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3 years ago

What is the radian value of arccos(-3/sqrt(2))?

Mathematics

1 answer:

Ksju [112]3 years ago

3 0

Answer:

Not defined over the real numbers

Step-by-step explanation:

Let

$x = arc \cos( \frac{ - 3}{ \sqrt{2} })$

This implies that:

$\cos(x) = \frac{ - 3}{ \sqrt{2} }$

This implies that:

$\cos(x) = - 2.12$

The range of the cosine function is -1≤y≤1

Therefore

$arc \cos( \frac{ - 3}{ \sqrt{2} })$

is not defined for over the real numbers.

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Least common denominator in 1/30 + 1/24

aev [14]

Answer:

The LCD in 1/30 + 1/24 is <u>90</u>.

8 0

2 years ago

You go shopping at a local department store with your friend and cousin. You buy one pair of jeans, four pairs of shorts, and tw

VashaNatasha [74]

Answer: Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

Step-by-step explanation:

Let x= cost per pair of jeans

y = Cost per pair of shorts

z= cost per shirt.

For you, total cost = x+4y+2z= 84

For your friend, total cost = 2x+y+3z=76

For cousin, total cost = x+2y+z= 52

Required system:

$x+4y+2z=84\ (i)\\ 2x+y+3z=76\ (ii)\\ x+2y+z=52\ (iii)$

from (i), $x=84-4y-2z$ (*)

put this in (ii) and (iii) we get

$2\left(84-4y-2z\right)+y+3z=76\\\Rightarrow\ -7y-z+168=76\ (iv)\\\\ 84-4y-2z+2y+z=52\\\Rightarrow\ -2y-z+84=52 \ (v)$

from (iv), $y=-\frac{z-92}{7}\ (vi)$

$\mathrm{Subsititute\:}y=-\frac{z-92}{7}\ \text{in}\ (v)$

$-2\left(-\frac{z-92}{7}\right)-z+84=52\\\\\Rightarrow\ -2\left(-\frac{z-92}{7}\right)-z=-32\\\\\Rightarrow\ -\frac{5z}{7}-\frac{184}{7}=-32\\\\\Rightarrow\ -5z-184=-224\\\\\Rightarrow\ -5z=-40\\\\\Rightarrow\ z=8$

$\mathrm{Subsititute\:}z=8\text{ in (vi)}$

$y=-\frac{8-92}{7}\\\\\Rightarrow \ y=12$

$\mathrm{Subsititute\:}z=8,\:y=12\text{ in (*)}$

$x=84-4\cdot \:12-2\cdot \:8\\\\\Rightarrow\ x= 20$

Hence, x= 20, y= 12 , z=8

So, Cost per pair of jeans = $ 20

Cost per pair of shorts = $12

Cost per shirt = $8

7 0

3 years ago

A population of rabbits in a lab, p(x), can be modeled by the function p(x) = 20(1.014)x , where x represents the number of days

Nitella [24]

Answer:

20 = initial population of the rabbits

1.014 = growth rate of the rabbits

the average rate of change from day 50 to day 100 is 0.8

Step-by-step explanation:

A population of rabbits in a lab, p(x), can be modeled by the function

p(x) = 20(1.014)^x

This model is exponential. Where 20 = initial population of the rabbits

1.014 = growth rate of the rabbits with 1.4% increase rate of the rabbits

To find the average rate of change from day 50 to day 100,

find the population p(50) and p(100). Subtract them and divide by 100 - 50 = 50.

p(50) = 20(1.014)50 = 40.08...

p(100) = 20(1.014)100 = 80.32...

(80.32 - 40.08) / (100 - 50) = 40.24/50 = 0.8048. which is approximately 0.8 to the nearest tenth.

The rate of change is 0.8.

7 0

3 years ago

G(x)=3x-4 find (gog) (x)

Anestetic [448]

Answer:

gog(x)=9x-16

Step-by-step explanation:

We are given g(x)=3x-4 and are asked to find (gog) (x)

gog(x)=g(g(x))

g(x)=3x-4

Hence

g(g(x))=g(3x-4)

=3(3x-4)-4

=9x-12-4

=9x-16

Hence

gog(x)=9x-16

5 0

3 years ago

Every 24 hours, Earth makes a full rotation around its axis. Earth's speed of rotation at the equator is 1.670 km per hour. What

Anna35 [415]

Answer:

The circumference of Earth's equator is 40,080 km.

Step-by-step explanation:

Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:

24 x 1,670 = X

40,080 = X

Therefore, the circumference of Earth's equator is 40,080 km.

3 0

2 years ago