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3 years ago

If an angle is acute, then it has a measure of 30°

1 answer:

3 0

That's not true at all.

Or rather I should say, that's only true if the angle happens to be 30° .

The statement that's ALWAYS true is:

If an angle is acute, then it has a
positive measure less than 90° .

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Angie wants to purchase mulch for her tulip garden. The dimensions of her garden are 6 feet by 8 feet. If mulch is sold by the s

kondaur [170]

Answer:

72 dollars

Step-by-step explanation:

5 0

3 years ago

The plane x + y + z = 12 intersects paraboloid z = x^2 + y^2 in an ellipse.(a) Find the highest and the lowest points on the ell

emmasim [6.3K]

Answer:

Highest (-3,-3)

Lowest (2,2)

Farthest (-3,-3)

Closest (2,2)

Step-by-step explanation:

To solve this problem we will be using Lagrange multipliers.

Let us find out first the restriction, which is the projection of the intersection on the XY-plane.

From x+y+z=12 we get z=12-x-y and replace this in the equation of the paraboloid:

$\bf 12-x-y=x^2+y^2\Rightarrow x^2+y^2+x+y=12$

completing the squares:

$\bf x^2+y^2+x+y=12\Rightarrow (x+1/2)^2-1/4+(y+1/2)^2-1/4=12\Rightarrow\\\\\Rightarrow (x+1/2)^2+(y+1/2)^2=12+1/2\Rightarrow (x+1/2)^2+(y+1/2)^2=25/2$

and we want the maximum and minimum of the paraboloid when (x,y) varies on the circumference we just found. That is, we want the maximum and minimum of

$\bf f(x,y)=x^2+y^2$

subject to the constraint

$\bf g(x,y)=(x+1/2)^2+(y+1/2)^2-25/2=0$

Now we have

$\bf \nabla f=(\displaystyle\frac{\partial f}{\partial x},\displaystyle\frac{\partial f}{\partial y})=(2x,2y)\\\\\nabla g=(\displaystyle\frac{\partial g}{\partial x},\displaystyle\frac{\partial g}{\partial y})=(2x+1,2y+1)$

Let $\bf \lambda$ be the Lagrange multiplier.

The maximum and minimum must occur at points where

$\bf \nabla f=\lambda\nabla g$

that is,

$\bf (2x,2y)=\lambda(2x+1,2y+1)\Rightarrow 2x=\lambda (2x+1)\;,2y=\lambda (2y+1)$

we can assume (x,y)≠ (-1/2, -1/2) since that point is not in the restriction, so

$\bf \lambda=\displaystyle\frac{2x}{(2x+1)} \;,\lambda=\displaystyle\frac{2y}{(2y+1)}\Rightarrow \displaystyle\frac{2x}{(2x+1)}=\displaystyle\frac{2y}{(2y+1)}\Rightarrow\\\\\Rightarrow 2x(2y+1)=2y(2x+1)\Rightarrow 4xy+2x=4xy+2y\Rightarrow\\\\\Rightarrow x=y$

Replacing in the constraint

$\bf (x+1/2)^2+(x+1/2)^2-25/2=0\Rightarrow (x+1/2)^2=25/4\Rightarrow\\\\\Rightarrow |x+1/2|=5/2$

from this we get

and the candidates for maximum and minimum are (2,2) and (-3,-3).

Replacing these values in f, we see that

f(-3,-3) = 9+9 = 18 is the maximum and

f(2,2) = 4+4 = 8 is the minimum

Since the square of the distance from any given point (x,y) on the paraboloid to (0,0) is f(x,y) itself, the maximum and minimum of the distance are reached at the points we just found.

We have then,

(-3,-3) is the farthest from the origin

(2,2) is the closest to the origin.

3 0

3 years ago

What is 89/100 as a percent?

masya89 [10]

89/100 as a precent is is 89% because if you change 89/100 to a decimal you get .89 and then you multiply that by 100 (or just move the decimal over 2 places to the right) and you will get 89% make since? and its the same way if your going from % to decimal except you divide by 100( or move the decimal over 2 places to the left) so to a percent is right and to a decimal is left. easy right?

4 0

3 years ago

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Please write a 5 sentence summary of fidel castro's life

adell [148]

Answer:

Fidel Castro, in full Fidel Alejandro Castro Ruz, (born August 13, 1926, near Birán, Cuba—died November 25, 2016, Cuba), political leader of Cuba (1959–2008) who transformed his country into the first communist state in the Western Hemisphere. Castro became a symbol of communist revolution in Latin America. He held the title of premier until 1976 and then began a long tenure as president of the Council of State and the Council of Ministers. He handed over provisional power in July 2006 because of health problems and formally relinquished the presidency in February 2008.

Step-by-step explanation: Hope it helps! Please rate brainliest

4 0

3 years ago

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Please help ASAP cannot get this question wrong!!

Yakvenalex [24]

Answer:

The answer is D

Step-by-step explanation:

6 0

3 years ago

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