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3 years ago

Hat is the 68th term of sequence -8.6,-7.2,-5.8,-4.4,

Mathematics

1 answer:

Umnica [9.8K]3 years ago

5 0

First find the law
8.6-1.4n
so, 64th is 8.6-1.4x64
I think is -81

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Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your ans

VikaD [51]

Answer:

The two iterations of f(x) = 1.5598

Step-by-step explanation:

If we apply Newton's iterations method, we get a new guess of a zero of a function, f(x), xₙ₊₁, using a previous guess of, xₙ.

xₙ₊₁ = xₙ - f(xₙ) / f'(xₙ)

Given;

f(xₙ) = cos x, then f'(xₙ) = - sin x

cos x / - sin x = -cot x

substitute in "-cot x" into the equation

xₙ₊₁ = xₙ - (- cot x)

xₙ₊₁ = xₙ + cot x

x₁ = 0.7

first iteration

x₂ = 0.7 + cot (0.7)

x₂ = 0.7 + 1.18724

x₂ = 1.88724

second iteration

x₃ = 1.88724 + cot (1.88724)

x₃ = 1.88724 - 0.32744

x₃ = 1.5598

To four decimal places = 1.5598

4 0

3 years ago

A rectangular storage container with a lid is to have a volume of 2 m3. The length of its base is twice the width. Material for

Scilla [17]

Answer:

Dimensions are 2 m by 1 meter by 1 meter,

Minimum cost is $ 18.

Step-by-step explanation:

Let w be the width ( in meters ) of the container,

Since, the length is twice of the width,

So, length of the container = 2w,

Now, if h be the height of the container,

Volume = length × width × height

2 = 2w × w × h

1 = w² × h

$\implies h=\frac{1}{w^2}$

Since, the area of the base = l × w = 2w × w = 2w²,

Area of the lid = l × w = 2w²,

While the area of the sides = 2hw + 2hl

= 2h( w + l)

$= 2\times \frac{1}{w^2}(w+2w)$

$=\frac{6w}{w^2}$

$=\frac{6}{w}$

Since, Material for the base costs $1 per m². Material for the sides and lid costs $2 per m²,

So, the total cost,

$C(w) = 1\times 2w^2+2\times 2w^2 + 2\times \frac{6}{w}$

$=2w^2+4w^2+\frac{12}{w}$

$=6w^2+\frac{12}{w}$

Differentiating with respect to w,

$C'(w) = 12w -\frac{12}{w^2}$

Again differentiating with respect to w,

$C''(w) = 12 + \frac{24}{w^3}$

For maxima or minima,

C'(w) = 0

$\implies 12w -\frac{12}{w^2}=0$

$\implies 12w^3 - 12=0$

$w^3-1=0\implies w = 1$

For w = 1, C''(w) = positive,

Hence, for width 1 m the cost is minimum,

Therefore, the minimum cost is C(1) = 6(1)²+12 = $ 18,

And, the dimension for which the cost is minimum is,

2 m by 1 meter by 1 meter.

7 0

3 years ago

Which point on the number line best represents the approximate value of 38?

Genrish500 [490]

Answer: Q

Step-by-step explanation: the 23 thing simplified would be 4 and a bunch of decimals. Q is the answer on four, and the 23 thing is closest to four, so Q would be the correct answer.

4 0

2 years ago

Read 2 more answers

What is 21 1/4% expressed as a fraction?

Neporo4naja [7]

Answer:

$\frac{17}{80}$

Step-by-step explanation:

we have

$21\frac{1}{4}\%$

Convert mixed number to an improper fraction

$21\frac{1}{4}=21+\frac{1}{4}=\frac{21*4+1}{4}=\frac{85}{4}$

$21\frac{1}{4}\%=\frac{85}{4}\%$

Convert percent number as a fraction

$\frac{85}{4}\%=\frac{85}{4}:100=\frac{85}{4*100}=\frac{85}{400}$

Simplify

Divide by 5 both numerator and denominator

$\frac{17}{80}$

8 0

3 years ago

If m<10=77,m<47 and m<16=139, find the measure of each missing angle

timofeeve [1]

I dont know if this could help you but if you can please try to answer those two that I didn't complete so you could have an idea on what there relationships are and things like that.

3 0

3 years ago