| u | = √(2² + (-1²)) = √5
| v | = √ ( 1² + (-8)² = √65
cos (u,v) = ( u * v ) / (| u | * | v |) =
(2 * 1 + ( -1 ) * ( - 8 )) / √5 √ 65 = (2 + 8) / √5 √65 = 10 / (√5 √ 65 )
The length of a larger diagonal:
d 1² = | u |² + 2 |u| |v| + | v |² = 5 + (2 √5 √65 * 10 / √5 √65 )+65
d 1² = 70 + 20 = 90
d 1 = √ 90 = 3√10
d 2² = 70 - 20 = 50
d 2 = √50 = 5√2
Answer:
The lengths of the diagonals are: 3√10 and 5√2 .
Volume of a volleyball (a sphere) = 4/3πr³
= 4/3π(11.4)³
= 1975.392π
= 6210 cm³ (to 3 significant figures)
The volume of a volleyball with a radius of 11.4 cm will be 6210 cm³.
Suppose that both planets are spherical. radius of Saturn =142984/2=71,492
Area of Jupiter = 4πr² ==>4π(71,492)² =6.4228 x 10^10
Area of Saturn ==>(6.4228 x 10^10)x(0.599) ==>3,84726 x 10^10
Radius of Saturn = 4πr² =3,84726 x 10^10==> r²=3,0219 x 10^10
and r √(,0219 x 10^10) = 174.000 km & D = 384,000 km
Answer:
(x - 5)² = 41
Step-by-step explanation:
* Lets revise the completing square form
- the form x² ± bx + c is a completing square if it can be put in the form
(x ± h)² , where b = 2h and c = h²
# The completing square is x² ± bx + c = (x ± h)²
# Remember c must be positive because it is = h²
* Lets use this form to solve the problem
∵ x² - 10x = 16
- Lets equate 2h by -10
∵ 2h = -10 ⇒ divide both sides by 2
∴ h = -5
∴ h² = (-5)² = 25
∵ c = h²
∴ c = 25
- The completing square is x² - 10x + 25
∵ The equation is x² - 10x = 16
- We will add 25 and subtract 25 to the equation to make the
completing square without change the terms of the equation
∴ x² - 10x + 25 - 25 = 16
∴ (x² - 10x + 25) - 25 = 16 ⇒ add 25 to both sides
∴ (x² - 10x + 25) = 41
* Use the rule of the completing square above
- Let (x² - 10x + 25) = (x - 5)²
∴ (x - 5)² = 41
Step-by-step explanation:
7z-5=4y-6
-4y=-6-7z+5
-4y=-1-7z
y=1/4+7/4z
y=7/4z+1/4
7z=4y-6+5
7z=4y-1
z=4/7y-1/7
