Answer:
a) 20
Step-by-step explanation:
when we have an exponent of an exponent, we simply multiply them for the overall exponent.
so, we actually have
a^((1/4)×12) × b^((1/3)×12) = a³b⁴ = 5000
let's find the prime factors of 5000 :
5000 ÷ 2 = 2500
2500 ÷ 2 = 1250
1250 ÷ 2 = 625
625 ÷ 3 no
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
so,
5000 = 2³ × 5⁴
so, a = 2, b = 5
a²b = 2²×5 = 4×5 = 20
Answer:
15.13 cm
Step-by-step explanation:
We are given:
Lateral surface area of a right circular cone : πr√r² + h²
From the question, we know that:
Lateral surface area = 236.64cm²
Radius = 4.75cm
Height = ?
Making h the subject of the formula
h = √[(A/r)² - πr²]/π
h = √[(236.64/4.75)² - π ×4.75²]/π
h = √(2481.9275169 - 70.882184247)/π
h = 15.12975 cm
Approximately to the nearest hundredth = 15.13cm
<span>[ (1 / 36) - (1 / x²) ] / [ (1 / 6) + (1 / x) ]
[ (x² - 36) / 36x² ] / [ (x + 6) / 6x ]
</span>remember that<span>:
x² - 36 = (x + 6)(x - 6)
so
[ (x+6)(x-6) / 36x² ] / [ (x + 6) / 6x ]
[ (x+6)(x-6) / 36x² ] * [ 6x / (x + 6) ]
6x / 36x² = 1 / 6x
[ (x+6)(x-6) / 6x ] * [ 1 / (x+6) ] -------------------- > </span>(x - 6) / 6x<span>
The answer is </span>(x - 6) / 6x<span>
</span>
Answer:
5/(1/2)(3.9)(4)² - 2/(2/5)(3.9)(4)² - 1/(3/5)(3.9)(4)² - 1/2(3.9)(4)²
Convert mixed numbers to improper fractions,
11/2(3.9)(4)² - 12/45(3.9)(4)² - 8/5(3.9)(4)² - 1/2(3.9)(4)²
Remove bracket,
11/2 × 3.9 × 4² - 12/45 × 3.9 × 4² - 8/5 × 3.9 × 4² - 1/2 × 3.9 × 4²
Factor out common term 3.9 × 4²,
3.9 × 4² (11/2 - 12/5 - 8/5 - 1/2)
Times,
3.9 × 16
Answer,
62.4
Tan(theta)= pi
Now, in order for you to find the angle (theta), you would inverse tan both the left and the right to find the value. The inverse of tan is tan^-1.
tan(theta)=pi ---> theta = tan^-1(pi)
Then, you would plug tan^-1(pi) into a calculator, giving you the value
1.26