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3 years ago

Suppose x and y vary together such that y = 2 x + 11 . Suppose x varies from x = 2 to x = 8.5 .

Mathematics

1 answer:

Stells [14]3 years ago

8 0

Answer:

a) x changes by 6.5 units

b) y changes by 13 units

Step-by-step explanation:

a. Over this interval, how much does x change by?

Initially, we have that x = 2.

In the end, we have that x = 8.5.

So x changes by 8.5-2 = 6.5 units

b. Over this interval, how much does y change by?

Initially, when x = 2, we have that y = 2x + 11 = 2*2 + 11 = 15

In the end, when x = 8.5, we have that y = 2*8.5 + 11 = 28

So y changes by 28 - 15 = 13 units

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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

0.6y + 0.8 = 0.28y + 1.12

gavmur [86]

Answer:

Step-by-step explanation:

$0.6y + 0.8 = 0.28y + 1.12$

Move the variable to L.H.S and change its sign:

$0.6y - 0.28y + 0.8 =1.12$

Move the constant to R.H.S and change its sign:

$0.6y - 0.28y = 1.12 - 0.8$

Calculate

$0.32y = 0.32$

Divide both sides of the equation by 0.32

$\frac{0.32y}{0.32} = \frac{0.32}{0.32}$

Calculate

$y = 1$

Hope this helps...

Good luck on your assignment..

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