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3 years ago

6

Please help! Question below (:

1 answer:

Ket [755]3 years ago

5 0

The 3 inside angles of a triangle need to equal 180 degrees.

You are given 28 for one.

The second on is adding 58 + 77 = 135 degrees.

X = 180 - 28 - 135 = 17 degrees

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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:

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

3 0

3 years ago

A cockroach traveling 2 feet per second takes how long to scurry a distance of 46 feet?

Fittoniya [83]

Answer:

23 Seconds

The roach is going 2 feet per second so you can split the amount of feet in half because he will go the same distance 2 times as fast.

5 0

3 years ago

Can u solve this problem in show your work

aksik [14]

Hey there!

We can solve this problem by doing PEMDAS, which lists:

$Parentheses \\ Exponents \\ Multiplication \\ Division \\ Addition \\ Subtraction$

We have in this equation

$Parentheses \\ Exponents \\ Dvision$

Let's sp;ve this equation now!

Parentheses ↓

$(6 -3) = 3$

Exponents ↓

$3^2 = 9$

Division ↓

$\frac{36}{9} = 9$

Okay now , I show you the steps so it can be easier to solve!

$\frac{36}{(6-3)^2} \\ \\ 6-3 = 3 \\ \\ \frac{36}{3^2} \\ \\ 3^2 = 9 \\ \\ \frac{36}{9} \\ \\ \\ \\ Answer: 4$

Good luck on your assignment and enjoy your day!

~ $LoveYourselfFirst:)$

5 0

4 years ago

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BRAINLYIST AND 20 PTS!!! What is the surface area of this design? 360in 280in 76in 392in

guapka [62]

Answer:

392 I got that correct as well

3 0

2 years ago

Read 2 more answers

WHAT IS THE SLOPE PLEASE??

strojnjashka [21]

Answer:

Step-by-step explanation:

take two points on the line ,i take (-4,0) and (0,-2)

slope=(y2-y1)/(x2-x1)=(-2-0)/(0+4)=-2/4=-1/2

6 0

3 years ago

Read 2 more answers