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3 years ago

- What value of x makes this equation true? - 8 = x - 2

Mathematics

1 answer:

777dan777 [17]3 years ago

4 0

Answer:

Step-by-step explanation:

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Jorge watches cars that pass in front of his house. He counts 25 red cars and 40 cars that are not red. What is the approximate

jenyasd209 [6]

Step-by-step explanation:

firstly you will add

the red cars and non red cars together and which is 65

probability of the red car = 25/65

to the lowest form is the 5/13(D)

8 0

3 years ago

Verify that:

Lelu [443]

Answer:

See Below.

Step-by-step explanation:

Problem 1)

We want to verify that:

$\displaystyle \left(\cos(x)\right)\left(\cot(x)\right)=\csc(x)-\sin(x)$

Note that cot(x) = cos(x) / sin(x). Hence:

$\displaystyle \left(\cos(x)\right)\left(\frac{\cos(x)}{\sin(x)}\right)=\csc(x)-\sin(x)$

Multiply:

$\displaystyle \frac{\cos^2(x)}{\sin(x)}=\csc(x)-\sin(x)$

Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:

$\displaystyle \frac{1-\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)$

Split:

$\displaystyle \frac{1}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)$

Simplify:

$\csc(x)-\sin(x)=\csc(x)-\sin(x)$

Problem 2)

We want to verify that:

$\displaystyle (\csc(x)-\cot(x))^2=\frac{1-\cos(x)}{1+\cos(x)}$

Square:

$\displaystyle \csc^2(x)-2\csc(x)\cot(x)+\cot^2(x)=\frac{1-\cos(x)}{1+\cos(x)}$

Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:

$\displaystyle \frac{1}{\sin^2(x)}-\frac{2\cos(x)}{\sin^2(x)}+\frac{\cos^2(x)}{\sin^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}$

Factor out the sin²(x) from the denominator:

$\displaystyle \frac{1}{\sin^2(x)}\left(1-2\cos(x)+\cos^2(x)\right)=\frac{1-\cos(x)}{1+\cos(x)}$

Factor (perfect square trinomial):

$\displaystyle \frac{1}{\sin^2(x)}\left((\cos(x)-1)^2\right)=\frac{1-\cos(x)}{1+\cos(x)}$

Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:

$\displaystyle \frac{(\cos(x)-1)^2}{1-\cos^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}$

Factor (difference of two squares):

$\displaystyle \frac{(\cos(x)-1)^2}{(1-\cos(x))(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}$

Factor out a negative from the first factor in the denominator:

$\displaystyle \frac{(\cos(x)-1)^2}{-(\cos(x)-1)(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}$

Cancel:

$\displaystyle \frac{\cos(x)-1}{-(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}$

Distribute the negative into the numerator. Therefore:

$\displaystyle \frac{1-\cos(x)}{1+\cos(x)}=\displaystyle \frac{1-\cos(x)}{1+\cos(x)}$

3 0

3 years ago

A city currently has 31,000 residents and is adding new residents steadily at the rate of 1200 per year. If the proportion of re

dlinn [17]

Answer:

Population of the city after 7 years from now, P(7) = 6370

Given:

Initial Population, $P_{i} = 31000$

rate, r(t) = 1200 /yr

S(t) = [/tex]\frac{1}{1 + t}[/tex]

Step-by-step explanation:

Let the initial population be $P_{i} = 31000$

The population after T years is given by the equation:

$P(T) = P_{i}S(T) + \int_{0}^{T}S(T - t)r(t) dt$ (1)

Thus, the population after 7 years from now is given by using eqn (1):

$P(7) = \frac{3100}{1 + 7} + 1200\int_{0}^{7}\frac{1}{8 - t} dt$

$P(7) = 3875 - 1200ln(8 - t)|_{0}^{7}$

$P(7) = 3875 - 1200(ln(1) - ln(8))$

$P(7) = 3875 + 2495 = 6370$

6 0

3 years ago

To an order of magnitude, how many piano tuners are in New York City? The physicist Enrico Fermi was famous for asking questions

Olin [163]

Suppose that the population of NYC is 10,000,000, and there're average of 3 people per household
= 3.3 million HHs
and 1 in 10 HHs has a piano
= 330,000 pianos

on average, a piano is tuned once a year
= 330,000 tuning per year
= 6,000 tunings per week

suppose a piano tuner works 5 days a week and handling 5 pianos a day. That will be 25 pianos a week

hence, you need 6,000/25 = 240 tuners

hope this helps

4 0

4 years ago

Jack's school is 6 km from his home. He goes to school by bus. One day on the way to school due to road construction the bus had

Setler79 [48]

Answer:

<h2>The bus was 1250 meters away from school</h2>

Step-by-step explanation:

Given that the total distance of the school from home is 6km

converting 6km to meters we have 6,000m

Since the bus stopped at 4750 meters from his home.

The remaining distance is the distance the bus is from his school

i.e $6000-4750= 1250 meters$

8 0

3 years ago