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2 years ago

8

OT−→− bisects ∠DOG. Find the measure of ∠DOG if ∠DOT = 4x + 4 and ∠TOG = 5x – 3

1 answer:

docker41 [41]2 years ago

5 0

Answer:

64

Step-by-step explanation:

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Albert sells furniture. His base salary is $300 per week, plus 5.5% commission. If his total sales for last week were $2950, wha

Andreas93 [3]

Answer:

16225

Step-by-step explanation:

You need to multiply

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3 years ago

Simplify 3x²y³ over 12x⁶y

Svetllana [295]

Answer:

12x^6y

Step-by-step explanation:

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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

Find the surface area of the prism below. See attachment, 58 cm is incorrect.

Masja [62]

Answer:

Surface area of the given figure = 48 cm^2

Step-by-step explanation:

Surface area is nothing area of all the sides.

We can find the area of each figure add them together.

There are two triangles with the same measures.

One rectangle with measure of 4 by 3.

Another rectangle with the measure of 5 by 3.

One square with the measure of 3.

Surface area = Area of two triangles + rectangle 1 + rectangle 2 + square

Formulas:

Area of the triangle = 1/2 base* height

Area of the rectangle = length * width

Area of the square = side x side

Applying the formula, we get

=2[1/2 (3*4)] + 4*3 + 5*3 + 3^2

= 12 + 12 + 15 + 9

Surface area of the given figure = 48 cm^2

Hope this will helpful.

Thank you.

3 0

3 years ago

Read 2 more answers

The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (2008 data). The average c

ivanzaharov [21]

Answer:

$n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94$

So the answer for this case would be n=94 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma= 500$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =120 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The confidence2 level is 98% or 0.98 then the significance level would be $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , the critical value for this case would be $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(500)}{120})^2 =93.928 \approx 94$

So the answer for this case would be n=94 rounded up to the nearest integer

8 0

3 years ago