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3 years ago

Which is the best approximation for the solution of the system of equations?

Mathematics

1 answer:

SpyIntel [72]3 years ago

5 0

Answer:

(0.88, 0,65)

Step-by-step explanation:

what do we have to do ? I assume we need to find the crossing point between the 2 lines.

when looking at the graphic, we can already rule out the first, third and fourth option.

none of the coordinates of that point is larger than 1 in any direction or smaller than 0.5.

so, just by looking at things I immediately "bet" on answer option 2 (0.88, 0.65).

but let's check.

y = -2x/5 + 1

y = 3x - 2

for the crossing point both functions must produce the same functional value.

-2x/5 + 1 = 3x - 2

-2x/5 + 5/5 = 15x/5 - 10/5

-2x + 5 = 15x - 10

15 = 17x

x = 15/17 = 0.88...

y = 3×0.88... -2 = 0.65...

hurray, our original observation and "suspicion" is confirmed.

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1 step: $S_{5}=T_{1}+T_{2}+T_{3}+T_{4}+T_{5}$ , $S_{3}=T_{1}+T_{2}+T_{3}$ , then
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and $\left \{ {{T_{6}-T_{4}= \frac{5}{2} } \atop {T_{5}+T_{4}=5}} \right.$ will have form $\left \{ {{T_1*q^{5}-T_{1}*q^{3}= \frac{5}{2} } \atop {T_{1}*q^{4}+T_{1}*q^{3}=5} \right.$ .

3 step: Solve this system $\left \{ {{T_1*q^{3}*(q^{2}-1)= \frac{5}{2} } \atop {T_{1}*q^{3}*(q+1)=5} \right.$ and dividing first equation on second we obtain $\frac{q^{2}-1}{q+1}= \frac{ \frac{5}{2} }{5}$ . So, $\frac{(q-1)(q+1)}{q+1} = \frac{1}{2}$ and $q-1= \frac{1}{2}$ , $q= \frac{3}{2}$ - the common ratio.

4 step: Insert $q= \frac{3}{2}$ into equation $T_{1}*q^{3}*(q+1)=5$ and obtain $T_{1}* \frac{27}{8}*( \frac{3}{2}+1 ) =5$ , from where $T_{1}= \frac{16}{27}$ .

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3 years ago

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Answer:

C and D

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