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2 years ago

2sinx / cos3x = tan3x - tanx -verify the identity-

Mathematics

1 answer:

scoundrel [369]2 years ago

6 0

Answer:

cos3x+tan3x=0

⟹cos3x=−tan3x

⟹cos3x=−sin3xcos3x

⟹cos23x=−sin3x

⟹1−sin23x=−sin3x

⟹sin23x−sin3x−1=0

This is a quadratic equation in sin3x.

sin3x=−(−1)±(−1)2−4×1×(−1)−−−−−−−−−−−−−−−−−√2×1

sin3x=1±5–√2

If x takes real values, the upper sign must be rejected.

sin3x=1−5–√2

⟹3x=nπ+(−1)nsin−11−5–√2

⟹x=13[nπ+(−1)nsin−11−5–√2]

Step-by-step explanation:

Hope this kind of helps

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Toby wants to find the volume of a solid toy soldier.

mr Goodwill [35]

Answer:

Toby wants to find the volume of a solid toy soldier.He fills a rectangular container 8 cm long, 6 cm wide,and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm. Which of the following is closest to the volume, in cubic centimeters, of the toy soldier?

A. 125 B. 156 C. 192 D. 208 E.317

The volume of the toy is 125 cubic cm ,option A is the closest answer.

Step-by-step explanation:

Given:

A rectangular container .

Length of the container =8 cm

Width of the container = 6 cm

Height of the container when water is filled = $(h_1)$ = 4 cm

Height of the container when the toy is submerged = $(h_2)$ =6.6 cm

Volume of the toy = Volume of the container with the toy - Volume of the container (with water)

Volume of the toy = $(l\times b\times h_2) - (l\times b\times h_1)$

= $(l\times b\times)(h_2-h1)$

= $(6\times 8)(6.6-4)$

= $48\times 2.6$

= $124.8$ cubic centimeters.

So,the closest value to the volume of the toy is 125 cubic centimeters.

6 0

3 years ago

Which set best represents the integers?

Blizzard [7]

Of course A does because integers are positive and negative

3 0

3 years ago

An animal shelter has 24 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the

34kurt

population *32% = 24

population *.32 = 24

population = 24/.32

population = 75

4 0

2 years ago

Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the wat

nirvana33 [79]

Answer:

$V = \pi r^2 h$

For this case we know that $r=5m$ represent the radius, $h = 10m$ the height and the rate given is:

$\frac{dV}{dt}= \frac{100 L}{min}$

$Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}$

And replacing we got:

$\frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}$

And that represent $0.127 \frac{cm}{min}$

Step-by-step explanation:

For a tank similar to a cylinder the volume is given by:

$V = \pi r^2 h$

For this case we know that $r=5m$ represent the radius, $h = 10m$ the height and the rate given is:

$\frac{dV}{dt}= \frac{100 L}{min}$

For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:

$\frac{dV}{dt}= \pi r^2 \frac{dh}{dt}$

And solving for $\frac{dh}{dt}$ we got:

$\frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}$

We need to convert the rate given into m^3/min and we got:

$Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}$

And replacing we got:

$\frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}$

And that represent $0.127 \frac{cm}{min}$

5 0

3 years ago

What is another name for plane z

jarptica [38.1K]

Plain Z<span> is the </span>plane<span> that is width basicly if looking at a 3d figure.</span>

4 0

2 years ago

Read 2 more answers