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3 years ago

8

16 POINTS!!! HELP ASAP

1 answer:

nadya68 [22]3 years ago

7 0

Answer:

The answer is 358.01

Step-by-step explanation:

Given:

$3\times 10^{2}+5\times 10^{1}+8\times 10^{0}+1\times \frac{1}{10^{2}}$

Now, to solve first we crack the power notation then multiply and then do the addition:

$3\times 100+5\times 10+8\times 1+1\times \frac{1}{100}$

(The value of $10^{1}$ is 10 and the value of $10^{0}$ is 1.)

$=300+50+8+\frac{1}{100}$

$=300+50+8+0.01$

$=358.01$ .

Therefore, the answer is 358.01 .

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What is the answer for 1/7(1,000)

12345 [234]

1/7(1000) = 1/7(7000/7)

1*7000
7*7

7000
49

1000
7

so 1/7(1000) = 1000/7 or 142 6/7

5 0

3 years ago

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Bas_tet [7]

Answer:

5

Step-by-step explanation:

The initial value is when x=0

When x=0, y =5

The initial value is 5

3 0

3 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

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3 years ago

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3 years ago

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Which expression is equivalent to 3(x + 4)?

Klio2033 [76]

Answer:

3x + 12

Step-by-step explanation:

Use the distributive property.

3(x + 4) = 3 * x + 3 * 4 = 3x + 12

Answer: 3x + 12

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3 years ago

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