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2 years ago

Cos(90 degrees + theta ) = - sin theta , why?

Mathematics

1 answer:

BigorU [14]2 years ago

3 0

Step-by-step explanation:

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

x = theta

y = 90°

cos(90) = 0

sin(90) = 1

cos(x)×0 - sin(x)×1 = - sin(x)

remember slopes of lines ?

and how the coordinates and the slope changed for a perpendicular line ?

the slope is y/x, and for the perpendicular line this turned into -x/y.

the same happens here.

sin(x) and cos(x) are the x and y coordinates of a point on the circle with the angle x to the horizontal axis.

if you add 90° to the angle, you create a perpendicular line or angle, and the coordinates follow the slope rules : cos turns into sin and vice versa, and the sign has to flip.

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Are the two expressions equivalent?

Diano4ka-milaya [45]

Answer:

Step-by-step explanation:

11z+9z (11+9)z

20z (20)z

(11•5)+(9•5) (11+9)5

55+45 (20)5

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3 0

4 years ago

Find the slope of ther line that goes through the points (-9,-4) and (-3,-6)

sleet_krkn [62]

Answer:

slope = - $\frac{1}{3}$

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 9, - 4) and (x₂, y₂ ) = (- 3, - 6)

m = $\frac{-6+4}{-3+9}$ = $\frac{-2}{6}$ = - $\frac{1}{3}$

5 0

4 years ago

A person invests 4000 dollars in a bank. The bank pays 5.5% interest compounded annually. To the nearest tenth of a year, how lo

Mademuasel [1]

if the person leaves the money in the bank, the time it will take for it to reach the given final amount is 6.3 years.

<h3>What is an interest in banking?</h3>

Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formular for calculating compound interest is expressed as;

A = P(1 + r/n)^(n*t)

Where A is final amount, P is initial principal balance, r is interest rate, n is number of times interest applied per time period and t is number of time periods elapsed.

Given the data in the question;

Initial principal balance P = $4000
Interest rate r = 5.5% anuually = 5.5/100 = 0.055
Final amount A = $5600
Time t = ?

We substitute our given values into the expression above.

A = P(1 + r/n)^(n*t)

5600 = 4000(1 + 0.055/1)^(1*t)

5600 = 4000( 1.055 )^t

( 1.055 )^t = 5600 / 4000

( 1.055 )^t = 1.4

We take log of each sides

0.02325t = 0.1461

t = 0.1461 / 0.02325

t = 6.3

Therefore, if the person leaves the money in the bank, the time it will take for it to reach the given final amount is 6.3 years.

Learn more about compound interest here: brainly.com/question/27128740

#SPJ1

8 0

2 years ago

Cuanto es r2-2r-7=0

vekshin1

Answer:

Step-by-step explanation:

The solution is attached

6 0

3 years ago

At one point in a Girl Scout cookie sales drive, region C had sold 1500 boxes of cookies, and region D had sold 1200 boxes of co

juin [17]

Answer:

a)After 6 days region D will catch region C

b) Region C will sell 13500 cookies and region D will sell 13600 cookies

Step-by-step explanation:

a) Cookies sold by region C more than region D= 1500-1200=300

But region D can sells 50 cookies every day i-e

50 cookies = 1 day

==> 1 cookie= 1÷50

==> 300cookies = 300÷50=6 days

So, after 6 days region D will catch up region C's

b) If sale stopped after 8 days;

Then sale of region C for 8 days = 1500×8=12000 cookies

so , total cookies sold = 1500 +12000=13500

For region D;

Before catching up region C cookies sold by region D = 1200

Till catching up region C - region D had also sold 1500 cookies,

and for 50 extra cookies than region C

next 8 days region D will sale =(1500+50)×8=1550×8=12400 cookies

So, total number of cookies sold by region D = 1200+12400=13600

3 0

3 years ago