Answer:
Savannah's age = 6 years
Step-by-step explanation:
Let
Savannah's age = x
Dylan's age = 15
Dylan is 15, which is 3 years older than twice his sister Savannah’s age
Dylan = 2x + 3
Find Savannah's age
2x + 3 = 15
Subtract 3 from both sides
2x + 3 - 3 = 15 - 3
2x = 12
Divide both sides by 2
2x / 2 = 12 / 2
x = 6
Therefore,
Savannah's age = x
= 6 years
Dylan's age = 2x +3
= 2*6 + 3
= 12 + 3
= 15 years
PEMDAS
12*(3/4) comes first
8+9=17
tis a little of plain differentiation.
we know the radius of the cone is decreasing at 10 mtr/mins, or namely dr/dt = -10, decreasing, meaning is negative.
we know the volume is decreasing at a rate of 1346 mtr/mins or namely dV/dt = -1346, also negative.
so, when h = 9 and V = 307, what is dh/dt in essence.
we'll be needing the "r" value at that instant, so let's get it
now let's get the derivative of the volume of the cone
![V=\cfrac{1}{3}\pi r^2 h\implies \cfrac{dV}{dt}=\cfrac{\pi }{3}\stackrel{product~rule}{ \left[ \underset{chain~rule}{2r\cdot \cfrac{dr}{dt}}\cdot h+r^2\cdot \cfrac{dh}{dt} \right]} \\\\\\ -1346=\cfrac{\pi }{3}\left[2\sqrt{\cfrac{307}{3\pi }}(-10)(9)~~+ ~~ \cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\right]](https://tex.z-dn.net/?f=V%3D%5Ccfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%5Cimplies%20%5Ccfrac%7BdV%7D%7Bdt%7D%3D%5Ccfrac%7B%5Cpi%20%7D%7B3%7D%5Cstackrel%7Bproduct~rule%7D%7B%20%5Cleft%5B%20%5Cunderset%7Bchain~rule%7D%7B2r%5Ccdot%20%5Ccfrac%7Bdr%7D%7Bdt%7D%7D%5Ccdot%20h%2Br%5E2%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%20%5Cright%5D%7D%20%5C%5C%5C%5C%5C%5C%20-1346%3D%5Ccfrac%7B%5Cpi%20%7D%7B3%7D%5Cleft%5B2%5Csqrt%7B%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%7D%28-10%29%289%29~~%2B%20~~%20%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%20%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cright%5D)
![-\cfrac{4038}{\pi }=-\cfrac{180\sqrt{307}}{\sqrt{3\pi }}+\cfrac{307}{3\pi } \cdot \cfrac{dh}{dt}\implies \left[ -\cfrac{4038}{\pi }+\cfrac{180\sqrt{307}}{\sqrt{3\pi }} \right]\cfrac{3\pi }{307}=\cfrac{dh}{dt} \\\\\\ -\cfrac{12114}{307}+\cfrac{180\sqrt{3\pi }}{\sqrt{307}}=\cfrac{dh}{dt}\implies -7.920939735970634 \approx \cfrac{dh}{dt}](https://tex.z-dn.net/?f=-%5Ccfrac%7B4038%7D%7B%5Cpi%20%7D%3D-%5Ccfrac%7B180%5Csqrt%7B307%7D%7D%7B%5Csqrt%7B3%5Cpi%20%7D%7D%2B%5Ccfrac%7B307%7D%7B3%5Cpi%20%7D%20%5Ccdot%20%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cimplies%20%5Cleft%5B%20-%5Ccfrac%7B4038%7D%7B%5Cpi%20%7D%2B%5Ccfrac%7B180%5Csqrt%7B307%7D%7D%7B%5Csqrt%7B3%5Cpi%20%7D%7D%20%5Cright%5D%5Ccfrac%7B3%5Cpi%20%7D%7B307%7D%3D%5Ccfrac%7Bdh%7D%7Bdt%7D%20%5C%5C%5C%5C%5C%5C%20-%5Ccfrac%7B12114%7D%7B307%7D%2B%5Ccfrac%7B180%5Csqrt%7B3%5Cpi%20%7D%7D%7B%5Csqrt%7B307%7D%7D%3D%5Ccfrac%7Bdh%7D%7Bdt%7D%5Cimplies%20-7.920939735970634%20%5Capprox%20%5Ccfrac%7Bdh%7D%7Bdt%7D)
Answer:
a(n)=1+(n-1)(-3)
Step-by-step explanation:
Notice there's a common difference of d=-3.
If we use the formula a(n)=a1+(n-1)d to find the nth term given the first term and the common difference, we will see that the function that describes the arithmetic sequence as a(n)=1+(n-1)(-3)
Problem 3: Let x = price of bag of pretzels Let y = price of box of granola bars
We have Lesley's purchase: 4x+2y=13.50
And Landon's: 1x+5y=17.55
We can use the elimination method. Let's negate Landon's purchase by multiplying by -1. -1x-5y=-17.55
We add this four times to Lesley's purchase to eliminate the x variable.
2y-20y=13.50-70.2
-18y=-56.7
y = $3.15 = Price of box of granola bars
Plug back into Landon's purchase to solve for pretzels.
x+5*3.15=17.55
x+15.75=17.55
x = $1.80 = price of bag of pretzels
Problem 4.
Let w = number of wood bats sold
Let m = number of metal bats sold
From sales information we have: w + m = 23
24w+30m=606
Substitution works well here. Solve for w in the first equation, w = 23 - m, and plug this into the second.
24*(23-m)+30m=606
552-24m+30m=606
6m=54
m=9 = number of metal bats sold
Therefore since w = 23-m, w = 23-9 = 14. 14 wooden bats were sold.
