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ser-zykov [4K]
3 years ago
8

The area is approximately ___ square units. Use 3.14 for π.

Mathematics
1 answer:
ss7ja [257]3 years ago
8 0

Answer:

A = 914 units

Step-by-step explanation:

The figure consists of a rectangle and a circle.

The sides of rectangle are 30 units and 20 units

The diameter of circle is 20 unit

Radius = 10 units

Required area = area of rectangle + area of circle

=l\times b+\pi r^2\\\\=30\times 20+3.14\times 10^2\\\\=914\ units

So, the area of the figure is equal to 914 units.

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N over 7= 20<br> solve for N
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Let f(x) = x^3 - 2x - 2. Then differentiating, we get

f'(x) = 3x^2 - 2

We approximate f(x) at x_1=2 with the tangent line,

f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18

The x-intercept for this approximation will be our next approximation for the root,

10x - 18 = 0 \implies x_2 = \dfrac95

Repeat this process. Approximate f(x) at x_2 = \frac95.

f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}

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f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}

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\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}

Compare this to the actual root of f(x), which is approximately <u>1.76929</u>2354, matching up to the first 5 digits after the decimal place.

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