This is very simple to do. Take out your calculator and insert 14.4. However, move the decimal two places to the left to get .144, and multiply it by 72.5 to get your answer of 10.44.

5 0

2 years ago

Triangle ABC is isosceles with AB=CB. Circle M is inscribed in Triangle ABC such that it is tangent at points D, E, and F. If th

Ierofanga [76]

Answer:

The answer is "12 inches".

Step-by-step explanation:

Please find the image file of the graph.

We know $AE = CF \ and \ EB = FB$ so because the triangle is isosceles.

$EB = 2x, FB = 2x,\ and \ CF = x$ when $AE$ is called by $x$ .

We know that $AE = AD = x$ since E and D are tangent points to a circle.

They have $CD = CF = x$ since D and F are tangent points only to circle.

Thus, if the perimeter is 32, the following is the result:

$\to AE + EB + BF + FC + CD + DA = 32\\\\\to x + 2x + 2x + x + x + x = 32\\\\\to 8x = 32\\\\\to x = 4$

Therefore the length of $BC = BF + FC = 2x + x = 3x = 12\ inches$

8 0

2 years ago

Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=

luda_lava [24]

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 $x_2 = \frac95$ .

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

Then

$\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}$

Once more. Approximate $f(x)$ at $x_3$ .

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

Then

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

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.

4 0

1 year ago