When converting units, summarize the steps using the Direct Method .

1 answer:

5 0

Steps are simple:
1- Write the standards of conversion
2- Write the value you want to convert
3- Use cross multiplication to get the converted value

Examples:
i- Say we want to convert 890 cm to meters.
We know that 1 cm = 0.01 meters
Now, we will write the number we want to convert and use cross multiplication as follows:
1 cm = 0.01 meters
890 cm = ?? meters
converted value = (890*0.01) / 1 = 8.9 meters

ii- Say we want to convert 568 kg to grams.
We know that 1 kg = 1000 grams
Now, we will write the number we want to convert and use cross multiplication as follows:
1 kg = 1000 gram
568 kg = ?? grams
converted value = (568*1000) / 1 = 568000 grams

Hope this helps :)

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A car travels 2.83 km in the x-direction, then turns left 65.3 ◦ to the original direction and travels an additional distance of

umka21 [38]

Answer:

4.24 km

Step-by-step explanation:

The x-component of the displacement after the turn is ...

d2·cos(θ) = (3.38 km)cos(65.3°) ≈ 1.41239 km

Adding this to the displacement before the turn, we have ...

x-component of displacement = 2.83 km + 1.41 km = 4.24 km

4 0

3 years ago

The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o

Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above