Answer:
137/(36π) ft/s
Step-by-step explanation:
The rate of change of volume will be the product of the rate of change of radius and the area of the sphere. The area of the sphere is ...
A = 4πr² = 4π(6 ft)² = 144π ft²
Then the relationship above is ...
dV/dt = A·dr/dt
548 ft³/s = (144π ft²)·dr/dt
dr/dt = (548 ft³/s)/(144π ft²) = 137/(36π) ft/s ≈ 1.2113 ft/s
Answer:
y = -1
x = -1
Step-by-step explanation:
Answer:
<h2>(h + k)(2) = 5</h2>
Step-by-step explanation:
![(h+k)(x)=h(x)+k(x)\\\\\bold{METHOD\ 1:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(k+h)(2)=h(2)+k(2)\\\\\text{Calculate}\ h(2)\ \text{and}\ k(2).\\\text{Put}\ x=2\ \text{to the equations of the functions}\\\\h(2)=2^2+1=4+1=5\\k(2)=2-2=0\\\\\text\\\\\text{Substitute:}\\\\(h+k)(2)=5+0=5](https://tex.z-dn.net/?f=%28h%2Bk%29%28x%29%3Dh%28x%29%2Bk%28x%29%5C%5C%5C%5C%5Cbold%7BMETHOD%5C%201%3A%7D%5C%5C%5C%5Ck%28x%29%3Dx-2%2C%5C%20h%28x%29%3Dx%5E2%2B1%5C%5C%5C%5C%28k%2Bh%29%282%29%3Dh%282%29%2Bk%282%29%5C%5C%5C%5C%5Ctext%7BCalculate%7D%5C%20h%282%29%5C%20%5Ctext%7Band%7D%5C%20k%282%29.%5C%5C%5Ctext%7BPut%7D%5C%20x%3D2%5C%20%5Ctext%7Bto%20the%20equations%20of%20the%20functions%7D%5C%5C%5C%5Ch%282%29%3D2%5E2%2B1%3D4%2B1%3D5%5C%5Ck%282%29%3D2-2%3D0%5C%5C%5C%5C%5Ctext%5C%5C%5C%5C%5Ctext%7BSubstitute%3A%7D%5C%5C%5C%5C%28h%2Bk%29%282%29%3D5%2B0%3D5)
![\bold{METHOD\ 2:}\\\\k(x)=x-2,\ h(x)=x^2+1\\\\(h+k)(x)=h(x)+k(x)=(x^2+1)+(x-2)=x^2+x-1\\\\(h+k)(2)-\text{put}\ x=2\\\\(h+k)(2)=2^2+2-1=4+2-1=6-1=5](https://tex.z-dn.net/?f=%5Cbold%7BMETHOD%5C%202%3A%7D%5C%5C%5C%5Ck%28x%29%3Dx-2%2C%5C%20h%28x%29%3Dx%5E2%2B1%5C%5C%5C%5C%28h%2Bk%29%28x%29%3Dh%28x%29%2Bk%28x%29%3D%28x%5E2%2B1%29%2B%28x-2%29%3Dx%5E2%2Bx-1%5C%5C%5C%5C%28h%2Bk%29%282%29-%5Ctext%7Bput%7D%5C%20x%3D2%5C%5C%5C%5C%28h%2Bk%29%282%29%3D2%5E2%2B2-1%3D4%2B2-1%3D6-1%3D5)
It would take 3 bottles. 25 twelve-ounce cups equals out to 300 ounces. There is only 128 ounces in a gallon.
Multiply the amount she puts in the account every week by the number of weeks (w) and add that to what she already has saved:
20w + 600 >= 2000