Answer:
x ≈ 14.30
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Trigonometry</u>
- sin∅ = opposite over hypotenuse
Step-by-step explanation:
<u>Step 1: Define variables</u>
∅ = 39°
opposite leg = 9
hypotenuse = x
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute: sin39° = 9/x
- Multiply <em>x</em> on both sides: xsin39° = 9
- Isolate <em>x</em>: x = 9/sin39°
- Evaluate: x = 14.3011
- Round: x ≈ 14.30
Which of the following is the simplified form of [1] fifth root of x times the [2] fifth root of x times [3] the fifth root of x times [4] the fifth root of x?
That's
![( \sqrt[5] x)^4 = x^{\frac 4 5}](https://tex.z-dn.net/?f=%20%28%20%5Csqrt%5B5%5D%20x%29%5E4%20%3D%20x%5E%7B%5Cfrac%204%205%7D)
That looks like the second choice.
Answer:
a)z1 +z2 =z2 + z1 ...proved.
b) z1 + ( z2+ z3 )=(z1+z2)+z3 ... proved.
Step-by-step explanation:
It is given that there are three vectors z1 = a1 + ib1, z2 = a2 + ib2 and z3 = a3 + ib3. Now, we have to prove (a) z1 + z2 = z2 + z1 and (b) z1 + (z2 +z3) = (z1 + z2) + z3.
(a) z1 + z2 = (a1 +ib1) + (a2+ ib2) = (a1 +a2) + i(b1 +b2) {Adding the real and imaginary parts separately}
Again, z2 + z1 =(a2 +ib2) + (a1 +ib1) = (a2 +a1) + i(b2 +b1) {Adding the real and imaginary parts separately}
Hence, z1 +z2 =z2 + z1 {Since, (a1 +a2) = (a2 +a1) and (b1 +b2) = (b2 +b1)}
(b) z1 + ( z2+ z3 ) = [a1 + ib1] + [(a2 + a3 ) + i(b2 + b3 )] = ( a1 + a2 + a3) + i( b1+ b2+b3) {Adding the real and imaginary parts separately}
Again, (z1+z2)+z3 = [(a1+a2) +i(b1+b2)]+[a3+ib3] = ( a1 + a2 + a3) + i( b1+ b2+b3) {Adding the real and imaginary parts separately}
Hence, z1 + ( z2+ z3 )=(z1+z2)+z3 proved.
In a direct variation relationship the values must satisfy that y = kx. This si y is always a constant value (k) times x.
So, you can find multiple values that meet this:
y = kx => k = y / x = 11 / 18
=> y = (11/18)x
Now you can give any value to x and fint the value of x that satisfy the relationship:
x y = (11/18)x
1 11/18
2 11/18 * 2 = 11/9
18 11/18 * 18 = 11
36 11/18 * 36 = 22
So, there you have several additional values for x and y in the same relationship that y = 11 and x = 18, and you can find many more using the same rule: y = (11/18)*x
1 ton= 2,000 pounds
250 x 8 = 2,000
final answer: it would take the elephant 8 days to eat a ton of food
*HOPE I HELPED!*
