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3 years ago

Cscθ - sinθ = _____

1 answer:

galina1969 [7]3 years ago

4 0

So you maybe know that $\csc x = \frac{1}{\sin x}$ . Now let us try to simplify the expression

$\csc x - \sin x = \frac{1}{\sin x} - \sin x = \frac{1}{\sin x} - \frac{\sin^2 x }{\sin x}=\frac{1-\sin^2 x}{\sin x} =$

$= \frac{\cos^2 x}{\sin x} = \cot x \cdot \cos x$

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Oliver works at a book store.He packed 20 identical paperbacks and 9 identical textbooks in a box .The total mass of the book wa

Natasha_Volkova [10]

Let x be the mass of the paperbacks and y be the mass of the textbook.

20x + 9y = 44.4 ----------- (1)
25x + 10y = 51 -------------(2)

(1) x 10:
200x + 90y = 444 --------(1a)

(2) x 9:
225x + 90y = 459 --------(2a)

(2a) - (1a):
25x = 15
x = 0.6 -------- sub into (1)

20 (0.6) + 9y = 44.4
12 + 9y = 44.4
9y = 44.4 - 12
9y = 32.4
y = 3.6

So the paperback's mass is 0.6 pounds and textbook is 3.6 pounds

7 0

3 years ago

mary will spin the spinner below 150 times. about how many times should mary expect the spinner to land on a number greater than

irga5000 [103]

Answer:

56 times (This is still assuming 1 isnt an option)

Step-by-step explanation:

0,2,3,4,5,6,7,8

There are 8 options, 3 of which are greater than 5

3/8

3/8 = x/150

3*150 = 450

8 * x = 8x

8x = 450

450/8 = 56.25

56 times

-- Gage Millar

5 0

2 years ago

Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

3 years ago

A=5x+20

kirza4 [7]

Answer:

video rum is eryn rice of a local food store to the point of the lord and of a man of his name poltergeist and the lord God is the lord God is not in the land and he is the lord of Israel as he will be the

Step-by-step explanation:

the company is the lord God of the world of Israel and is a great place for people who are in his life 6th and I have to do that in a different way of doing school work and I am a little bit of the opposite who have not given me the opportunity for a long hub experience and I am a little more interested and I have to be a

3 0

3 years ago

Evaluate 23x + 4y when x=20 and y=23

never [62]

Answer:

552

Step-by-step explanation:

23x + 4y when x=20 and y=23

if x=20 and y=23 all you have to do is replace the numbers and solve

23(20) + 4(23)

Multiply 23*20 which is equal to 460

Then you multiply 4*23 which is equal to 92

The problem is now 460 + 92

add it, and you get 552.

Hope this helps!!

-Ketifa

3 0

3 years ago