16,80, 400,...<br> Find the 6th term.

The point (16, 12) lies on the terminal side of an angle. find cos, tan, and sin

frez [133]

The terminal side means that it's 16 to the right and 12 up. Which means that the triangle made from this has the sides of 16 and 12 and the hypotenuse is 20 units long. Theta, in this case, would have 16 as it's adjacent and 12 as it's opposite.
Therefore, using the Pythagorean identities:
<span> $sin(\theta) = \frac{12}{20} = \boxed{\frac{3}{5}} \\\ cos(\theta) = \frac{16}{20} = \boxed{\frac{4}{5}} \\\ tan(\theta) = \frac{12}{16} = \boxed{\frac{3}{4}}$ </span>

8 0

3 years ago

if 5 litres of water are drawn from a cylindrical container of internal diameter 56cm find the drop in the level of water in the

AlexFokin [52]

Answer:

the drop in the level of water in the container is 2.03 cm

Step-by-step explanation:

The volume of a cylinder can be written as;

$V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter$

the change in height when the volume changes can be derived by differentiating the equation.

$dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}$

substituting the given values;

$\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.$

$dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm$

the drop in the level of water in the container is 2.03 cm

4 0

3 years ago

I need to make a matrix in reduced row echelon form

a_sh-v [17]

Let the three apartments be A, B & C

The rent of A is $x

The rent of B is $y

The rent of C is $z

So x + y + z = 1600 .......(1)

Now

Maintenance of A is 20% of x = 0.20x

Maintenance of B is 20% of y = 0.20y

Maintenance of C is 25% of z = 0.25z

0.20x + 0.20y + 0.25z = 345

Multiplying by 100 we get

20x + 20y + 25 z = 34500

Dividing by 5 we get

4x + 4y + 5z = 6900 .......(2)

Monthly fee of A is 10% of x = 0.10x

Monthly fee of B is 20% of y = 0.20 y

Monthly Fee of C is 10% of z = 0.10z

Now

0.10x + 0.20y + 0.10 z= 1820 - 1600

0.10x + 0.20y + 0.10z = 220

Multiplying by 100 we get

10x + 20y + 10z = 22000

Dividing by 10

x + 2y + z = 2200 ....(3)

Making a Matrix of equation (1), (2) & (3)

$\left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right]$

is the required matrix

7 0

3 years ago

Read 2 more answers

Here is a picture of Rectangle R, which has been evenly divided into smaller rectangles. Two of the smaller rectangles are label

notka56 [123]

Answer:

poop

Step-by-step explanation:

WEVTRGTY JY

5 0

2 years ago

Kevin is an auto mechanic. He spends 2 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He wo

mr Goodwill [35]

Answer:

Kevin should do 21 shock replacements and 6 brake replacements every week to maximize his weekly income.

Step-by-step explanation:

Since either job takes 2 hours to complete, the total number of jobs that Kevin can complete working 54 hours a week is:

$n=\frac{54}{2}\\n=27\ jobs$

Since replacing shocks gives him a greater income, he should aim to do as little break replacements as possible and as many shock replacements as possible in order to maximize income.

If he has to complete at least 6 break replacements out of the 27 jobs possible, the number of shock replacements he should do is:

$S=27-6\\S=21$

Kevin should do 21 shock replacements and 6 brake replacements every week to maximize his weekly income.

5 0

3 years ago

16,80, 400,... Find the 6th term.