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3 years ago

9

Are the expressions

1 answer:

Dima020 [189]3 years ago

8 0

Answer:

Yes it is equivalent

Step-by-step explanation:

Simply 5(x+2)+10 and you will get 5x+12

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Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 4y sqrt (x) , (4, 5) max

liubo4ka [24]

Answer:

Remember that the maximum rate of change of f at a point u is the length of the of the gradient vector evaluate in u, and the direction in which it occurs is in direction of the gradient vector evaluate in u.

The gradient vector of f is

$\triangledown f(x,y)=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})=(2yx^{-\frac{1}{2}}, 4\sqrt x)$

Then, the maximum rate of change is $|\triangledown f(4,5)|=|(2*5*4^{-\frac{1}{2}}, 4\sqrt 4)|=|(5,8)|=\sqrt{5^2+8^2}=\sqrt89$ in the direction of (5,8).

4 0

3 years ago

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has <u>13 sides.</u>

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has <u>7 sides.</u>

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a <u>Square.</u>

<u>(c)</u>The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The <u>sum of the exterior angle of a polygon is 360 degrees.</u>

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle <u>does not change either in a regular or irregular polygon.</u>

3 0

3 years ago

Solve the inequality<br>-6p<12 <br><br><br>Ah this is due by tomorrow

777dan777 [17]

-6p < 12 Divide -6 on both sides to get "p" by itself

$\frac{-6p}{-6} < \frac{12}{-6}$

p > -2

When you divide or multiply a negative number to both sides of the inequality, the sign (< , > , ≤ , ≥) is flipped.

3 0

3 years ago

Someone please help with 4-6?

forsale [732]

4-6=-2 hope that helps!

5 0

3 years ago

Read 2 more answers

Help asap. Like hurry

skelet666 [1.2K]

Answer:

53.85

Step-by-step explanation:

7 0

3 years ago