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3 years ago

Find the value of. x part 1c

Mathematics

1 answer:

Dmitry [639]3 years ago

3 0

The bisector splits this shape into two triangles. It is easier if we find the degrees of each triangle in this shape separately

We know that one angle of the top triangle is 65 degrees. Since another angle is congruent to the known angle we can assume that the other angle is 65 degrees as well. You can see this labeled in the image below.

The sum of all the angles of a triangle is 180 degrees. Since we know the degrees of two angles, which are both 65 degrees, we can make a formula to find the third angle:

180 = 65 + 65 + x

180 = 130 + x

This means that the last angle is 50 degrees

^^^We need to know this so that we can find the angle complimentary to the 50 degree angle, which will be the angle that is included in the bottom triangle

Complimentary angles are angles who's sum is 90 degrees. You can find the 50 degree angles complimentary angle by making a formula like so:

90 = 50 + x

Now we have the first angle of the second triangle. The second two angles can be found easily. Since the other two angles are congruent all we need to do is subtract 40 from 180 then divide the answer by 2 like so:

180 - 40 = 140

140 / 2 = 70

The other two angles are 70 degrees!

The measure of angle 2 is supplementary to one of the 70 degree angles. This means that you can find the value of angle 2 by subtracting 70 from 180

180 - 70 = 110

To find x set the equation equal to 110 and solve

110 = x + 120

x = -10

Hope this helped!

~Just a girl in love with Shawn Mendes

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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

PLEASE HELP ASAP! Question 12. Thank you

a_sh-v [17]

Answer:

Step-by-step explanation:

In the first column, put days at the top and pounds at the bottom.

So Day 1 = 75 pounds, Day 2=150 pounds, Day 3 = 225 pounds, etc..

8 0

3 years ago

Bill's Bargains sells 16 ounces of Circle O's cereal for $3.36. Debbie's Deals sells 40 ounces of Circle O's cereal for $7.60. W

astraxan [27]

Answer:

Debbie's Deals has the better deal with a price of $0.19 per ounce compared to Bill's Bargains at $0.21 per ounce.

Step-by-step explanation:

Divide $3.36 by 16 = $0.21

Divide $7.60 by 40 = $0.19

Debbie's Deals sells the Circle O's cereal for a cheaper per ounce price thus it's the better price and the better deal.

Good luck!

7 0

3 years ago

This is a pyramid problem so please help out

Degger [83]

Answer:

Step-by-step explanation:

LA, Laterial Surface Area, is the lateral surface area of a pyramid. In this case, it is the sum of five triangles with base of 12cm and height that can be calculated as follow:

height^2 = 8.26^2 + 20^2 = 468.23

height = 21.64cm

LA = 5*1/2*12*21.64

= 649.2cm^2

SA, Surface Area, is the sum of LA and base area.

Base area = 5*1/2*12*8.26 = 247.8cm^2

SA = 649.2 + 247.8 =897cm^2

Volume, V = 1/3 * base area * height

= 1/3 * 247.8 * 20

= 1652cm^3

4 0

3 years ago

Read 2 more answers

Dedra used coupons 6 times at the store last month.

AVprozaik [17]

Answer:

The mean is 42, rounded to the nearest cant would be 42.00. IF this helped subscribe to Amiredagoat Yt

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the value of. x part 1c​

Find the value of. x part 1c