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3 years ago

8. Find the perimeter and the area

Mathematics

1 answer:

kupik [55]3 years ago

4 0

Answer:

Goals of Union:maintain unity,maintain state sovereignty,defend home ground from enemy boost

Goals of Confederacy in Civil War: protect the institution of slavery,abolish slavery,international trade

Step-by-step explanation:

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In ΔDEF,{EF}\cong{DE} EF ≅ DE and m∠E = 104°. Find m∠D.

Alexeev081 [22]

The 3 inside angles need to equal 180.

Subtract E from 180 to find the sum of the other two angles:

180 - 104 = 76

Now because EF ≅ DE , angle D and F would be the same so divide 76 by 2

Angle D = 38

7 0

3 years ago

V(t) = 1 + 2sin(t^2/2) solve for t

Crank

Answer:

omg i'm so sorry thats the wronge answer i ment this to go to a diffrent question

Step-by-step explanation:

7 0

3 years ago

XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3

nataly862011 [7]

<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = $\frac{1}{2}$ x b x h -------------(i)

Where;

A = 18 $\sqrt{3}$

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

Substitute these values into equation(i) and solve as follows:

18 $\sqrt{3}$ = $\frac{1}{2}$ x b x 6

18 $\sqrt{3}$ = 3b

Divide through by 3

6 $\sqrt{3}$ = b

Therefore, b = XZ = 6 $\sqrt{3}$

Now, assume that the circle is centered at O;

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180° [sum of angles in a triangle]

=> XOZ + 30° + 30° = 180°

=> XOZ + 60° = 180°

=> XOZ = 180° - 60°

=> XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

$\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}$

$\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}$

$\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}$

$\frac{1}{12} = \frac{1}{2|OZ|}$

$\frac{1}{6} = \frac{1}{|OZ|}$

|OZ| = 6

The radius of the circle is therefore 6.

Now, let's calculate the length of the arc XZ

The length(L) of an arc is given by;

L = θ / 360 x 2 π r ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

5 0

3 years ago

Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v

blagie [28]

U = ( -8 , -8)
v = (-1 , 2 )
the magnitude of vector projection of u onto v =
dot product of u and v over the magnitude of v = (u . v )/ ll v ll

ll v ll = √(-1² + 2²) = √5

u . v = ( -8 , -8) . ( -1 , 2) = -8*-1+2*-8 = -8
∴ (u . v )/ ll v ll = -8/√5
∴ the vector projection of u onto v = [(u . v )/ ll v ll] * [v/ ll v ll]

 = [-8/√5] * (-1,2)/√5 = ( 8/5 , -16/5 )

The other orthogonal component = u - ( 8/5 , -16/5 )
= (-8 , -8 ) - ( 8/5 , -16/5 ) = (-48/5 , -24/5 )

So, u as a sum of two orthogonal vectors will be

u = ( 8/5 , -16/5 ) + (-48/5 , -24/5 )

3 0

3 years ago

Read 2 more answers

4/y+2 - 9/y-2 = 9/y^2-4

Evgesh-ka [11]

Going off the idea that this is 4/(y+2) - 9/(y-2) = 9/(y^2-4), let's first rewrite y^2-4 in the form of a^2-b^2, where a=y and b=2.
y/(y+2)-9/(y-2)=9/(y^2-2^2)
Now, use difference of squares: a^2-b^2=(a+b)(a-b)
4/(y+2)-9/(y-2)=9/((y+2)(y-2))
Multiply both sides by the Least Common Denominator: (y+2)(y-2)
4(y-2)-9(y+2)=9
Then keep on simplifying until you get your answer
-5y-26=9
-5y=9+26
-5y=35
y=35/-5
y=-7
Yay! Our answer is y=-7!

8 0

3 years ago

Read 2 more answers