If f(y) = 8 + e-9y, find f'(y). Use exact values.

Mathematics

1 answer:

mestny [16]3 years ago

3 0

Answer:

$f'(y) = -9e^{-9y}$

Step-by-step explanation:

The given function is :

$f(y) = 8 + e^{-9y}$

We need to find the value of f'(y).

$f'(y)=\dfrac{d}{dy}[8+e^{-9y}]$

$=\dfrac{d}{dy}(8)+\dfrac{d}{dy}(e^{-9y})\\\\=0+e^{-9y}\dfrac{d}{dy}(-9y)\\\\=-9e^{-9y}$

So, the value of f'(y) is equal to $-9e^{-9y}$ .

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!!Please Help!! Find the value of z to the nearest tenth.

serg [7]

Answer:

x = 14 $\sqrt{2}$

y = 14

z= 14 $\sqrt{3}$

Step-by-step explanation:

Notice that the top triangle is a 45-45-90 triangle and the triangle below is a 30-60-90 triangle.

Using the fact that the top triangle is a 45-45-90 triangle and also an isosceles triangle, we can see that x will be the same as its respective leg, 14 $\sqrt{2}$

Now, we must find a side length of the bottom triangle. We can use the Pythagorean Theorem to find the third side of the top triangle, which is also a side of the bottom triangle. We can find that the third side must be 28. We can now use this to find the other sides of the bottom triangle.

Since y is opposite to the 30 degree angle, it is half of the hypotenuse. The hypotenuse which we found earlier is 28, therefore, y is 14. z is then 14 $\sqrt{3}$ using either Pythagorean Theorem or special right triangle properties for 30-60-90.

7 0

3 years ago

51 times the difference between a number and 21 is equal to the number plus 58.

Lerok [7]

51(x - 21) = x + 58

Distributive property

51x - 1071 = x + 58

Subtract x from both sides

50x - 1071 = 58

Add 1071 to both sides

50x = 1129

Divide both sides by 50