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3 years ago

Multivariable Calculus Question:

1 answer:

3 0

$f(2,-1)=2^2-(-1)^2=3$

so we're considering the level curve

$x^2-y^2=3$

The tangent line to this curve at (2, -1) will be the value of $\dfrac{\mathrm dy}{\mathrm dx}$ at this point. Differentiating yields

$2x-2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac xy$

and so the slope of the tangent would be $\dfrac2{-1}=-2$ .

The tangent line then has equation

$y-(-1)=-2(x-2)\implies y=-2x+3$

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A recipe for individual chocolate hazelnut tarts calls for ½ cup of hazelnuts per tart. If 1 cup of hazelnuts weighs 4 ounces, w

DerKrebs [107]

Answer:

The amount is sufficient to make 75 tarts.

Step-by-step explanation:

We have been given that a recipe for individual chocolate hazelnut tarts calls for ½ cup of hazelnuts per tart and 1 cup of hazelnuts weighs 4 ounces.

The half cup of hazelnuts will weigh 2 ounces $(\frac{4}{2}=2)$ .

1 kg equals 35.274 ounces.

$\text{5 kg}=5\times 35.274\text{ ounces}$

$\text{5 kg}=176.37\text{ ounces}$

Since each tart needs ½ cup of hazelnuts and half cup of hazelnuts will weigh 2 ounces, so we will divide 176.37 ounces by 2 to find number of tarts.

$\frac{176.37}{2}=88.185\approx 88$

Since we can make 88 tarts from 5 kg hazelnuts, therefore, the 5-kilogram bag of hazelnuts be sufficient to make 75 tarts.

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3 years ago

Which graph represents the function f (x) = StartFraction 2 Over x minus 1 EndFraction + 4?

Pepsi [2]

Answer:

On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4

Step-by-step explanation:

The given function is presented as follows;

$f(x) = \dfrac{2}{x - 1} + 4$

From the given function, we have;

When x = 1, the denominator of the fraction, $\dfrac{2}{x - 1}$ , which is (x - 1) = 0, and the function becomes, $\dfrac{2}{1 - 1} + 4 = \dfrac{2}{0} + 4 = \infty + 4 = \infty$ therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote

Also we have that in the given function, as x increases, the fraction $\dfrac{2}{x - 1}$ tends to 0, therefore as x increases, we have;

$\lim_ {x \to \infty} \dfrac{2}{(x - 1)} \to 0, and \ \dfrac{2}{(x - 1)} + 4 \to 4$

Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1

When -∞ < x < 1, we also have that as x becomes more negative, f(x) → 4. When x = 0, $\dfrac{2}{0 - 1} + 4 = 2$ . When x approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left

Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.

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3 years ago

Choose the situation which would best be modeled by an exponential decay function.

Softa [21]

A) is the answer. The island in decaying by 10% each year, which means the amount will change within the period of the decay.

Hope this Helps! :)

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3 years ago

Read 2 more answers

A family drove a total of 5,300 miles.They drove 10 more miles in tj second half of the trip than the first half. How many did t

AVprozaik [17]

If they drove a total of 5,300 miles in 2 days, and on the second day they drove 10 more miles then the 1st day.

5,300 ÷ 2 = 2,650

they drove 10 miles less on the first day

2,650 - 10 = 2,640

They drove 2,640 miles on the first day.

Hope this helps. :)

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3 years ago

The population of rabbits on an island is growing exponentially. In the year 2008, the population of rabbits was 7100, and by 20

olganol [36]

Answer:

Unknown answer so ye that mean I'm not sure about it

Step-by-step explanation:

Unknown answer so ye that mean I'm not sure about it

4 0

3 years ago