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3 years ago

What is the approximate diagonal distance from one corner of a 3 inch by 5 inch index card to the opposite corner

Mathematics

1 answer:

77julia77 [94]3 years ago

7 0

Answer:

5.83 inches

Step-by-step explanation:

The card is a rectangular shaped object, drawing a diagonal from one corner to the other, divides the rectangle into two right angled triangles with the diagonals as the hypothenuse.

Using Pythagoras theorem.

c^2 = a^2 + b^2

Given;

Side a = 3

Side b = 5

Substituting the given values;

c^2 = 3^2 + 5^2

c = √(9+25)

c = √34

c = 5.83 inches

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2. The water level of a river was measured each day during a two-week period. The

vampirchik [111]

Step-by-step explanation:

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2 years ago

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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

2 years ago

the time t required to drive a certain distance varies inversely with the speed, r. if it takes 4 hours to drive the distance at

valina [46]

Hello,

Answer A

d :the distance in miles
t: the time in hours
v: the speed in miles/hours (vistesse)

d=v*t
==>d=40*4=160(mi)

d=55*x=160==>x=160/55=2.909090... (mi/(mi/h)=h)≈2.91(hours)

8 0

3 years ago

68.64 divided by 2.4 SHOW WORK PLEASE

34kurt

Answer:28.6

I started by seeing how many 2.4 can go into 68.64. I found that it is pretty easy to find that if you multiply the 2.4 by ten you get 24 so we do that twice and have 48. We then subtract 48 from the 68.64 which leaves us with 20.64. If we multiply 2.4 by 5 we get 12 so once again subtract 12 from that 20.64 and now we are left with 8.64. So now we need to figure out how many more 2.4 are left well it is more than three because three gives us 7.2 so let’s subtract that from it now we are left with 1.44. Now we need to find out what times 2.4 gives us 1.44. Well it would be .6. So now if we add up everything we get the answer of 28.6. Sorry if this very complicated

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3 years ago

Factorise fully 2x^2-8x

Molodets [167]

Answer:

2x(x-4)

Step-by-step explanation:

2 $x^{2}$ -8x= 2( $x^{2}$ -4x)= 2x(x-4)

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2 years ago

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