the area of a square is side length squared. Therefore, the area of the square base can be calculated as follows:

Area of base = side length * side length = 12 in * 12 in = 144 square inches.

Since we have the slant height of the pyramid (11 inches) and the base side length (12 inches), we can find the height of the triangle (distance from the base to the apex) using the Pythagorean theorem.

Let 'h' be the height of the triangle:

h² + (1/2 * base)² = slant²

h² + (1/2 * 12)² = 11²

h² + 36 = 121

h² = 121 - 36

h² = 85

h = √85 ≈ 9.22 inches (rounded to two decimal places).

Now that we have the height of the triangular face, we can calculate its area using the formula:

Area of triangle = (1/2 * base * height)

= (1/2 * 12 in * 9.22 in) ≈ 55.32 square inches

Find the Total Surface Area

To find the total surface area of the pyramid, we add the area of the base and the four triangular lateral faces:

Total Surface Area = Area of base + 4 * Area of triangle

Total Surface Area = 144 square inches + 4 * 55.32 square inches

Total Surface Area ≈ 345.28 square inches

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➷ It would help if you drew it out as a triangle

You will notice that you need to use tan

tan70 = 39/x

x = 39/tan70

x = 14.194

The correct option would be 14.2 ft

You will need to use tan

tan51 = 6/x

x = 6/tan51

x = 4.8587

The correct option would be 4.9m

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

48°

Step-by-step explanation:

The sum of the three angles of a right triangle is 180°.

If one angle is 90° and another is 42°, then

90° + 42° + x = 180°

    132°    + x = 180°

                  x = 180° - 132° = 48°

The third angle is 48°.

Answer:

144

Step-by-step explanation:

Height and Length are A and Hypotenuse is Asqrt(2)

Set hyp = 24 and solve for a.

a = 24/sqrt(2)

Area of Tri = 1/2*(A^2)

Answer:

144

Step-by-step explanation:

Assuming that N is the midpoint of QR, its coordinates are the average of the coordinates of Q and R. So, we have

[tex] N = \left(\dfrac{0+2c}{2},\dfrac{2b+0}{2}\right)=(c,b)[/tex]

Answer:

Circle table

Step-by-step explanation:

More people will fit around the circle table then the rectangle table. You can find the distance around using the circumference.

C = πr² = π(4)²=16π = 50.24 feet

The perimeter of a rectangle table is P = 2l+2w = 2(10) + 2(5) = 30 feet.

With more than 20 feet more, the circle table will fit more.

Check the picture below.

Answer:

The correct option is A.

Step-by-step explanation:

A  relation is called a function if for each values of x, there exist a unique value of y.

A graph show a function if it passes the vertical line test. It means the function intersect each vertical at most once.

From the given graph it is clear that the graph passes the vertical line test because the the function intersect each vertical at most once and for each values of x, there exist a unique value of y.

Hence the correct option is A.

Answer: 32

Step-by-step explanation:

3,584 / 112 = 32

Answer:

A square that has sides of 4.5 units, or a rectangle that is 1 unit wide and 8 units long.

Step-by-step explanation:

First, you need to find the perimeter in the first place. Since there are two sides of the same number, you would double each number.

2 would become 4

6 would become 12

Add 4+12=18

So, our rectangle has to have a perimeter of 18 units. Because a square is a rectangle, you can divide 18 and 4, since a square has 4 sides. You get 4.5. Each side can be 4.5 units.

Or, you can have a rectangle. What I thought first was a length of 9, but I knew that wouldn't work. I drew a rectangle and tried 8. If I put it on the top and bottom, which you need to to find the perimeter, it was only 16. Then I knew I could use 1 as a side length. If you added the sides, it would equal 2, and when you add 16 and 2, it's 18. So, you can use a rectangle that has a length of 8 units and a width of 1 unit.

Answer:

x < -12

Step-by-step explanation:

-1/2x > 6

Multiply by -2 to isolate x

Remember that when multiplying by a negative, we flip the inequality

-2 * -1/2x < 6*-2

x < -12

The length of a rectangle with an area of 81 - x² square meters and a width of 9 - x meters is (81 - x²) / (9 - x) .

To find the expression that represents the length of the rectangle, we need to use the formula for the area of a rectangle, which is:

Area = Length × Width

Given that the area of the rectangle is 81 - x² square meters and the width is 9 - x meters, we can set up the equation as:

81 - x² = Length × (9 - x)

To isolate the Length, we divide both sides of the equation by the Width (9 - x):

Length = (81 - x²) / (9 - x)

Therefore, the expression that represents the length of the rectangle is:

Length = (81 - x²) / (9 - x)

Complete Question:
The rectangle below has an area of 81- x² square meters and a width of 9 - x meters. What expression represents the length of the rectangle?

Answer:

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Step-by-step explanation:

Answer:

1/100

Step-by-step explanation:

Answer:

7 crayons in each pack

Step-by-step explanation:

1. subtract the 3 found crayons from the total (24)

    24-3 = 21

2. divide 21 by 3 packs

   21/3 = 7

Final answer:

Eleni ended up with 24 crayons after buying 3 packs and finding 3 more in her desk. To find the number of crayons per pack, we subtract the 3 found crayons from the total, giving us 21 crayons that came from the packs. Dividing 21 by the 3 packs she bought, we get 7 crayons per pack.

Explanation:

The subject of this question is mathematics, specifically an arithmetic problem that involves addition and division. Eleni bought 3 packs of crayons and found 3 more crayons in her desk, which resulted in her having a total of 24 crayons. To solve for the number of crayons in each pack, we start by subtracting the 3 crayons she found from the total, leaving us with 21 crayons that came from the packs. We then divide this number by the number of packs to find out how many crayons were in each pack.

Here's a step-by-step solution:

Start with the total number of crayons Eleni has after finding the extra ones in her desk: 24 crayons.

Subtract the 3 crayons found in her desk: 24 crayons - 3 crayons = 21 crayons.

Divide the resulting number of crayons by the number of packs she bought: 21 crayons \/ 3 packs = 7 crayons per pack.

Therefore, there were 7 crayons in each pack.

Answer:

Final answer is approx x=-0.66.

Step-by-step explanation:

Given equation is [tex]5^{-2x-1}=4^{4x+3} [/tex].

Now we need to solve equation [tex]5^{-2x-1}=4^{4x+3} [/tex] and round to the nearest hundredth.

[tex]5^{-2x-1}=4^{4x+3} [/tex]

[tex]\log(5^{-2x-1})=\log(4^{4x+3}) [/tex]

[tex](-2x-1)\log(5)=(4x+3)\log(4) [/tex]

[tex]-2x \log(5)- \log(5)=4x \log(4)+3 \log(4) [/tex]

[tex]-2x \log(5) -4x \log(4)=3 \log(4) +\log(5)[/tex]

[tex]x=\frac{\left(3\log(4)+\log(5)\right)}{\left(-2\log(5)-4\log(4)\right)}[/tex]

Now use calculator to calculate log values, we get:

[tex]x=-0.65817959094[/tex]

Round to the nearest hundredth.

Hence final answer is approx x=-0.66.

Answer:

Even

Step-by-step explanation:

The function Y=-6x^6-5x^2- 2 is a polynomial. A polynomial function is a function where a whole number exponent greater than 1 is on the variable. All polynomial functions have a degree known as the highest exponent. This degree also determines if the functions is even, odd or neither.

The highest exponent on the polynomial is 6 which is an even number. This polynomial is even.

Answer:even

Step-by-step explanation:

got it right on edg. quiz

Answer: [tex]\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}[/tex]

               b) 5314

               c) ln 2.7

               d) 4.6 hrs

Step-by-step explanation:

[tex]P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}[/tex]

[tex]10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}[/tex]

Final answer:

The question involves solving an exponential growth problem, often modeled by the equation P(t) = P0ekt, to determine the bacterial population at specific times and the growth rate after 4 hours, as well as the time it takes to reach a certain population size.

Explanation:

The student's question falls into the realm of differential equations and specifically pertains to exponential growth in the context of a bacteria population. When dealing with bacterial growth, the formula used is P(t) = P0ekt, where P0 is the initial population, e is the base of the natural logarithm, k is the rate constant, and t is the time in hours.

To find the expression for P(t), we first need to determine the value of k using the information that after one hour the population has increased from 100 to 270 cells. We can then use this value to determine P(4), the population after 4 hours, and P'(4), the rate of growth after 4 hours. Finally, to find when the population reaches 10,000 cells we solve P(t) = 10,000.

Here are the steps we follow:

Answer:

Step-by-step explanation:

How long it takes to reach the ground is a y-dimension thing, and horizontal displacement is an x-dimension thing.  So let's set up a table with the info we have in each dimension:

                           x                             y

V₀                     10.0 m/s               10.0 m/s

Δx                        ?                       -122.5 m

a                       0 m/s/s                -9.8 m/s/s

v                       10.0 m/s                    ?

t                           ?                             ?

That seems like an awful lot of question marks, doesn't it?

The first question asks us for the time, t, it takes for the pathetic and greatly disliked Justin Bieber to hit the ground.  We will use the equation:

Δx = V₀t + 1/2at²

Filling in our values using the y-dimension stuff only:

[tex]-122.5 = 10.0t+\frac{1}{2}(-9.8)t^2[/tex] which simplifies to

[tex]-122.5=10.0t-4.9t^2[/tex]

Hmmm...this is beginning to resemble a parabolic equation you probably already studied in Algebra 2!

We can solve for t by getting everything on one side and setting the equation equal to 0.  We set it equal to 0 since the height on the ground is 0:

[tex]-4.9t^2+10.0t+122.5=0[/tex]

When you factor that for the 2 values of t, you get

t = -4.1 and 6.1

Of course, since time can't EVER be negative, we use a t value of 6.1.  That's how long it takes to hit the ground.  That t value can now be filled into the t values in our table above.  We need that t value for the next part that asks us the horizontal displacement, Δx.  This is x-dimension stuff now.  Using the same equation:

Δx =[tex]10.0(6.1)+\frac{1}{2}(0)(6.1)^2[/tex]

Of course since the acceleration in the x-dimension is always 0, the whole portion of the equation after the equals sign is eliminated, leaving us with

Δx = 10.0(6.1)

Δx = 61 m

Poor Justin, upon his demise, hits the ground.  Therefore, his final velocity is 0, since his body met the ground and stopped dead.

Answer:

Step-by-step explanation:

see attached

Answer:

$1280.59

53 years

Step-by-step explanation:

To find how much we will get in 5 years, we use the formula:

[tex]A=Pe^{rt}[/tex]

P = $1200

r = 1.3% or 0.013

t = 5

Now that we have our values, let's plug them into the formula.

[tex]A=1200e^{0.013(5)}[/tex]

[tex]A=1200e^{0.065}[/tex]

[tex]A=1280.59[/tex]

We will have $1280.59 after 5 years.

Now to find how long it will take for our investment to double.

t = ln(A/P)/r

A = 2400

P = 1200

r = 1.3 or 0.013

Let's plug it in.

t = ln(2400/1200)/0.013

t = ln(2)/0.013

t = 53.32 or 53 years

Set the two equations to equal each other and solve:

3x-2 = x+2

Subtract x from each side:

2x -2 = 2

Add 2 to each side:

2x = 4

Divide both sides by 2:

x = 4/2 = 2

Now replace x with 2 in one of the equations and solve for y:

y = 3x -2 = 3(2) - 2 = 6-2 = 4

X = 2, Y = 4

(2,4)

Answer:

The answer in the procedure

Step-by-step explanation:

step 1

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=10\ cm[/tex]

[tex]h=9\ cm[/tex]

substitute

[tex]V=\pi (10)^{2}(9)=900\pi\ cm^{2}[/tex]  

step 2

Find the volume of the cone

The volume of the cone is equal to

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

we have

[tex]r=10\ cm[/tex]

[tex]h=9\ cm[/tex]

substitute

[tex]V=(1/3)\pi (10)^{2}(9)=300\pi\ cm^{2}[/tex]  

therefore

we have

[tex]Vcylinder=900\pi\ cm^{2}[/tex]  

[tex]Vcone=300\pi\ cm^{2}[/tex]  

so

[tex]Vcylinder=3Vcone[/tex]  

Answer:

NO = 4.5

MO = 3.5

LN = sqrt(44)

Step-by-step explanation:

Since the value of the base of the triangles is 8, and the value of NO is 4.5, the value of MO is MN - NO, which is 8 - 4.5, which comes out to 3.5.

Then, we apply the quadratic formula to triangle MLO to find that the middle line value is sqrt(23.75). Then we use the quadratic formula on traingle OLN to find the LN is sqrt(44).

Answer:

An ellipse and a rectangle.

Step-by-step explanation:

If Jamal cuts the right circular cylinder anywhere but its extremities, the resulting shapes on both pieces will be an ellipse.  

If he cuts precisely in a perpendicular way in relation to the ends, he will then form two new right circular cylinders, then the ellipses obtained would be circles.

If Jamal cuts the right circular cylinder lengthwise, going from one end to the other, even if it's not perpendicular to the base, he will obtain a rectangular shape.

A two-dimensional plane section that could result from slicing a right circular cylinder into two congruent pieces is a circle.

When a right circular cylinder is sliced at the center of the vertical height, the surface of either section is a circle.

However, when a right circular cylinder is sliced at the center of the circular surface, the surface of either section is a rectangle.

Hence, the resulting shapes are circles and rectangles

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Answer:

$97.38

Step-by-step explanation:

Subtract the finance charge and new purchases from the previous balance.

    102.35 - 1.24 - 15.73 = 85.38

Add the payment/credit

85.38 + 12 = 97.38

Answer:

$107.32

Step-by-step explanation:

New balance = previous balance + finance charge + purchases - payments

Previous balance = $102.35

Finance charge = $1.24

Purchases = $15.73

Payments = $12.00

New balance

Fill in the given information and do the arithmetic.

... New balance = previous balance + finance charge + purchases - payments

... New balance = $102.35 + $1.24 + $15.73 - $12.00

... New balance = $107.32

Answer:

2.5

Step-by-step explanation:

so LM is 3 right, right?

so PQ is 6

what they did to get that is they doubled 3 so 3x2=6

so if we divide 5 by 2 we get 2.5 because 2.5+2.5= 5

and that is how i got 2.5

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[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{cos^2(\theta )-cos^4(\theta )}{tan(\theta )}\implies \cfrac{cos^2(\theta )[1-cos^2(\theta )]}{\frac{sin(\theta )}{cos(\theta )}}\implies \cfrac{cos^2(\theta )[sin^2(\theta )]}{\frac{sin(\theta )}{cos(\theta )}} \\\\\\ \cfrac{cos^2(\theta )[sin^2(\theta )]}{1} \cdot \cfrac{cos(\theta )}{sin(\theta )}\implies cos^3(\theta )sin(\theta )[/tex]

Answer: There is exactly 1 million in 1 kilogram

Step-by-step explanation:

Answer:

ello mate

Step-by-step explanation: