Divide (5 1/4) divided by (-2 1/2)

geniusboy [140]

Answer:

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}$

Step-by-step explanation:

$\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\$

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}$

8 0

3 years ago

A bicycle has a listed price of 837.95 before tax if the sales tax rate is 7.5% find the total cost of the bicycle with a sales

Andru [333]

Answer:

The total cost of a bicycle after the tax = $900.8

Step-by-step explanation:

Given

The cost of a bicycle before tax = 837.95 (let say in $)

Sales tax = 7.5% = 0.075

To determine

The total cost of the bicycle with a sales tax include

The tax amount can be calculated by multiplying Sales tax i.e. 0.075 with the cost of bicycle before tax i.e. 837.95.

Thus,

Tax amount = 7.5% × 837.95

= 0.075 × 837.95

= $62.85

Thus, the tax amount is: $62.85

Total cost after the tax can be calculated by adding the Tax amount and the cost before tax.

Therefore,

The total cost of a bicycle after the tax = $62.85 + $837.95

= $900.8

Hence, the total cost of a bicycle after the tax = $900.8

4 0

2 years ago

Read 2 more answers

Are the following lines parallel? y = -3x + 1 y = 4 - 3x

PIT_PIT [208]

Answer:

Simple! The answer is yes.

Step-by-step explanation:

Simply put the equations into Desmos graphing calculator and it will show you that the equations are parallel. :))

4 0

2 years ago

joe is in debt $250, but he's saving $30 each month. using the equation, y=30x-250, how long will it take joe to have $230?

Vsevolod [243]

Answer:

16

Step-by-step explanation:

so in this equation we have 2 variables, and we must figure out what those variables mean:

y: "y" is the total amount of money joe has after subtracting his debt from it

x: "x" is the # of months as the cost of each month(30) is placed just before this variable

as y is the total amount of money joe has we need to substitute it for 230 to figure out how long it took for joe to recieve that much money

230=30x-250

480=30x

x=16

it took joe 16 months to get $230

3 0

3 years ago

If angle YWZ = 17, what is angle WXY?

marusya05 [52]

We know that

step 1
if ∡YWZ=17°
then
∡XWZ=17°*2-----> 34°----> because triangle XWY and triangle YWZ are congruents

step 2
∡WXY=∡WZY-------> because triangle XWY and triangle YWZ are congruents
we know that
the sum of the internal angles of a triangle is 180 degrees
so
180°=∡XWZ+2*∡WXY---------> ∡WXY=[180-∡XWZ]/2
∡WXY=[180-34°]/2-------> ∡WXY=73°

the answer is
∡WXY=73°

5 0

3 years ago