Answer:
sin(-255°) = √2 + √6/4
Step-by-step explanation:
We need to find sin -255°
We know that sin(-a) = - sin(a)
so, sin(-255°) = - sin 255°
We know that 180° + 75° = 255°
Now we can write sin(255°) = sin(180° + 75°)
We can use the identity:
sin(x+y) = sin(x) cos(y)+cos(x)sin(y)
x = 180° , y = 75°
Solving,
sin(x+y) = sin(x) cos(y)+cos(x)sin(y)
sin(180° + 75°) = sin(180°) cos(75°)+cos(180°)sin( 75°)
sin(180°) = 0
cos(75°) = √6 -√2/4
cos(180°) = -1
sin( 75°) = √2 + √6/4
Putting values,
sin(180° + 75°) = 0 (√6 -√2/4) + (-1)(√2 + √6/4)
sin(180° + 75°) = -(√2 + √6/4)
We know that sin(-255°) = -sin(255°)
Putting value of sin(255°)
sin(-255°) = -(-(√2 + √6/4))
sin(-255°) = √2 + √6/4
The weight of one foot of the steel pipe is 1.24 pounds or more accurately, 1.239905.... pounds.
This type of problem is solved using cross multiplication. You know the length (16.84 feet), and the weight (20.88 pounds), of the steel pipe. But what you do not know is the weight of one foot of the steel pipe. Since that is what we are solving for, the weight of one foot of the steel pipe will be our x variable.
This is how I set it up...
16.84 1
——— * ———
20.88 x
I came up with this equation. The length of the pipes I put in the numerator (top), and the weight I put in the denominator (bottom). Since 16.84 feet of a steel pipe weighs 20.88 pounds, 1 foot of a steel pipe weighs x pounds. After you have the equation set up you then move on to cross multiplication.
Step 1: Multiply the top number of the first fraction by the bottom number of the second fraction.
16.84*x= 16.84x
Step 2: Multiply the bottom number of the first fraction by the top number of the second fraction.
20.88*1=20.88
Step 3: Set the answers from step 1 and step 2 equal to each other.
16.84x=20.88
Step 4: Divide 16.88 on both sides so x is by itself.
16.84x 20.88
——— = ———
16.84 16.84
And after you divide on each side you have your answer which should be x=1.24
Answer:
The 5 bags of pretzels.
Step-by-step explanation:
Because if you were to buy 5 individual bags you would end up paying $20.00, instead of $12.00
(0,-3) is the point which is your system of equations using elimination answer
Step-by-step explanation:
LHS:
\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\ldots \ldots \ldots \ldots \ldots+\frac{1}{\sqrt{8}+\sqrt{9}}1+21+2+31+3+41+……………+8+91
Rationalizing the denominator, we get
\Rightarrow\left(\frac{1}{1+\sqrt{2}} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}\right)+\left(\frac{1}{\sqrt{2}+\sqrt{3}} \times \frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)+\left(\frac{1}{\sqrt{3}+\sqrt{4}} \times \frac{\sqrt{3}-\sqrt{4}}{\sqrt{3}-\sqrt{4}}\right)+\cdots \ldots+\left(\frac{1}{\sqrt{8}+\sqrt{9}} \times \frac{\sqrt{8}-\sqrt{9}}{\sqrt{8}-\sqrt{9}}\right)⇒(1+21×1−21−2)+(2+31×2−32−3)+(3+41×3−43−4)+⋯…+(8+91×8−98−9)
We know that,
\left(a^{2}-b^{2}\right)=(a+b)(a-b)(a2−b2)=(a+b)(a−b)
Now, on substituting the formula, we get,
=\frac{1-\sqrt{2}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+\frac{\sqrt{3}-\sqrt{4}}{3-4}+\cdots \ldots \cdot \frac{(\sqrt{8}-\sqrt{9})}{8-9}=1−21−2+2−32−3+3−43−4+⋯…⋅8−9(8−9)
\Rightarrow \frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\cdots+\frac{1}{\sqrt{8}+\sqrt{9}}=(\sqrt{2}-1)+(\sqrt{3}-\sqrt{2})+(\sqrt{4}-\sqrt{3})+\cdots+(\sqrt{9}-\sqrt{8})⇒1+21+
