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3 years ago

Find the equation of the parabola with a vertex of (5, -2) and a focus of (5, -3)

1 answer:

6 0

Use the form $\left(x-h\right)^2=\frac{1}{4p}\left(y-k \right)$
Then we have the vertex is $(h,k)$ and the distance from the vertex to the focus is p. Therefore we have $\left(x-5\right)^2=-\frac{1}{4}\left(y+2\right)$ . It is negative because the parabola is pointing downwards.

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What is the future value (total amount due) on a $12,000 loan at 8% compounded

svp [43]

Answer: $20,780.10

Step-by-step explanation:

You need the Compound Interest Formula

A = P(1 + r/n)^nt

Step 1: Create the equation.

12,000(1 + 0.08/2)¹⁴

Step 2: Solve the equation.

Follow PEMDAS (parenthesis, exponents, multiplication...)

Parenthesis: (1 + 0.08/2) = (1 + 0.04) = (1.04)

Exponents: (1.04)¹⁴ = (1.73168)

Multiplication: 12,000(1.73168) = 20,780.1

3 0

3 years ago

If f is a scalar field and F, G are vector fields, then f F, F · G, and F × G are defined by the following. (f F)(x, y, z) = f(x

valentina_108 [34]

Answer:

Step-by-step explanation:

Consider curl $(fF)$ where $f$ is a scalar function and F is a vector function

$F=F_{1}i +F_{2}j +F_{3}k$

i j k

$curl(fF) = \frac{\partial}{\partial x}$ $\frac{\partial}{\partial y}$ $\frac{\partial}{\partial z}$

$fF_{1}$ $fF_{2}$ $fF_{3}$

$curl(fF)=i(\frac{\partial}{\partial y}(fF_{3})-\frac{\partial}{\partial z}(fF_{2}))-j(\frac{\partial}{\partial x}(fF_{3})-\frac{\partial}{\partial z}(fF_{1}))+k(\frac{\partial}{\partial x}(fF_{2})-\frac{\partial}{\partial y}(fF_{1}))$

$=i(\frac{\partial}{\partial y}(F_{3})+\frac{\partial}{\partial y}(f)-\frac{\partial}{\partial z}(F_{2})-\frac{\partial}{\partial z}(f))-j(\frac{\partial}{\partial x}(F_{3})+\frac{\partial}{\partial x}(f)-\frac{\partial}{\partial z}(F_{1})-\frac{\partial}{\partial z}(f))+k(\frac{\partial}{\partial x}(F_{2})+\frac{\partial}{\partial x}(f)-\frac{\partial}{\partial y}(F_{1})-\frac{\partial}{\partial y}(f))$

$curl(fF)=f(\Delta\times F)+(\Delta f)\times F$

3 0

3 years ago

Reposting because I seriously need help. Please, this is time sensitive!

Anni [7]

From the graph, see where the two lines cross. That is the correct answer. The answer is (4,-3.4)

7 0

3 years ago

Read 2 more answers

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goblinko [34]

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2 years ago

A house purchased for $216,500 gains 2% of its value every year. If this growth rate continues, in how many years will the house

NikAS [45]

Answer: 36 years

Step-by-step explanation:

You can use the Rule of 72 to calculate how long it might take the house to double in value.

The Rule of 72 works by dividing 72 by the interest rate as a whole number and the result will be a rough estimate of the time in years it will take for the investment to double in size:

= 72 / 2

= 36 years

3 0

3 years ago