The shadow of the tree is 12ft long. Divide the height of the tree (24) by Victors height (6), which will equal 4. Then multiple 4 and the height of victors shadow. (this is my first time doing this, hope it helped:)
Answer:
If you are asking what is 40% of 50,000, then it should be 20,000.
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
given the expression
7x²y
to evaluate substitute x = 5 and y = 3 into the expression
= 7 × 5² × 3
= 7 × 25 × 3 = 175 × 3 = 525 → c
Answer:
Step-by-step explanation:
Given the equation 4x²+ 49y² = 196
a) Differentiating implicitly with respect to y, we have;
![8x + 98y\frac{dy}{dx} = 0\\98y\frac{dy}{dx} = -8x\\49y\frac{dy}{dx} = -4x\\\frac{dy}{dx} = \frac{-4x}{49y}](https://tex.z-dn.net/?f=8x%20%2B%2098y%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%200%5C%5C98y%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20-8x%5C%5C49y%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20-4x%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B49y%7D)
b) To solve the equation explicitly for y and differentiate to get dy/dx in terms of x,
First let is make y the subject of the formula from the equation;
If 4x²+ 49y² = 196
49y² = 196 - 4x²
![y^{2} = \frac{196}{49} - \frac{4x^{2} }{49} \\y = \sqrt{\frac{196}{49} - \frac{4x^{2} }{49} \\} \\](https://tex.z-dn.net/?f=y%5E%7B2%7D%20%3D%20%20%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D%20%5C%5Cy%20%3D%20%5Csqrt%7B%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D%20%5C%5C%7D%20%5C%5C)
Differentiating y with respect to x using the chain rule;
Let ![u= \frac{196}{49} - \frac{4x^{2} }{49}](https://tex.z-dn.net/?f=u%3D%20%20%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D)
![y = \sqrt{u} \\y =u^{1/2} \\](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7Bu%7D%20%5C%5Cy%20%3Du%5E%7B1%2F2%7D%20%5C%5C)
![\frac{dy}{dx} = \frac{dy}{du} * \frac{du}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%5Cfrac%7Bdy%7D%7Bdu%7D%20%2A%20%5Cfrac%7Bdu%7D%7Bdx%7D)
![\frac{dy}{du} = \frac{1}{2}u^{-1/2} \\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdu%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7Du%5E%7B-1%2F2%7D%20%5C%5C)
![\frac{du}{dx} = 0 - \frac{8x}{49} \\\frac{du}{dx} =\frac{-8x}{49} \\\frac{dy}{dx} = \frac{1}{2} ( \frac{196}{49} - \frac{4x^{2} }{49})^{-1/2} * \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} ( \frac{196-4x^{2} }{49})^{-1/2} * \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} ( \sqrt{ \frac{49}{196-4x^{2} })} * \frac{-8x}{49}\\\frac{dy}{dx} = \frac{1}{2} *{ \frac{7}\sqrt {196-4x^{2} }} * \frac{-8x}{49}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%20%200%20-%20%5Cfrac%7B8x%7D%7B49%7D%20%5C%5C%5Cfrac%7Bdu%7D%7Bdx%7D%20%3D%5Cfrac%7B-8x%7D%7B49%7D%20%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Cfrac%7B196%7D%7B49%7D%20%20-%20%5Cfrac%7B4x%5E%7B2%7D%20%7D%7B49%7D%29%5E%7B-1%2F2%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%20%5Cfrac%7B196-4x%5E%7B2%7D%20%7D%7B49%7D%29%5E%7B-1%2F2%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Csqrt%7B%20%5Cfrac%7B49%7D%7B196-4x%5E%7B2%7D%20%7D%29%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%7B%20%5Cfrac%7B7%7D%5Csqrt%20%7B196-4x%5E%7B2%7D%20%7D%7D%20%2A%20%20%5Cfrac%7B-8x%7D%7B49%7D%5C%5C)
![\frac{dy}{dx} = \frac{-4x}{7\sqrt{196-4x^{2} } }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B7%5Csqrt%7B196-4x%5E%7B2%7D%20%7D%20%7D)
c) From the solution of the implicit differentiation in (a)
![\frac{dy}{dx} = \frac{-4x}{49y}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B49y%7D)
Substituting
into the equation to confirm the answer of (b) can be shown as follows
![\frac{dy}{dx} = \frac{-4x}{49\sqrt{\frac{196-4x^{2} }{49} } }\\\frac{dy}{dx} = \frac{-4x}{49\sqrt{196-4x^{2}}/7} }\\\\\frac{dy}{dx} = \frac{-4x}{7\sqrt{196-4x^{2}}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-4x%7D%7B49%5Csqrt%7B%5Cfrac%7B196-4x%5E%7B2%7D%20%7D%7B49%7D%20%7D%20%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%20%5Cfrac%7B-4x%7D%7B49%5Csqrt%7B196-4x%5E%7B2%7D%7D%2F7%7D%20%7D%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%20%5Cfrac%7B-4x%7D%7B7%5Csqrt%7B196-4x%5E%7B2%7D%7D%7D)
This shows that the answer in a and b are consistent.
8, 1 on top 2 and keep going . answer 8