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3 years ago

A line passes through points (8, -7) and (-2,9) in the standard (x, y) coordinate plane. What is the slope of this

Mathematics

1 answer:

Alexxx [7]3 years ago

6 0

Answer:

-8/5

Step-by-step explanation:

We can find the slope by using

m= (y2-y1)/(x2-x1)

= (9 - -7)/(-2 - 8)

= (9+7)/(-2-8)

= 16/-10

= -8/5

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the smallest known bacteria are from a genus mycoplasma and can measure as small as 300 nanometers in diameter. given that 1 met

vesna_86 [32]

Length of 1 = 300 = 3 *10^2 nanometers
= 3*10^2/1*10^9 m
= 3*10^(2-9)
= 3*10^-7m

3 0

3 years ago

Read 2 more answers

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

4 0

2 years ago

Calculate the noon sun angles for new orleans, usa and helsinki, finland on september 22. in the answer below, new orleans answe

Otrada [13]

We need to calculate noon sun angle. Noon sun angle is an angle at which sun-rays fall at noon on a given date.
On September 22, the sun’s rays form a 90° angle at noon at the equator.

Formula for calculating noon sun angle is:

Noon_sun_angle = 90° - Zenith angle

We have complementary angles so we need to substract zenith angle from 90°.

The zenith angle is the distance between subsolar point (point where sun is at 90°) and the latitude of an observer. In our case this angle will have same value as latitude because subsolar point is at equator 0°. If our latitude and subsolar point are at same hemisphere we substract values. Otherwise we add values.

New Orleans, USA
Latitude = 30°
Noon_sun_angle = 90° - 30° = 60°

Helsinki, Finland
Latitude = 60°
Noon_sun_angle = 90° - 60° = 30°

4 0

3 years ago

Read 2 more answers

2x^2+7x-k=0 find all the values of k

mojhsa [17]

Answer:

Find ur attachment here plz thankyou

Step-by-step explanation: