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3 years ago

If x^2+y^2 =25 and dy/dt =6, find dx/dt when y=4

1 answer:

4 0

2x dx/dt +2y dy/dt =0
x dx/dt +y (6)=0
dx/dt= -6y/x
dx/dt= -6*4 /x
dx/dt=-24/x
<span>also from the given equation x^2= 25-16=9 or x=3
using this we get</span>
dx/dt=-24/3 =-8

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Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what coul

aev [14]

The length of the rug is 4 ft.

The width of the rug is 2.5 ft.

Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

Let us convert the inches to feet.

Thus, $18 inches = 1.5 ft$

Thus, the length of the rug is $l=1.5+w$

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

$A=length\times width$

$10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0$

Solving the expression using the quadratic formula,

$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Substituting the values, we have,

$$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\$

$w=\frac{-15 \pm \sqrt{4225}}{20}$

$w=\frac{-15 \pm 65}{2 0}$

Thus,

$w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5$ and $w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4$

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

Substituting $w=2.5$ in $l=1.5+w$ , we get,

$l=1.5+2.5\\l=4$

Thus, the length of the rug is 4 ft.

4 0

3 years ago

The price for strawberries is currently $ 6.40 per pack. next week,strawberries will be on sale at a 20% discount. what is the t

notka56 [123]

Answer:

answer is $5.12

Step-by-step explanation:

Using the formula two and replacing the given values:

Sale Price = Original Price - Amount Saved. So,

Sale Price = 6.40 - 1.28

Sale Price = $5.12 (answer)

This means, the cost of the item to you is $5.12.

You will pay $5.12 for an item with original price of $6.40 when discounted 20%. In other words, if you buy an item at $6.40 with 20% discounts, you pay $6.40 - 1.28 = $5.12

Suppose Have you received a amazon promo code of 1.28. If the price is $6.40 what was the amount saved in percent:

3) 1.28 is what percent off $6.40?

Using the formula two and replacing the given values:

Amount Saved = Original Price x Discount % /100. So,

1.28 = 6.40 x Discount % / 100

1.28 / 6.40 = Discount % /100

100 x 1.28 / 6.40 = Discount %

128 / 6.40 = Discount %, or

Discount % = 20 (answer)

8 0

4 years ago

Evaluate.

Alex787 [66]

2 - 12 + 18
= -10 + 18
= 8
The answer is D.

4 0

3 years ago

Ashley uses 1/2 cup of melted butter to spread equally on 12 slices of toast. How much melted butter is on each slice of toast?

Sholpan [36]

Answer: 1/24

Step-by-step explanation:

1/2 divided by 12

3 0

3 years ago

What does one third equal

monitta

Divide $\frac{1}{3}$ . 1÷3=0.33333333333333 $\frac{1}{3}$ equals 0.333333333333333

5 0

3 years ago