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scoundrel [369]

3 years ago

13

Please help me.. thanks if you do

2 answers:

S_A_V [24]3 years ago

8 0

Answer:

B.

Step-by-step explanation:

Here's a picture of me graphing it:

Sorry for dark mode :/

Paladinen [302]3 years ago

6 0

Answer:

B

Step-by-step explanation:

We can graph the line using the y and x-intercepts. To find the y-intercept, we substitute x = 0 into y = -2x - 2 so the y-intercept is (0, -2). To find the x-intercept, we substitute y = 0 into y = -2x - 2 so the x-intercept is (-1, 0). The line that goes through both of these points is line B.

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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

Find the 8th term of the geometric sequence show below

vivado [14]

Answer:

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6 0

3 years ago

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What is the answer to this equation t+t+t=12

OLEGan [10]

Answer:

t = 4

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS
Equality Properties

<u>Algebra I</u>

Combining Like Terms

Step-by-step explanation:

<u>Step 1: Define equation</u>

t + t + t = 12

<u>Step 2: Solve for </u><em><u>t</u></em>

Combine like terms (t): 3t = 12
Divide 3 on both sides: t = 4

<u>Step 3: Check</u>

<em>Plug in t into the original equation to verify it's a solution.</em>

Substitute in <em>t</em>: 4 + 4 + 4 = 12
Add: 8 + 4 = 12
Add: 12 = 12

Here we see that 12 does indeed equal 12.

∴ t = 4 is a solution of the equation.

3 0

3 years ago

Two lines and a point are guaranteed to be coplanar If..

Roman55 [17]

Two lines and a point are guaranteed to be coplanar if the two lines share only a single point.

Hope this helped :)

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4 years ago

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(2x + 3)(5x2 - 2x - 1) = Ax3 + Bx2 + Cx + D. What are the values of B and C?

Sati [7]

Answer:

B = 11; C = -8

Step-by-step explanation:

When simplified I get 10x^3 + 11x^2 - 8x - 3

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3 years ago