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Vlad [161]
3 years ago
8

What is (1.7x10^4)x(8.5x10^-2) in standard form

Mathematics
2 answers:
Vladimir79 [104]3 years ago
8 0

Answer:

1.445 × 10³ hope it helped goodluck!

Temka [501]3 years ago
4 0

Answer:

1.445 × 10³

Step-by-step explanation:

Standard form is a way of writing a small number or a large number easily.

We should give the final answer in standard form.

1) (1.7 × 10⁴) × (8.5 × 10⁻²)

We enter this directly into the calculator to obtain a solution.

= 1445

We write this in standard form we have :

1.445 × 10³

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Consider the equation below. (If an answer does not exist, enter DNE.)
storchak [24]

Answer:

a. f is increasing in the interval (-4,0) and decreasing in the intervals \left ( -\infty ,-4 \right )\,,\,\left ( 0,4 \right )

b.  local maximum value of the function is 6, -250 and Local minimum value of the function is -250

c.  inflexion points are \left ( \frac{-4\sqrt{3}}{3},\frac{-1226}{9} \right )\,,\,\left ( \frac{4\sqrt{3}}{3},\frac{-1226}{9} \right )

f is concave up in intervals \left ( -\infty ,\frac{-4\sqrt{3}}{3} \right )\,,\,\left ( \frac{4\sqrt{3}}{3},\infty  \right ) and concave down in interval \left (\frac{-4\sqrt{3}}{3},\frac{4\sqrt{3}}{3} \right )

Step-by-step explanation:

Given: f(x)=x^4-32x^2+6

To find: interval on which f is increasing and decreasing, local minimum and maximum values of f, inflection points and interval on which f is concave up and concave down

Solution:

A function f is increasing in the interval in which f'>0 and decreasing in the interval in which f''

If a function is increasing before a point and decreasing after that point, the point is said to be a point of local maxima.

If a function is decreasing before a point and increasing after that point, the point is said to be a point of local minima.

An inflection point is a point on the graph of a function at which the concavity changes. Put second derivative equal to zero as check if concavity changes at the points obtained. Such points are said to be points of inflexion.

A function f is concave up in the interval in which  f''>0 and concave down in the interval in which f''

a.

f(x)=x^4-32x^2+6\\f'(x)=4x^3-64x\\=4x(x^2-16)\\=4x(x+4)(x-4)

f'(x)=0\\4x(x+4)(x-4)=0

Observe the attached table.

So, f is increasing in the interval (-4,0) and decreasing in the intervals \left ( -\infty ,-4 \right )\,,\,\left ( 0,4 \right )

b.

From the table,

a function f has a local maxima at x=0,4 and local minima at x=-4

f(-4)=(-4)^4-32(-4)^2+6=256-512+6=-250\\f(0)=0^4-32(0)^2+6=6\\f(4)=4^4-32(4)^2+6=256-512+6=-250

So, local maximum value of the function is 6, -250

Local minimum value of the function is -250

c.

f'(x)=4x^3-64x\\f''(x)=12x^2-64=4(3x^2-16)\\f''(x)=0\Rightarrow 4(3x^2-16)=0\\3x^2-16=0\\x^2=\frac{16}{3}\\x=\pm \frac{4}{\sqrt{3}}=\pm \frac{4\sqrt{3}}{3}

See the attached table

So, f is concave up in intervals \left ( -\infty ,\frac{-4\sqrt{3}}{3} \right )\,,\,\left ( \frac{4\sqrt{3}}{3},\infty  \right )

and concave down in interval \left (\frac{-4\sqrt{3}}{3},\frac{4\sqrt{3}}{3} \right )

Also,

f\left ( \frac{-4\sqrt{3}}{3} \right )=\left ( \frac{-4\sqrt{3}}{3} \right )^4-32\left ( \frac{-4\sqrt{3}}{3} \right )^2+6=\frac{-1226}{9}\\f\left ( \frac{4\sqrt{3}}{3} \right )=\left ( \frac{4\sqrt{3}}{3} \right )^4-32\left ( \frac{4\sqrt{3}}{3} \right )^2+6=\frac{-1226}{9}

So, inflexion points are \left ( \frac{-4\sqrt{3}}{3},\frac{-1226}{9} \right )\,,\,\left ( \frac{4\sqrt{3}}{3},\frac{-1226}{9} \right )

4 0
3 years ago
Na
Bumek [7]

Answer:

6,874.70

Step-by-step explanation:

You are going to want to use the compound interest formula, which is shown below.

P(1+\frac{r}{n} )^{nt}

<em>P = initial balance </em>

<em>r = interest rate </em>

<em>n = number of times compounded annually </em>

<em>t = time </em>

Now lets plug in the values into the equation.

5,000(1+\frac{0.04}{4})^{8(4)} = 6,874.70

Your answer is 6,874.70.

8 0
3 years ago
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