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3 years ago

11

A radio station has no more than $25000 to give away

1 answer:

konstantin123 [22]3 years ago

6 0

I'd like to answer your question but there's not enough information.

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PLEASE ANSWER THIS FAST Will the red square and the orange square always equal the blue square? What colored square is the hypot

Vikentia [17]

Step-by-step explanation:

The area of the blue square will always equal the sum of the area of the orange and red rectangles

The pythagorian theorem:

a²+b² = c²

now let a be the side of the red triangle and b the side of the orange one

so a² is the area of the red triangle and b² is the area of the orange one

Let c be the side of the blue rectangle

so c² is the area of it

then what we concluded is right

the hypotenuse is the blue side since it is the larger one

6 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:

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

3 0

3 years ago

Solve. the square root of 44-2x = x-10

Anuta_ua [19.1K]

44-2x=x-10 subtract 44 from both sides -2x= x-54 subtract x from both sides -3x= -54 divide by -3 x= 18 square root of 18= 4.24 in radical form 3 square root of 2 hope this helps

5 0

3 years ago

Read 2 more answers

A factory purchased a machine for $35,000. The value of the machine depreciates at a rate of 10% each year. Complete the followi

Olegator [25]

Inital value= 35,000
depreciation value= .10 or 10%
value after 4 yrs= 22,963.5

6 0

3 years ago

Someone who can do this help me please.

lianna [129]

Answer:

x= 2

Step-by-step explanation:

the shapes are 6 in apart

5 0

3 years ago