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1 year ago

Graph the line passing through the given point and having the given slope. (1,-1), m= - 3/4

Mathematics

1 answer:

serious [3.7K]1 year ago

7 0

Answer: y=-3x/4 -1/4

Step-by-step explanation:

y=mx+b

-1=-3/4 * 1 +b

-1=-3/4 + b

(-1=-3/4 + b)*4

-4=-3+4b

4b=-1

b=-1/4

y=-3x/4 -1/4

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The total number of fungal spores can be found using an infinite geometric series where a1 = 8 and the common ratio is 4. Find t

GalinKa [24]

Answer:

$S_{n} = \frac{2(4^{n}-1) }3} if r>1$

Step-by-step explanation:

Explanation:-

<u>Geometric sequence</u>:-

The geometric sequence is of the form

$a,ar,ar^{2},ar^{3}$ ……… be an infinite sequence

here first term is 'a' and ratio is 'r '

In this geometric sequence 'n' t h term is $t_{n} = a r^{n-1}$ ....(1)

Given data a1 term is '8 ' and ratio is '4'

substitute n=1 in equation(1)

$t_{1} = a r^{1-1}$ = 8

$ar=8$ ...........(2)

substitute r= 4 in equation(2)

now we get a(4)=8

dividing "4" on both sides , we get a = 2

<u>Geometric series</u>:-

$a+ar+ar^{2}+ar^{3}+$ .....is an infinite geometric series.

sum of this infinite series will be the upper limit of the fungal spores

that is we have to find sum of infinite series

$S_{n} = \frac{a(r^{n}-1) }{r-1} if r>1$

$S_{n} = \frac{2(4^{n}-1) }{4-1} if r>1$

$S_{n} = \frac{2(4^{n}-1) }3} if r>1$

<u>Final answer:</u>-

sum of this infinite series will be the upper limit of the fungal spores

$S_{n} = \frac{2(4^{n}-1) }3} if r>1$

5 0

3 years ago

Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Oxana [17]

Answer:

The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Step-by-step explanation:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$

Multiply and Divide by $2cos(\frac{\pi }{14})$

= $\frac{2sin(\frac{\pi }{14})cos(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})}{2cos(\frac{\pi }{14})}$

⇒ Let $\frac{\pi }{14}$ = Ф and 7Ф = $\frac{\pi }{2}$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

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4 0

3 years ago

I need help on number 8

tester [92]

Answer:

(-3,5) (-3,4)

5-4/-3--3=1/0

It is a vertical line so it's y∈R

Step-by-step explanation:

5 0

3 years ago

What is the relationship between 0.8 ÷ 10^2 and 0.8×10^2

AleksandrR [38]

$0.8\times10^2\ \text{is 10,000 times greater than}\ 0.8\div10^2\\\\\dfrac{0.8\times10^2}{0.8\div10^2}=\dfrac{10^2}{1\div10^2}=\dfrac{10^2}{\frac{1}{10^2}}=10^2\times10^2=10^4=10,000$

5 0

3 years ago

If log(16)=s, what is the value of 2/3 log(6400) - 1/3 log(1600) in terms of s?

eduard

The value of $\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)$ in terms of s will be

$\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)$

<h3>What is Logrithm?</h3>

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

Here we have the expression:-

$\dfrac{ 2}{3} log(6400) - \dfrac{1}{3} log(1600)$

So in terms of s the expression will become:-

$\dfrac{2}{3}(400s)-\dfrac{1}{3}(1000s)$

To know more about logarithm follow

brainly.com/question/25710806

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8 0

2 years ago