What is

The focal lengths of the objective lens and the eyepiece of a microscope are 0.50 cm and 2.0 cm, respectively, and their separat

VladimirAG [237]

Answer:

- 103.7

Step-by-step explanation:

Given:

Focal length of the eyepiece, f = 2.0 cm

Focal length of the objective lens, f' = 0.50 cm

Separation for minimum eyestrain = 6,0 cm

Image distance, v = - 25 cm

Now, from the lens formula,

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

here, u is the object distance

on substituting the respective values, we get

$\frac{1}{2}=\frac{1}{u}+\frac{1}{-25}$

or

u = 1.852 cm

also, the separation is adjusted for minimum eyestrain,

therefore, image distance for the objective lens, v' = 6 - 1.852 = 4.148 cm

Now, for the objective lens

using the lens formula, we get

$\frac{1}{0.5}=\frac{1}{u'}+\frac{1}{4.418}$

Here, u' is the distance between the physical object and objective lens

or

u' = 0.568 cm

Thus,

Magnification, m = $-\frac{vv'}{ff'}$

or

m = $-\frac{25\times4.418}{0.5\times2}$

or

m = - 103.7

4 0

2 years ago

What is the value of t=1 ∑³ (4 x 1/2^t-1)

Stels [109]

Answer:

7

Step-by-step explanation:

$\sum\limits_{t=1}^{3}(4\cdot(\frac{1}{2})^{t-1})$

This is the sum of the first three terms of a geometric sequence, where the first term is 4 and the common ratio is ½.

We can use a formula to find the sum, or, since there's only three terms, we can find the value of each term then add up the results.

4 · (½)¹⁻¹ = 4

4 · (½)²⁻¹ = 2

4 · (½)³⁻¹ = 1

4 + 2 + 1 = 7

4 0

3 years ago

Hi, I don’t understand this question

meriva

Given that

z₁ = 15 (cos(90°) + i sin(90°))

z₂ = 3 (cos(10°) + i sin(80°))

we get the quotient z₁/z₂ by dividing the moduli and subtracting the arguments:

z₁/z₂ = 15/3 (cos(90° - 10°) + i sin(90° - 10°))

z₁/z₂ = 5 (cos(80°) + i sin(80°))

so that z₁ is scaled by a factor of 1/3 and is rotated 10° clockwise.

4 0

2 years ago

Probabilities with possible states of nature: s1, s2, and s3. Suppose that you are given a decision situation with three possibl

amm1812

Answer:

1. $P(s_1|I)=\frac{1}{11}$

2. $P(s_2|I)=\frac{8}{11}$

3. $P(s_3|I)=\frac{2}{11}$

Step-by-step explanation:

Given information:

$P(s_1)=0.1, P(s_2)=0.6, P(s_3)=0.3$

$P(I|s_1)=0.15,P(I|s_2)=0.2,P(I|s_3)=0.1$

(1)

We need to find the value of P(s₁|I).

$P(s_1|I)=\frac{P(I|s_1)P(s_1)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_1|I)=\frac{(0.15)(0.1)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_1|I)=\frac{0.015}{0.015+0.12+0.03}$

$P(s_1|I)=\frac{0.015}{0.165}$

$P(s_1|I)=\frac{1}{11}$

Therefore the value of P(s₁|I) is $\frac{1}{11}$ .

(2)

We need to find the value of P(s₂|I).

$P(s_2|I)=\frac{P(I|s_2)P(s_2)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_2|I)=\frac{(0.2)(0.6)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_2|I)=\frac{0.12}{0.015+0.12+0.03}$

$P(s_2|I)=\frac{0.12}{0.165}$

$P(s_2|I)=\frac{8}{11}$

Therefore the value of P(s₂|I) is $\frac{8}{11}$ .

(3)

We need to find the value of P(s₃|I).

$P(s_3|I)=\frac{P(I|s_3)P(s_3)}{P(I|s_1)P(s_1)+P(I|s_2)P(s_2)+P(I|s_3)P(s_3)}$

$P(s_3|I)=\frac{(0.1)(0.3)}{(0.15)(0.1)+(0.2)(0.6)+(0.1)(0.3)}$

$P(s_3|I)=\frac{0.03}{0.015+0.12+0.03}$

$P(s_3|I)=\frac{0.03}{0.165}$

$P(s_3|I)=\frac{2}{11}$

Therefore the value of P(s₃|I) is $\frac{2}{11}$ .

4 0

3 years ago

What is the length of leg s in the right triangle shown?

Amiraneli [1.4K]

Answer:

5

Step-by-step explanation:

Using pythagoras theorem

4 0

3 years ago