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8_murik_8 [283]
3 years ago
5

What is an equation of the line that passes through the points (1,3) and (8,5)?

Mathematics
1 answer:
slamgirl [31]3 years ago
4 0

Answer:

y=2/7x+19/7

Step-by-step explanation:

Slope = m = (y₂-y₁)/(x₂-x₁) = (5-3)/(8-1) = 2/7

Therefore, our equation so far is y=2/7x+b where we can calculate b, the y-intercept by plugging in one of our given points [I used (1,3)]:

y=2/7x+b

3=2/7(1)+b

3=2/7+b

21/7=2/7+b

19/7=b

Therefore, our final equation is y=2/7x+19/7

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When driving in England, Brian drove through several speed cameras. On one drive, Brian left his hotel and after 7 minutes he wa
DedPeter [7]

Solution :

The formula for the linearization of a function $f(x)$ at a point $x$ = a is given as

$L(x)=f(a)+(x-a)f'(a)$

Assuming the time is t and the distance travelled is $f(t)$, that makes the speed as $f'(t)$.

So substituting them in the linearization formula,

A. At t = 7 minutes

   f(7) = 2.5 km

    f'(7) = 0.5 kpm

  ∴ $L_7(t)=f(7)+(t-7)f'(7)$

             $=2.5+(t-7)0.5$

              $=2.5+0.5t-3.5$

              $=0.5t-1$

B. At t = 18 minutes

      f(18) = 14.8 km

    f'(18) = 0.8 kpm

  ∴ $L_{18}(t)=f(18)+(t-18)f'(18)$

               $=14.8+(t-18)0.8$

              $=14.8+0.8t-14.4$

              $=0.8t-0.4$

C. Substituting the value of t as 14 in both the linearization to determine the position at 14 minutes, we get

$L_7(14)=0.5(14)-1.0$

          = 7 - 1

          = 6 km

$L_{18}(14)=0.8(14)+0.4$

            = 11.2 + 0.4

            = 11.6 km

D. According to the linearization at 7, the distance travelled between the 7 minutes and 14 minutes is = 6 km - 2.5 km

                                           = 3.5 km

And between the 14 minutes and 18 minutes is = 14.8 km - 6 km

                                                                              = 8.8 km

This is an average speed of 0.5 kpm in the first interval and an average speed of 2.2 kpm.

Now, according to the linearization of 18, the distance travelled between the 7 minutes and the 14 minutes is = 11.6 km - 2.5 km

                                                           = 9.1 km

And between 14 minutes and 18 minutes is = 14.8 km - 11.6 km

                                                                       = 3.2 km

This gives an average speed of 1.3 kpm in the first interval and 0.8 kpm in the second interval.

Therefore, the second approximation is the better one since the average speed are closer to the actual readings in the second linearization.  

4 0
3 years ago
Please help me answer this!!!
Sedaia [141]

Answer:

the process of being a differential is that the process of moving to the different people in a very good process of being the speaker of speaker and the senate speaker and the author organizes a different speech to the topic and i  

Step-by-step explanation:

the process is important as the speaker of speaker is the process of speech to a speech in speech speech and speech in speech and speech

7 0
3 years ago
I need some help...
bixtya [17]
-------------------------------------
Question
-------------------------------------
17x³ + (3x + 8x³<span>)

-------------------------------------
Remove the bracket
</span>-------------------------------------
17x³ + 3x + 8x³

-------------------------------------
Combine like terms
-------------------------------------
25x³ + 3x

-------------------------------------
Take out common factor
-------------------------------------
x(25x² + 3)

-------------------------------------
Answer: x(25x² + 3)
-------------------------------------
7 0
3 years ago
Based on a sample of 150 textbooks at the store, you find an average of 70.69 and a standard deviation of 29.6. The point estima
Ugo [173]

Answer:

Step-by-step explanation:

Given that:

The sample size = 150

The sample mean = 70.69

The standard deviation = 29.60

The sample mean is equal  to the point estimate of the population = 70.69

At 99% confidence interval level is:

∝ = 1 - 0.99

∝ = 0.01

The critical value:

Z_{\alpha/2} = Z_{0.01/2} \\ \\  Z_{0.005} = 2.58  \ using \ Z \ tables

The Margin of error = Z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}

= 2.58 \times \dfrac{29.6}{\sqrt{150}}

= 2.58 × 2.4168

≅ 6.235

At 99% confidence interval; the estimate of the population mean lies within the interval:

= \overline x - E < \mu \ < \overline x + E

= 70.69 - 6.235 < μ <  70.69 + 6.235

= 64.455  < μ < 76.925

= (64.455 , 76.925 )

6 0
3 years ago
All the information in the photo.
a_sh-v [17]

Answer:

Two angles are called complementary when their measures add to 90 degrees. ∠1 is 60 degrees ∠2 is 30 degrees so if you add it up, the answer is  90 degrees.

∠4 + ∠3 = answer has to be 90 degrees to call it a complementary angle

30 degrees + 60 degrees = 90 degrees

6 0
3 years ago
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