6)
91 is a composite number because it's divisible by 7 and 13
7)
477 is divisible by 3 and 9, since the sum of its digits (18) is divisible by 3 and 9 ( or the sum is a multiple of 3 and 9) .Not divisible by 6
8)
348:is divisible by 4 because the last 2 digits (48) are a multiple of 4
348:is NOT divisible by 5 because the last digit is neither 5 nor 0
348:is divisible by 6 because it's divisible by 2 and also by 3
9)
23624 is divisible by 8 because te last 3 digits (624) are divisible y 8
(624/8 =78)
None of the others are divisible by 8
10) A number is divisible by 6 IF IT'S DIVISIBLE BY 2 AND BY 3:
213 NO
468 is divisible by 2 since the last digit is divisible by 2. It's also divisible by
3 since the sum of its digits [18] is divisible by 3, hence 468 is divisible by 6
621 it's divisible by 3 but NOT by 2, then it's not divisible by 6
Answer:
8 seconds
Step-by-step explanation:
d(t)=400
4t^2+18t=400
4t^2+18t-400=0 subtract 400 from both sides
2t^2+9t-200=0 divide by 2 on both sides
x=8; -25/2 solve using quadratic formula
<span>(1 + cos² 3θ) / (sin² 3θ) = 2 csc² 3θ - 1
Starting with the left: Note that cos²θ + </span><span>sin²θ = 1.
In the same way: </span><span>cos²3θ + <span>sin²3θ = 1
</span></span>Therefore cos²3θ = 1 - <span>sin²3θ
</span> From the top: (1 + cos² 3θ) = 1 + 1 - sin²3θ = 2 - <span>sin²3θ
</span>
(1 + cos² 3θ) / (sin² 3θ) = (<span>2 - sin²3θ) / (sin² 3θ) = 2/</span><span>sin² 3θ - </span><span>sin²3θ/</span>sin²3θ
= 2/<span>sin² 3θ - 1; But 1/</span><span>sinθ = csc</span><span>θ, Similarly </span>1/sin3θ = csc3θ
= 2 *(1/sin<span>3θ)² - 1</span>
= 2csc²3θ - 1. Therefore LHS = RHS. QED.
<span>Wanda started walking along a path 27 seconds before Dave. Wanda walked at a constant rate of 3 feet per second. Dave walked along the same path at a constant rate of 4.5 feet per second. How long after Dave starts walking will he catch up with Wanda ?
***
let x=travel time of Dave
x+27=travel time of Wanda
speed*travel time=distance (same for both Wanda and dave)
..
4.5x=3(x+27)
4.5x=3x+81
1.5x=81
x=54
How long after Dave starts walking will he catch up with Wanda ? 54 sec</span>
This is an example of the quotient of powers property and tells us that when you divide powers with the same base you just have to subtract the exponents. When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1.
