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3 years ago

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Euler's formula, V – E + F = 2 relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedro

n. How many faces does a polyhedron with 5 vertices and 8 edges have?

1 answer:

denis23 [38]3 years ago

8 0

V – E + F = 2

5 - 8 + F = 2

- 3 + F = 2

F = 2 + 3

F = 5

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Given that secant theta = Negative StartFraction 37 Over 12 EndFraction, what is the value of cotangent theta, for StartFraction

Iteru [2.4K]

$cot\theta$ $=\frac{12}{35}$

Step-by-step explanation:

$sec\theta =\frac{37}{12}$

⇔ $\frac{1}{cos \theta} =\frac{37}{12}$

⇔ $cos \theta = \frac{12}{37}$

we know that

$sin \theta = \sqrt{1-cos^2\theta}$

$sin\theta =\sqrt{1-(\frac{12}{37})^2 }$

$sin\theta=\sqrt{\frac{1225}{1369} }$

$sin\theta = \frac{35}{37}$

Therefore $cot\theta =\frac{cos\theta}{sin\theta}$ $=\frac{\frac{12}{37} }{\frac{35}{37} }$ $=\frac{12}{35}$ , for $\frac{\pi}{2}$

8 0

4 years ago

Read 2 more answers

In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C an

Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

$P(x)=Ca^{x-2000}$

So, the population in 2000,

$P(2000)=Ca^{2000-2000}$

$=Ca^{0}$

$=C$

According to the question,

$P(2000)=1$

$\implies C=1$

(b) Similarly,

The population in 2025,

$P(2025)=Ca^{2025-2000}$

$=Ca^{25}$

$=a^{25}$ (∵ C = 1)

Again according to the question,

$P(2025)=1.2$

$a^{25}=1.2$

Taking ln both sides,

$\ln a^{25}=\ln 1.2$

$25\ln a = \ln 1.2$

$\ln a = \frac{\ln 1.2}{25}\approx 0.00729$

$a=e^{0.00729}=1.00731$

Thus, the function that shows the population in year x,

$P(x)=(1.00731)^{x-2000}$ ...... (1)

The population in 2010,

$P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555$

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

$1.4=(1.00731)^{x-2000}$

$\ln 1.4=(x-2000)\ln 1.00731$

$0.33647 = (x-2000)0.00728$

$0.33647 = 0.00728x-14.56682$

$0.33647 + 14.56682 = 0.00728x$

$14.90329 = 0.00728x$

$\implies x=\frac{14.90329}{0.00728}\approx 2047$

Therefore, the country's population might reach 1.4 billion in 2047.

3 0

3 years ago

Ella and Iris are planning trips to nine countries this year. There are 12 countries they would like to visit. They are deciding

NISA [10]

Using the combination formula, it is found that there are 220 ways to decide which countries to skip.

The order in which the countries are skipped is not important, hence the <em>combination formula </em>is used to solve this question.

<h3>What is the combination formula?</h3>

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, 3 countries are skipped from a set of 12, hence the number of ways is given by:

$C_{12,3} = \frac{12!}{3!9!} = 220$

More can be learned about the combination formula at brainly.com/question/25821700

#SPJ1

5 0

2 years ago

40. What is the system of inequalities associated with the following graph?

SpyIntel [72]

Answer:

The bottom answer

Step-by-step explanation:

4 0

4 years ago

Answer the following: GCF of 20 & 32 GCF of 45 & 75

Jet001 [13]

Answer:

GCF OF 20 AND 32: 4

Gcf of 45 and 75: 15

Step-by-step explanation:

GcF of 20 and 32

Factors of 20: 1, 2, 4, 5, 10, 20

Factors of 32: 1, 2, 4, 8, 16, 32

COMMON FACTORS: 1, 2, 4

GCF:4

Gcf of 45 and 75

Factors of 45: 15, 9, 5, 3, 1.

Factors of 75: 25, 15, 5, 3, 1.

CommoN factors: 1, 3, 5, 15

GCF:15

HOPE OT HELPED

3 0

3 years ago

Read 2 more answers