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3 years ago

What is the measure of ehg?

Mathematics

2 answers:

Evgesh-ka [11]3 years ago

6 0

Answer:

The measure of EHG = 120°

Step-by-step explanation:

There are three vectors originating from point H and joining three points E, F and G.

The given angles between vector HG and HF is 30° and between vector HE = 90°

Therefore, Angle between vector HE and HG = angle between HE and HF + angle between HF and HG.

∠ EHG = ∠ EHF + ∠ FHG

= 90° + 30°

= 120°

The measure of EHG = 120°

Jobisdone [24]3 years ago

4 0

(Answer: 120) angle EHF = 90 degrees+30 degrees=120 angle

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Answer:

Gail will need 12 yards of white fur, 8 yards of blue striped and 2 yards of the pink felt.

Step-by-step explanation:

We are given that,

The amount of yards for making one costume of different fabrics are,

White fur fabric = $1\frac{1}{2}$ = $\frac{3}{2}$ yards

Blue striped fabric = 1 yard

Pink felt for ears = $\frac{1}{4}$ yards.

So, we have,

The amount required to make 8 costumes are,

White fur fabric = $\frac{3}{2}\times 8$ = 3×4 = 12 yards

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3 years ago

find real numbers a, b, and c so that the graph of the function y=ax^2+c contains the points (-1,6), (2,7), and (0,1)

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This gives you three simultaneous equations:

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3 years ago

Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat

tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

Step 1:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane. Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

Step( ii):

By using Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ y z + λ ( 1) = 0

⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

δ f / δ x +λ δ Ф / δ x =0

⇒ x z + λ ( 9) = 0

⇒ $\frac{xz}{9}$ = - λ .......(b)

Obtain the equations are δ F / δ z = 0

δ f / δ x +λ δ Ф / δ z =0

x y + λ ( 4) = 0

⇒ $\frac{xy}{4}$ = - λ .......(c)

Step (iii):-

Equating (a) and (b) equations

we get $y z = \frac{xz}{9}$

cancel 'z' value we get x = 9y .......(d)

Equating (b) and (c) equations

we get $\frac{xy}{4} = \frac{xz}{9}$

cancel 'x' value on both sides , we get

4z =9y ......(e)

substitute (d) (e) values in equation (1) we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

27y -27 =0

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

therefore the dimensions are x =9 , y=1 and z = 9 /4

Conclusion:-

The largest volume of the rectangular box V = x y z

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

9 + 9 + 4(9/4) = 27

27 =27

so satisfied equation

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3 years ago