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3 years ago

Solve the compound inequality. -2x<-10 and x-3<4

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

4 0

Answer:

x > -7/12. This is the answer to this question.

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Trigonometry problem

IgorC [24]

Answer:

The values are x = 0° or x = 60°

Step-by-step explanation:

Given:

$\cos x + \frac{1}{\sqrt{3} }\times \sin x = 1$

Let it be in the form of

$a\cos x + b\sin x = 1$ such that

a = 1

$b=\frac{1}{\sqrt{3} }$

We have

$\sqrt{(a^{2}+b^{2} )}=\sqrt{(1^{2}+(\frac{1}{\sqrt{3} }) ^{2} )}\\=\sqrt{\frac{4}{3}}\\=\frac{2}{\sqrt{3} }$

Now, Dividing both the side by $\frac{2}{\sqrt{3} }$ we get

$\frac{\sqrt{3} }{2}\cos x + \frac{1}{2}\sin x =\frac{\sqrt{3} }{2}\\$

We Know

$\sin 60 =\frac{\sqrt{3} }{2}\\and\\\cos 60 = \frac{1}{2}$

Now by replacing with above values we get

$\sin 60\times \cos x + \cos 60\times \sin x = \frac{\sqrt{3} }{2}\\$

Also we have formula

$\sin A\times \cos B + \cos A\times \sin B = \sin (A+B)$

By applying the above Formula we get

$\sin (60+x)=\frac{\sqrt{3} }{2}\\$

Also ,

$\sin (60)=\frac{\sqrt{3} }{2}\\and\\\sin (120)=\frac{\sqrt{3} }{2}$

Comparing we get

60 + x = 60 or 60 + x = 120

∴ x = 0° ∴ x = 120 - 60 = 60°

Therefore, the values are x = 0° or x = 60° i.e between 0° to 360°

5 0

3 years ago

HELP ME OUT PLS !!!! THIS IS EASY

MakcuM [25]

Answer:

C) 123 cm^2

Step-by-step explanation:

well if we find CD we can cut striat down C and do area of a triangle plus the area of the rectangle.

to find CD you need length of BC

BC^2 = AC^2-AB^2 --> BC^2 = 400-100 --> BC^2 = 300

BC = 300^2 --> about 17 causeing CD being 4

now we have info

triangle area is BxHx 1/2 --> 17x10x1/2 --> 85cm^2

Now we do the small rectangle area is BxH --> 4x10 --> 40cm^2

85 + 40 = 125cm^2

the only one close is 123cm^2

4 0

3 years ago

Solve the following proportion; -5/3=2-3a/7

Varvara68 [4.7K]

Answer:

a = 77

This is the answer

6 0

3 years ago

Find the product (-3) • (1.2) A. 4.5 B. -3.6 C. -4.6 D. 5.3

NikAS [45]

The answer is b -3.6 hope this helps and god bless my friend

4 0

3 years ago

Read 2 more answers

A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a heig

vazorg [7]

Answer:

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

Step-by-step explanation:

The water tower has the shape of a cylinder with a cone on top . The volume of the water tower can be find when you find the sum of the volume of the cylinder and the cone.

Therefore,

volume of the cylinder = πr²h

where

r = 12/2 = 6 ft

h = 15 ft

volume = π × 6² × 15

volume = π × 36 × 15

volume of the cylinder = 540π

Volume of the cone = 1/3πr²h

r = 6 ft

Using tangential ratio we can find the height which is the opposite side of the triangle

tan 25° = opposite/adjacent

tan 25° = h/6

cross multiply

h = 6 tan 25°

h = 6 × 0.46630765815

h = 2.79784594893

h = 2.8 ft

volume of the cone = 1/3πr²h

volume = 1/3 × π × 36 × 2.8

volume = 100.8π/3

volume = 33.6π

Volume of the tower system = 540π + 33.6π = 573.6π

volume of the tower system = 573.6 × 3.14 = 1801.104 ft³

1 cubic ft = 7.48 gallons

1801.104 cubic fit = ? gallons

cross multiply

gallons = 1801.104 × 7.48

gallons = 13472.25792 gallons

The residents drains the water at the rate of 56 gallons per minute. Therefore,

56 gallons = 1 minutes

13472.25792 gallons = ? minutes

number of minutes = 13472.25792 /56

number of minutes = 240.576034286

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

7 0

3 years ago

Solve the compound inequality. -2x<-10 and x-3<4​

Solve the compound inequality. -2x<-10 and x-3<4