Answer:
Θ = 84°
Step-by-step explanation:
using the identity
cosx = sin(90 - x) , then
cos6° = sin(90 - 6)° = sin84°
that is Θ = 84°
Answer:
Multiply each side by −5, add 25 to each side
Step-by-step explanation:
-1/5(x-25) = 7
Multiply each side by -5/1 to clear the fraction
-5/1* -1/5(x-25) = 7*-5/1
x-25 = -35
Then add 25 to each side
x-25+25 = -35+25
x = -10
Answer:
![\huge\boxed{(2,\ 3);\ (-1,\ 6)}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%282%2C%5C%203%29%3B%5C%20%28-1%2C%5C%206%29%7D)
Step-by-step explanation:
![f(x)=x^2-2x+3\to y=x^2-2x+3\\f(x)=-x+5\to y=-x+5\\\\\left\{\begin{array}{ccc}y=x^2-2x+3&(1)\\y=-x+5&(2)\end{array}\right](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-2x%2B3%5Cto%20y%3Dx%5E2-2x%2B3%5C%5Cf%28x%29%3D-x%2B5%5Cto%20y%3D-x%2B5%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dy%3Dx%5E2-2x%2B3%26%281%29%5C%5Cy%3D-x%2B5%26%282%29%5Cend%7Barray%7D%5Cright)
substitute (1) to (2):
add x to both sides
![x^2-2x+x+3=-x+x+5](https://tex.z-dn.net/?f=x%5E2-2x%2Bx%2B3%3D-x%2Bx%2B5)
subtract 5 from both sides
![x^2-x+3-5=5-5](https://tex.z-dn.net/?f=x%5E2-x%2B3-5%3D5-5)
![x^2-x-2=0\\\\x^2+x-2x-2=0\\\\x(x+1)-2(x+1)=0\\\\(x+1)(x-2)=0\iff x+1=0\ \vee\ x-2=0\\\\\boxed{x=-1\ \vee\ x=2}](https://tex.z-dn.net/?f=x%5E2-x-2%3D0%5C%5C%5C%5Cx%5E2%2Bx-2x-2%3D0%5C%5C%5C%5Cx%28x%2B1%29-2%28x%2B1%29%3D0%5C%5C%5C%5C%28x%2B1%29%28x-2%29%3D0%5Ciff%20x%2B1%3D0%5C%20%5Cvee%5C%20x-2%3D0%5C%5C%5C%5C%5Cboxed%7Bx%3D-1%5C%20%5Cvee%5C%20x%3D2%7D)
substitute the values of x to (2):
![x=-1\\\\y=-(-1)+5=1+5=6\\\\\huge\boxed{(-1,\ 6)}\\\\x=2\\\\y=-2+5=3\\\\\huge\boxed{(2,\ 3)}](https://tex.z-dn.net/?f=x%3D-1%5C%5C%5C%5Cy%3D-%28-1%29%2B5%3D1%2B5%3D6%5C%5C%5C%5C%5Chuge%5Cboxed%7B%28-1%2C%5C%206%29%7D%5C%5C%5C%5Cx%3D2%5C%5C%5C%5Cy%3D-2%2B5%3D3%5C%5C%5C%5C%5Chuge%5Cboxed%7B%282%2C%5C%203%29%7D)
Answer:
The width W is :
![W=\frac{3}{5}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B3%7D%7B5%7D)
Step-by-step explanation:
<em>Let A be the area of the rectangle </em>
<em>Let L be the length of the rectangle</em>
<em>Let W be the width of the rectangle </em>
______
Formula:
A = L × W
__________
![\begin{aligned}A &=L \times W \\\Rightarrow W &=\frac{A}{L} \\\Rightarrow W &=\frac{\frac{3}{8}}{\frac{5}{8}} \\&=\frac{3}{8} \times \frac{8}{5} \\&=\frac{3 \times 8}{8 \times 5} \\&=\frac{3}{5}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%20%26%3DL%20%5Ctimes%20W%20%5C%5C%5CRightarrow%20W%20%26%3D%5Cfrac%7BA%7D%7BL%7D%20%5C%5C%5CRightarrow%20W%20%26%3D%5Cfrac%7B%5Cfrac%7B3%7D%7B8%7D%7D%7B%5Cfrac%7B5%7D%7B8%7D%7D%20%5C%5C%26%3D%5Cfrac%7B3%7D%7B8%7D%20%5Ctimes%20%5Cfrac%7B8%7D%7B5%7D%20%5C%5C%26%3D%5Cfrac%7B3%20%5Ctimes%208%7D%7B8%20%5Ctimes%205%7D%20%5C%5C%26%3D%5Cfrac%7B3%7D%7B5%7D%5Cend%7Baligned%7D)
Subtract L from both sides.
the expression now becomes,
<span>S−L=−rL</span>
2)Divide by L on both sides.
<span><span><span>S−L</span>L</span>=−r</span>
3)Multiply with a negative sign on both sides in the final step to obtain the expression in terms of r so the answer is<span> #(L-S)/L = r#</span>