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SashulF [63]
3 years ago
11

At a restaurant you only have $30 to spend on dinner. In addition to the cost of the meal you must pay a 8% sales tax and leave

a 20% tip. What is the most expensive item you can order?

Mathematics
1 answer:
DIA [1.3K]3 years ago
5 0
Grand Total: $29.81
Total Bill: $24.84
Sales Tax (8%): $1.84
Total Tip (20%): $4.97
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(1 point) (a) Find the point Q that is a distance 0.1 from the point P=(6,6) in the direction of v=⟨−1,1⟩. Give five decimal pla
natima [27]

Answer:

following are the solution to the given points:

Step-by-step explanation:

In point a:

\vec{v} = -\vec{1 i} +\vec{1j}\\\\|\vec{v}| = \sqrt{-1^2+1^2}

    =\sqrt{1+1}\\\\=\sqrt{2}

calculating unit vector:

\frac{\vec{v}}{|\vec{v}|} = \frac{-1i+1j}{\sqrt{2}}

the point Q is at a distance h from P(6,6) Here, h=0.1  

a=-6+O.1 \times \frac{-1}{\sqrt{2}}\\\\= 5.92928 \\\\b= 6+O.1 \times \frac{-1}{\sqrt{2}} \\\\= 6.07071

the value of Q= (5.92928 ,6.07071  )

In point b:

Calculating the directional derivative of f (x, y) = \sqrt{x+3y} at P in the direction of \vec{v}

f_{PQ} (P) =\fracx{f(Q)-f(P)}{h}\\\\

            =\frac{f(5.92928 ,6.07071)-f(6,6)}{0.1}\\\\=\frac{\sqrt{(5.92928+ 3 \times 6.07071)}-\sqrt{(6+ 3\times 6)}}{0.1}\\\\= \frac{0.197651557}{0.1}\\\\= 1.97651557

\vec{v} = 1.97651557

In point C:

Computing the directional derivative using the partial derivatives of f.

f_x(x,y)= \frac{1}{2 \sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{2 \sqrt{22}}\\\\f_x(x,y)= \frac{1}{\sqrt{x+3y}}\\\\ f_x (6,6)= \frac{1}{\sqrt{22}}\\\\f_{(PQ)}(P)= (f_x \vec{i} + f_y \vec{j}) \cdot \frac{\vec{v}}{|\vec{v}|}\\\\= (\frac{1}{2 \sqrt{22}}\vec{i} + \frac{1}{\sqrt{22}} \vec{j}) \cdot   \frac{-1}{\sqrt{2}}\vec{i} + \frac{1}{\sqrt{2}} \vec{j}

4 0
3 years ago
If these two shapes are similar, what is the measure of the missing length n?
scoundrel [369]

Answer:

39in.

Step-by-step explanation:

due to scale, cant be 15, as that would be the same length as other side

cant be 91 otherwise it wouldnt be similar if it had the same length as blue triangle which has 39 not 15 as the top side

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In your own words, explain why when we multiply terms that have the same bases, we add the exponents.
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When multiplying exponents, remember the first rule: when multiplying similar bases, add powers together. 52% + 56% =? The bases of the equation remain unchanged, while the exponents' values are added together. Adding the exponents is only a quick way to get at the answer. Simply add the exponents to multiply exponential expressions with the same base. Simplify. The product rule applies because the base of both exponents is a. With a common basis, add the exponents.

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