Answer:
Step-by-step explanation:
We will first find the derivative of the function to get the formula for the slope of the tangent. Using implicit differentiation, we find that:
and
Solving for the derivative and at the same time simplifying within the parenthesis:
so
If our tangent line is vetical, that means that the slope is undefined. Our slope is undefined where y = 0. Therefore, we need to find x when y = 0 in our original equation. If y = 0, then
becomes
and
That means that x = 0 (we divide away the negative on the x, and since 0 isn't negative or positive, we get that x^4 = 0)
That means that the point at which the tangent is vertical is (0, 0)
Answer:
2.6
Step-by-step explanation:
Given:
f(x) = 0.80x
where,
f(x) = the cost
x = weight of apples in pounds
Pounds of apples = 3.25 pounds
Find the cost?
f(x) = 0.80x
Substitute into the equation x = 3.25
f(x) = 0.80x
= 0.80(3.25)
= 2.6
f(x) = 2.6
Therefore, the cost of 3.25 pounds of apples is 2.6
Let Q = quarters and D = dimes
There are a total of 1202 coins, so we have to add the quarters and dimes together to get this.
Q + D = 1202
Quarters have a value of 25 cents or 0.25, dimes have a value of 10 cents or 0.10. The combination of the amount of quarters and their respective value and the amount of dimes and their respective value equate to $123.50.
0.25Q + 0.10D = 123.50
Put the two equations together. Your system of equations is:
Q + D = 1202
0.25Q + 0.10D = 123.50
Answer:
<em>r</em>=2<em>p</em>
Step-by-step explanation:
If <em>r </em>is ruler and <em>p </em>is pen, ruler equals pen times 2, so its <em>r</em>=2<em>p</em>
Answer:
white: 1/3, blue: 1/4, red: 5/12
Step-by-step explanation:
Take the amount of balls each color has and divide by 12.
White:
4/12 = 1/3
Blue:
3/12 = 1/4
Red:
5/12 (can't simplify)