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3 years ago

Object a has a mass of 20 g, what is the density?

Mathematics

1 answer:

horrorfan [7]3 years ago

4 0

Volume is needed to answer. the equation is density = mass (divided by) volume<span />

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If csc ( x ) = 4, for 90 ∘ < x < 180, then sin ( x 2 ) = ? cos ( x 2 ) = ? tan ( x 2 ) = ?

svetlana [45]

Answer:

I'm assuming where you wrote x2, you meant 2x.

Anyway, if csc (x) = 2, since csc(x) = 1/sin(x), we know that 1/sin x = 2, so sin (x) = 1/2. Since sin2x + cos2x = 1, cos2x = 1 - sin2x, so cos x = √1 - sin2x. In this case, cos x = √ 1 - (1/2)2 = √(3/4) = (√3)/2. Finally, since sin x = opp / hyp , cos = adj/ hyp: sin x / cos x = (opp/hyp)/(adj/hyp) = opp/adj = tan x. So this means that tan x = sin x / cos x = 1/2 / √ 3 / 2 = 1/√3 = √3 / 3

At this point, all that is necessary is to use the double angle formulas for sin, cos, and tan.

sin (2x) = 2 sin x cos x = 2 (1/2) (√3/2) = √3 / 2

cos (2x) = cos2x - sin2x = (√3/2)2 - (1/2)2 = 3/4 - 1/4 = 1/2

tan (2x) = 2 tan x / (1 - tan2x) = 2 (√3 / 3) / ( 1 - (√3/3)2) = 2/√3 / (1 - 1/3) = 2/√3 / (2/3) = 3/√3 = √3

To sum up, sin (2x) = √4 / 2, cos (2x) = 1/2, and tan(2x) = ✓3.

Step-by-step explanation:

BRAIN LY FAST

MARK A BRAINLESS

5 0

2 years ago

There are infinite numbers of rational number between any 2 rational numbers which one of the following lies between 20/30 and 4

miv72 [106K]

Answer: B 11/15

Step-by-step explanation: 11/15 = 22/30> 20/30

but 11/15 = 110 /150 < 120/150 = 30/50

4 0

3 years ago

A certain bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover

riadik2000 [5.3K]

Answer:

<h2>See the explanation.</h2>

Step-by-step explanation:

(a)

$\left[\begin{array}{cccc}T&H&S&P\\S&600&1300&2000\\L&400&300&400\end{array}\right]$ = A.

In the above matrix A, the columns refers the three type of books and the rows refers the from which stores the books are been sold.

The numbers represents the corresponding sales in the month of January.

The sale is same for the 6 months.

Hence, 6A = $\left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right]$ . This matrix 6A represents the total sales over the 6 months.

(b)

If we denote the books in stock at the starting of January by B, then

B = $\left[\begin{array}{cccc}T&H&S&P\\S&1000&3000&6000\\L&1000&6000&3000\end{array}\right]$ .

Each month, the chain restocked the stores from its warehouse by shipping 500 hardcover, 1,400 softcover, and 1,400 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles.

If we represent the amount restocked books at the end of each month by another matrix C, then

C = $\left[\begin{array}{cccc}T&H&S&P\\S&500&1400&1400\\L&500&500&500\end{array}\right]$ .

This restocking will be done for 5 times before the end of June.

If there would be no sale, then the stock would be

B + 5C = $\left[\begin{array}{cccc}T&H&S&P\\S&1000+2500&3000+7000&6000+7000\\L&1000+2500&6000+2500&3000+2500\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right]$ .

Since, the total sale is given by 6A, at the end of June, the inventory in each store can be shown as following,

B+5C-6A $\left[\begin{array}{cccc}T&H&S&P\\S&3500&10000&13000\\L&3500&8500&5500\end{array}\right] - \left[\begin{array}{cccc}T&H&S&P\\S&3600&7800&12000\\L&2400&1800&2400\end{array}\right] \\= \left[\begin{array}{cccc}T&H&S&P\\S&-100&2200&1000\\L&1100&6700&3100\end{array}\right]$

6 0

3 years ago

Given that y= 12 cm and θ= 24 °, work out x rounded to 1 DP.<br><br> (not drawn to scale.)

padilas [110]

Answer:

$\huge\boxed{\sf x = 5.3}$

Step-by-step explanation:

<h3><u>Given:</u></h3>

y = 12 cm

θ = 24°

Using trigonometric ratio, tan.

$\displaystyle \boxed{tan \theta = \frac{opposite}{adjacent} }\\\\tan \ 24 = \frac{x}{12} \\\\0.445 = \frac{x}{12} \\\\Multiply \ 12 \ to \ both \ sides\\\\0.445 \times 12 = x\\\\5.3 = x\\\\x = 5.3\\\\\rule[225]{225}{2}$