Wichstate had a poppulation of eith hundred four thosand, one hundred nunety

If angle a has the terminal ray that falls in the fourth quadrant and cosine a equals 5/9 then determine the value of sin a in s

Tema [17]

Answer: $-\dfrac{2\sqrt{14}}{9}$

Step-by-step explanation:

Given

$\cos a=\dfrac{5}{9}$

$a$ lies in the fourth quadrant

So, sine must be negative in the fourth quadrant

Using identity $\sin ^2 x+\cos^2 x=1$ to find sine value

$\Rightarrow \sin^2 a=1-\dfrac{5^2}{9^2}$

$\\\\\Rightarrow \sin^2 a=1-\dfrac{25}{81}\\\\\\\Rightarrow \sin^2 a=\dfrac{56}{81}\\\\\\\Rightarrow \sin a=-\sqrt{\dfrac{56}{81}}\\\\\\\Rightarrow \sin a=-\dfrac{2\sqrt{14}}{9}$

8 0

3 years ago

7-18 use part 1 of the fundamental theorem of calculus to find the derivative of the function.

blondinia [14]

$\displaystyle h(x)=\int\limits_{1}^{\sqrt{x}}~\cfrac{z^2}{z^4+1}dz~\hspace{10em}\cfrac{dh}{du}\cdot \stackrel{chain~rule}{\cfrac{du}{dx}\implies \cfrac{dh}{dx}} \\\\[-0.35em] ~\dotfill\\\\ u=\sqrt{x}\implies \cfrac{du}{dx}=\cfrac{1}{2\sqrt{x}} \\\\[-0.35em] ~\dotfill$

$\cfrac{dh}{dx}\implies \displaystyle \cfrac{d}{du}\left[ \int\limits_{1}^{u}~\cfrac{z^2}{z^4+1}dz \right]\cdot \cfrac{1}{2\sqrt{x}}\implies \left[ \cfrac{u^2}{u^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}} \\\\\\ \stackrel{substituting~back}{\left[ \cfrac{(\sqrt{x})^2}{(\sqrt{x})^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}}}\implies \cfrac{x}{x^2+1}\cdot \cfrac{1}{2\sqrt{x}}\implies \cfrac{\sqrt{x}}{2x^2+2}$

7 0

2 years ago

Coefficient of y^15x^2 in expansion of (y^3+x)^7

Hitman42 [59]

The coefficient of y∧15×∧2 in expansion of (y∧3+x)∧7 is (15×2)+(3×7)= 51

7 0

3 years ago

Read 2 more answers

Grace is planning on purchasing an Akai Professional MPC5000 drum machine for $2195. She's been pre-approved to finance her purc

Genrish500 [490]

1) Her monthly payment is $40.97 if she finance the total amount

2) She will pay $2458.2 for the MPC5000

3)Her monthly payment will be $26.50 if she pay her saved up money upfront

4) She will pay $2365.4 for the MPC5000

5) Yes, I recommend to pay the $775 upfront . If she pay upfront, then the amount she needs to pay for the MPC5000 is less.

Step-by-step explanation:

The cost of the drum machine is $2195

The APR is 12% over 60 months

1) the APR for 60 months is 12%

So, the APR for 1 month is

12/60 = 0.2%

The interest per month = 0.2% of 2195

= (0.2 x 2195) / 100

= 4.39

The amount to be paid per month is

= monthly amount + interest

= (2195/60) + 4.39

= 36.58 + 4.39

=$ 40.97

2) If she pays $40.97 per month then the total payment (for 60 months) for the drum machine

= 40.97 x 60

= $ 2458.2

3) the total cost is $2195 out of which she pays $775 upfront.

So she have to borrow less .

The amount to be financed is

2195- 775= $1420

The monthly interest is,

(0.2 x 1420) /100 = 2.84

Monthly she have to pay

23.66+ 2.84= $26.50

4) If she pay $775 upfront then the remaining $1420 is financed

Her monthly payment is $26.50

Then for 60 months she will pay,

26.50 x 60= $1590.4

The total amount paid for the drum machine is

775+1590.4 =$2365.4

4 0

3 years ago

Need help ASAP. Please and thanks!:

Nuetrik [128]

Answer:

The answer is x=294 (B)

Step-by-step explanation:

Remember, all interior angles of a hexagon add to 720.

So add all the given numbers first.

92+100+94+140+x= 720

426+x=720

-426 from both sides

x= 294

I know this is a week later since you posted the question, sorry.

3 0

3 years ago

Wichstate had a poppulation of eith hundred four thosand, one hundred nunety_ four