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3 years ago

What is a1 of the arithmetic sequence for which a3=10 and a51=−182?

Mathematics

1 answer:

LenaWriter [7]3 years ago

6 0

Answer:

a₁ = 18

Step-by-step explanation:

The n th term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 10 and a₅₁ = - 182, then

a₁ + 2d = 10 → (1)

a₁ + 50d = - 182 → (2)

Subtract (1) from (2) term by term to eliminate a₁

48d = - 192 ( divide both sides by 48 )

d = - 4

Substitute d = - 4 into (1) and evaluate for a₁

a₁ + 2(- 4) = 10

a₁ - 8 = 10 ( add 8 to both sides )

a₁ = 18

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Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of

Tom [10]

Question:

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below.

$\frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}$

Which is Abel’s error?

Abel should have written the ratio as $24 metres/7 metres$

Abel should have written the ratio as $24 metres/42 metres$

Abel should have divided both numbers by 6.

Abel should have divided both numbers by 4.

Answer:

Abel should have divided both numbers by 6.

Step-by-step explanation:

Given

Measured Length of backyard = 42m

Actual Length of backyard = 24m

Measured Ratio: $\frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}$

Required

Error in calculation of measured ratio

From Abel's calculation:

It can be observed that He divided both numbers by 7

Though 42/7 = 6 but that's not so for 24/7

24/7≠4;

Instead 24/7 = 3.43 (Approximated)

To get the actual ration, he has to divide both numbers by the highest common factor

The common factors of 42 and 24 include 2,3,6 of which the highest is 6

Hence; HCF of 42 and 24 = 6

So, we can conclude that the error in his calculation is having not dividing both numbers by 6

7 0

3 years ago

Read 2 more answers

Please help me with precalculus??<br>linear and angular speed

Anit [1.1K]

13)

there are 2π radians in 1 revolution, and there are 60 seconds in 1 minute, so keeping that in mind, then,

$\bf \cfrac{4\underline{\pi} }{5~\underline{s}}\cdot \cfrac{rev}{2\underline{\pi} }\cdot \cfrac{60~\underline{s}}{min}\implies \cfrac{4\cdot 60~rev}{5\cdot 2~min}\implies \cfrac{240~rev}{10~min}\implies 24\frac{rev}{min}$

14)

$\bf \textit{linear velocity}\\\\
v=rw\quad 
\begin{cases}
r=radius\\
w=angular~speed\\
----------\\
v=32\frac{m}{sec}\\
w=100\frac{rev}{min}
\end{cases}\\\\
-------------------------------\\\\
\textit{let's convert \underline{w} to }\frac{radians}{sec}$

$\bf \cfrac{100~\underline{rev}}{\underline{min}}\cdot \cfrac{2\pi }{\underline{rev}}\cdot \cfrac{\underline{min}}{60~sec}\implies \cfrac{100\cdot 2\pi }{60~sec}\implies \cfrac{10\pi }{3~sec}\implies \cfrac{10\pi }{3}\frac{radians}{sec}\\\\
-------------------------------\\\\
v=rw\implies \cfrac{v}{w}=r\implies \cfrac{\frac{30~m}{sec}}{\frac{10\pi }{3~sec}}\implies r=\cfrac{30~m}{\underline{sec}}\cdot \cfrac{3~\underline{sec}}{10\pi }
\\\\\\
r=\cfrac{90}{10\pi }m$

15)

what is the radians per seconds "w" in revolutions per minute? just another conversion like in 13)

$\bf \cfrac{\underline{\pi} }{3~\underline{sec}}\cdot \cfrac{rev}{2\underline{\pi }}\cdot \cfrac{60~\underline{sec}}{min}\implies \cfrac{60 ~rev}{3\cdot 2 ~min}\implies \cfrac{60 ~rev}{6 ~min}\implies 10\frac{rev}{min}$

4 0

3 years ago

Whats the error?katie divided 4.25 by 0.25 and a got a quotient of 0.17.

m_a_m_a [10]

The answer is 17. The decimal point needed to be moved by 2 places to the right since the divisor is a decimal.

6 0

3 years ago

What is slope and how do you find it??

lions [1.4K]

the formula for slope is

$\frac{(y2-y1)}{(x2-x1)}$