3 years ago

Any of these please I’m having difficulty

Mathematics

1 answer:

frosja888 [35]3 years ago

7 0

Answer:

864 squared meters

Step-by-step explanation:

Set up a proportion. The scale between 270 and 360 should be the same as 648 to the fourth yard.

$\frac{270}{360} = \frac{648}{x}\\270x = (360)(648)\\270x = 233280\\x = 864 m^2$

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Find n for the sequence for which a1 = 30, d = -4 and sn= -210.

REY [17]

$n\in\mathbb{N^+}$

The formula of the sum of an arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

We have:

$a_1=30;\ d=-4;\ S_n=-210$

substitute:

$\dfrac{2\cdot30+(n-1)(-4)}{2}\cdot n=-210\ \ \ |\cdot2\\\\(60-4n+4)n=-420\\\\(64-4n)n=-420\\\\64n-4n^2=-420\ \ \ |:(-4)\\\\n^2-16n=105\ \ \ |-105\\\\n^2-16n-105=0\\\\n^2+5n-21n-105=0\\\\n(n+5)-21(n+5)=0\\\\(n+5)(n-21)+0\iff n+5=0\ \vee\ n-21=0\\\\n=-5\notin\mathbb{N^+}\ \vee\ n=21\in\mathbb{N^+}$