Answer:
20.07 cm³
Step-by-step explanation:
Volume of Cylinder = 1.54 liters = 1540 cm³.
Area of its base = 77 cm².
πr² = 77
(22/7) * r² = 77
r = 4.94
Now,
Volume of cylinder = πr²h
⇒ 1540 = (22/7) * (4.94)² * h
⇒ h = 20.07 cm³
Answer:
![\displaystyle \sf h( - 1) = - \frac{ 2}{3}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%20%5Csf%20h%28%20-%201%29%20%3D%20%20%20-%20%5Cfrac%7B%20%20%20%202%7D%7B3%7D%20)
Step-by-step explanation:
we are given a function
![\displaystyle \sf h(x) = \frac{2x - 6}{4 {x}^{2} + 8}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Csf%20h%28x%29%20%3D%20%20%5Cfrac%7B2x%20-%206%7D%7B4%20%7Bx%7D%5E%7B2%7D%20%20%2B%208%7D%20)
we would like to simplify it for h(-1)
in order to do so
substitute the value of x
![\displaystyle \sf h( - 1) = \frac{2 \cdot - 1- 6}{4 { (- 1)}^{2} + 8}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Csf%20h%28%20-%201%29%20%3D%20%20%5Cfrac%7B2%20%5Ccdot%20-%201-%206%7D%7B4%20%7B%20%28-%201%29%7D%5E%7B2%7D%20%20%2B%208%7D%20)
by order of PEMDAS
simplify square:
![\displaystyle \sf h( - 1) = \frac{2 \cdot - 1- 6}{4 { ( 1)}^{} + 8}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Csf%20h%28%20-%201%29%20%3D%20%20%5Cfrac%7B2%20%5Ccdot%20-%201-%206%7D%7B4%20%7B%20%28%201%29%7D%5E%7B%7D%20%20%2B%208%7D%20)
simplify multiplication:
![\displaystyle \sf h( - 1) = \frac{ - 2 - 6}{4 { }^{} + 8}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Csf%20h%28%20-%201%29%20%3D%20%20%5Cfrac%7B%20-%202%20-%206%7D%7B4%20%7B%20%7D%5E%7B%7D%20%20%2B%208%7D%20)
simplify addition:
![\displaystyle \sf h( - 1) = \frac{ - 2 - 6}{12}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Csf%20h%28%20-%201%29%20%3D%20%20%5Cfrac%7B%20-%202%20-%206%7D%7B12%7D%20)
simplify subtraction:
![\displaystyle \sf h( - 1) = \frac{ - 8}{12}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Csf%20h%28%20-%201%29%20%3D%20%20%5Cfrac%7B%20%20%20-%208%7D%7B12%7D%20)
reduce fraction:
![\displaystyle \sf h( - 1) = - \frac{ 2}{3}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%20%5Csf%20h%28%20-%201%29%20%3D%20%20%20-%20%5Cfrac%7B%20%20%20%202%7D%7B3%7D%20)
Var[2X + 3Y] = 2² Var[X] + 2 Cov[X, Y] + 3² Var[Y]
but since X and Y are given to be independent, the covariance term vanishes and you're left with
Var[2X + 3Y] = 4 Var[X] + 9 Var[Y]
X follows an exponential distribution with parameter <em>λ</em> = 1/6, so its mean is 1/<em>λ</em> = 6 and its variance is 1/<em>λ</em>² = 36.
Y is uniformly distributed over [<em>a</em>, <em>b</em>] = [4, 10], so its mean is (<em>a</em> + <em>b</em>)/2 = 7 and its variance is (<em>b</em> - <em>a</em>)²/12 = 3.
So you have
Var[2X + 3Y] = 4 × 36 + 9 × 3 = 171
An arrowhead or point is the usually sharpened and hardened tip of an arrow, which contributes a majority of the projectile mass and is responsible for impacting and penetrating a target, as well as to fulfill some special purposes such as signaling.
Answer:
A
Step-by-step explanation: