Answer: (a) e ^ -3x (b)e^-3x
Step-by-step explanation:
I suggest the equation is:
d/dx[integral (e^-3t) dt
First we integrate e^-3tdt
Integral(e ^ -3t dt) as shown in attachment and then we differentiate the result as shown in the attachment.
(b) to differentiate the integral let x = t, and substitute into the expression.
Therefore dx = dt
Hence, d/dx[integral (e ^-3x dx)] = e^-3x
(2.6 * 10^9) / (1.3 * 10^2) =
(2.6 / 1.3) * (10^9) / (10^2) =
2 * 10^7 or 20,000,000 <===
Answer:
12:6 or $12 for every $6 he saves
Step-by-step explanation:
If he spends $6.00 for every $3.00, he would save $6 if he spends $12. In this case you could multiple or divide 6 by any number, and do the same to 3 to get an equivalent ratio. Ex. Multiple 6 times 2 to get $12 and 3 times 2 to get $6.
784/4 = 196
196 * 4 = 784
4 * 196 = 784
So the answer is : 196
For this case we have the following expression:
![2(\sqrt[4]{16x})-2(\sqrt[4]{2y})+3(\sqrt[4]{81x})-4(\sqrt[4]{32y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B16x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B81x%7D%29-4%28%5Csqrt%5B4%5D%7B32y%7D%29)
Rewriting the numbers within the roots we have:
![2(\sqrt[4]{2*2*2*2x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3*3*3*3x})-4(\sqrt[4]{2*2*2*2*2y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%2A3%2A3%2A3x%7D%29-4%28%5Csqrt%5B4%5D%7B2%2A2%2A2%2A2%2A2y%7D%29)
Then, by properties of powers we have:
![2(\sqrt[4]{2^4x})-2(\sqrt[4]{2y})+3(\sqrt[4]{3^4x})-4(\sqrt[4]{2^42y})](https://tex.z-dn.net/?f=2%28%5Csqrt%5B4%5D%7B2%5E4x%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%28%5Csqrt%5B4%5D%7B3%5E4x%7D%29-4%28%5Csqrt%5B4%5D%7B2%5E42y%7D%29)
Then, by radical properties we have:
![2(2\sqrt[4]{x})-2(\sqrt[4]{2y})+3(3\sqrt[4]{x})-4(2\sqrt[4]{2y})](https://tex.z-dn.net/?f=2%282%5Csqrt%5B4%5D%7Bx%7D%29-2%28%5Csqrt%5B4%5D%7B2y%7D%29%2B3%283%5Csqrt%5B4%5D%7Bx%7D%29-4%282%5Csqrt%5B4%5D%7B2y%7D%29)
Rewriting the expression we have:
![4\sqrt[4]{x}-2\sqrt[4]{2y}+9\sqrt[4]{x}-8\sqrt[4]{2y}](https://tex.z-dn.net/?f=4%5Csqrt%5B4%5D%7Bx%7D-2%5Csqrt%5B4%5D%7B2y%7D%2B9%5Csqrt%5B4%5D%7Bx%7D-8%5Csqrt%5B4%5D%7B2y%7D)
Finally, adding similar terms we have:
![(4+9)\sqrt[4]{x}-(2+8)\sqrt[4]{2y}](https://tex.z-dn.net/?f=%284%2B9%29%5Csqrt%5B4%5D%7Bx%7D-%282%2B8%29%5Csqrt%5B4%5D%7B2y%7D)
![13\sqrt[4]{x}-10\sqrt[4]{2y}](https://tex.z-dn.net/?f=13%5Csqrt%5B4%5D%7Bx%7D-10%5Csqrt%5B4%5D%7B2y%7D)
Answer:
The simplified form of the expression is:
