Answer:
117
Step-by-step explanation:
Let d represent the number of stamps Derek had at first. After he gave 1/9 of his stamps to Ahmad, Ahmad had (d -104) +(d/9). Derek had 4 times this number after giving away d/9 stamps:
(d -d/9) = 4((d -104) +d/9)
(8/9)d = 4d -416 +(4/9)d
416 = (32/9)d . . . . add 416 -8/9d
117 = d . . . . . . . . . . multiply by 9/32
Derek had 117 stamps at first.
_____
<em>Check</em>
1/9 of Derek's collection is 13 stamps. 104 less than Derek's collection is 13 stamps.
So, Ahmad started with 13 stamps and was given 13 stamps by Derek. Meanwhile, Derek started with 117 stamps and gave away 13, so ended with 104 stamps. That number (104) is 4 times Ahmad's new number (26), as it should be.
Answer:
4096π / 5
Step-by-step explanation:
∫∫∫ (x² + y² + z²) dV
In spherical coordinates, x² + y² + z² = r², and dV = r² sin φ dr dθ dφ.
E is the range 0 ≤ r ≤ 4, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π.
∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r²) (r² sin φ dr dθ dφ)
∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r⁴ sin φ) dr dθ dφ
Evaluate the first integral.
∫₀ᵖⁱ∫₀²ᵖⁱ (⅕ r⁵ sin φ)|₀⁴ dθ dφ
∫₀ᵖⁱ∫₀²ᵖⁱ (¹⁰²⁴/₅ sin φ) dθ dφ
¹⁰²⁴/₅ ∫₀ᵖⁱ∫₀²ᵖⁱ (sin φ) dθ dφ
Evaluate the second integral.
¹⁰²⁴/₅ ∫₀ᵖⁱ (θ sin φ)|₀²ᵖⁱ dφ
¹⁰²⁴/₅ ∫₀ᵖⁱ (2π sin φ) dφ
²⁰⁴⁸/₅ π ∫₀ᵖⁱ sin φ dφ
Evaluate the third integral.
²⁰⁴⁸/₅ π (-cos φ)|₀ᵖⁱ
²⁰⁴⁸/₅ π (-cos π + cos 0)
²⁰⁴⁸/₅ π (1 + 1)
⁴⁰⁹⁶/₅ π
Answer:
b=-19
Step-by-step explanation:
We know that one of the solutions is x=-4/5
That is a solution to x. So if we plug in (-4/5) into the x in the equation, then it should equal 0.
5(-4/5)^2+b(4/5)+12=0
Now, just solve for b.
5(16/25)+b(4/5)+12=0
(16/5)+(4/5)b+12=0
(76/5)+(4/5)b=0
(4/5)b=-(76/5)
b=-19
Answer:
Follows are the solution is this query:
Step-by-step explanation:
In point a:
The explicatory variable mostly on X-axis is obtained only at the two-dimensional level or the Y-axis dependent variables, instead of catching the information, they also get diffusion plotted in the attached file please find it.
In point b:
Draw on the scatter diagram as just below the minimum-square correlation axis, which is defined in the attached file please find it.
In point c:
From the plot above, a positive relationship among even in the analysis of bone density, the dominant and non-dominant Arm. They can forecast its bone using bone density throughout the non-dominant arm and the Dominant arm power. They can conclude from the slopes of its regression model, which is inside a non-dominant arm, each unit raises bone strength by 0.936 throughout the dominant atm.
