To start a board game, the player who rolls two sixes gets to go first. What is the probability that a player will roll two

1. Sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. (a) How fast is

solong [7]

Answer:

The volume is increasing at a rate of 16286 in³/min.

Step-by-step explanation:

a) The volume of a cone is given by:

$V = \frac{1}{3}h\pi r^{2}$

Where:

r: is the radius

h: is the height

The rate of change of the volume can be calculated by using the chain rule:

$\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]$

Since h = 4/3 r we have:

$\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]$

$\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}]$

$\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}]$ (1)

With:

$\frac{dr}{dt}$ = 3 in/min

$r = 3 ft*\frac{12 in}{1 ft} = 36 in$

And by entering the above values into equation (1) we have:

$\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]$

$\frac{dV}{dt} = 16286 in^{3}/min$

Therefore, the volume is increasing at a rate of 16286 in³/min.

I hope it helps you!

3 0

3 years ago

Triangle IJK is similar to triangle LMN. Find the measure of side LM. Round your answer to the nearest tenth if necessary.

Andre45 [30]

Answer:

It's either 39.2 or 39.3 (a more accurate answer) because it depends on what you round by. since it's Delta Math, you should get 2 attempts.

Step-by-step explanation:

Since they are similar, they are proportional.

54/11=4.90909091 or 4.9

Multiply 11 by 4.90909091 and you get 54

Multiply 8 by 4.90909091 and you get 39.3

if you multiply by 4.9 you get 39.2

8 0

2 years ago

The number of miles USC employees commute to campus is normally distributed. To estimate the mean of this distribution, four emp

Aleksandr [31]

Yfiyfidy. It’s soot ioydotdi

It’s Bc. H. Dey h. Yes so I’m hehe what crazy now

7 0

2 years ago

Value of P: 3/15(p+10)=-15

ArbitrLikvidat [17]

Step 1 : 1 Simplify — 5 Equation at the end of step 1 : 1 (— • (p + 10)) - -15 = 0 5 Step 2 :Equation at the end of step 2 : (p + 10) ———————— - -15 = 0 5 Step 3 :Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 5 as the denominator :

-15 -15 • 5 -15 = ——— = ——————— 1 5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(p+10) - (-15 • 5) p + 85 —————————————————— = —————— 5 5 Equation at the end of step 3 : p + 85 —————— = 0 5 Step 4 :When a fraction equals zero : 4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

p+85 ———— • 5 = 0 • 5 5

Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
p+85 = 0

Solving a Single Variable Equation :

4.2 Solve : p+85 = 0

Subtract 85 from both sides of the equation :
 p = -85

One solution was found : p = -85

7 0

3 years ago

Choose the correct translation of the following statement into symbolic form using the uppercase letters available. If neither w

Over [174]

Answer:

¬(W∨S)→¬(J∨E)

D→(B∨C)

X is true

No

Step-by-step explanation:

The hypotheses "neither water nor soft drinks can quench your thirst" translates to ¬(W∨S) ("neither nor" negates the disjunction W∨S). The "if,... then" translates to the implication symbol (arrow). The conclusion "juice will not do it, unless the juice contains electrolytes" translates to ¬(J∨E). This is because if J or E were true, then J would be true (because E implies J), contrary to the conclusion that J is false ("juice will not do it"), then J∨S is false.

The hypothesis here is "the dyer breaks" hence D is the hypothesis. The conclusion is "we will hang the clothes to dry, or take the clothes to a coin-operated laundry" which is the same as (B∨C).

The proposition p→p is always true (according to truth tables). In this case, p:=X is true, then p is true and X is true.

X∨Y is false if and only if X is false and Y is false, so both statements X,Y must be false.

5 0

3 years ago