Answer:
Step-by-step explanation:
To calculate the lenght of the diagonal d across the square, we can assume that the square it is compound of two right triangles. So, we can resolve this exercise using The Pythagorean Theorem.
<em>The Pythagorean theorem</em> states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.
If in a right triangle there are legs of length a and b, and the measure of the hypotenuse is c, then the following relation is fulfilled:
a is the height, b is the base, and c is
the hypotenuse.
To obtain the value of the hypotenuse
To find the value of the lenght of the diagonal d across the square, we have:
Where a = b = 20
Substituting the values
Round the answer to 2 decimal places
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Answer:
The unit vector u is (-5/√29) i - (2/√29) j
Step-by-step explanation:
* Lets revise the meaning of unit vector
- The unit vector is the vector ÷ the magnitude of the vector
- If the vector w = xi + yj
- Its magnitude IwI = √(x² + y²) ⇒ the length of the vector w
- The unit vector u in the direction of w is u = w/IwI
- The unit vector u = (xi + yj)/√(x² + y²)
- The unit vector u = [x/√(x² + y²)] i + [y/√(x² + y²)] j
* Now lets solve the problem
∵ v = -5i - 2j
∴ IvI = √[(-5)² +(-2)²] = √[25 + 4] = √29
- The unit vector u = v/IvI
∴ u = (-5i - 2j)/√29 ⇒ spilt the terms
∴ u = (-5/√29) i - (2/√29) j
* The unit vector u is (-5/√29) i - (2/√29) j
Here are all of the answers:
1. yes, it is evenly divisible by 17 equally: 4,165 / 17 = 245
2. 194,610 / 26 = 7,485
3. 750 bananas divided equally by 50 students is 15 bananas per student:
750 / 50 = 15
4. 2400 / 15 = 160
5. 94,104 is not divisible by 12 evenly: 94,104 / 12 = 6,273.6
6. 44,237 / 31 = 1,427
7. 35 roses divided equally among 5 rows equals 7 roses per row: 35 / 5 = 7
8. 16,606 / 19 = 874
9. 83,525 is evenly divisible by 13: 83,525 / 13 = 6,425
10. $3,600 worth of toys divided by $18 per toy equals 200 toys: $3,600 / $18 = 200
6(f+4) + 2(f+4)
Use the distributive property:
6f+24 + 2f + 8
Now combine like terms:
8f +32
The answer is 8f + 32
