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3 years ago

Triangle ABC is shown BCD=30 D is a point on side AC such that BD=DA=AB prove that AD =DC

Mathematics

2 answers:

babymother [125]3 years ago

6 0

Answer:

<BAC=<BAD=60° (ΔABD is an equilateral triangle (all sides are equal) so each angle measures 60°)

All the angles in a triangle add to 180, so for ΔABC, we can write <ABC=180-60-30=90. So ΔABC is a right angled triangle with hypotenuse AC.

sinA=opposite/hypotenuse

sin30=AB/AC

1/2=AB/AC

AC=2AB=2AD

AC=AD+DC

AD+DC=2AD

DC=AD

QED

maw [93]3 years ago

5 0

Answer:

Step-by-step explanation:

what grade are you on lemme help you

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(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.

valentinak56 [21]

Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.

-4x + 2y - z = 1 ==> z = -4x + 2y - 1

3x - 2y + 2z = 1 ==> z = (1 - 3x + 2y)/2

==> -4x + 2y - 1 = (1 - 3x + 2y)/2

==> -8x + 4y - 2 = 1 - 3x + 2y

==> -5x + 2y = 3

==> y = (3 + 5x)/2

==> z = -4x + 2 (3 + 5x)/2 - 1 = x + 2

So if we take x = t, the line of intersection is parameterized by

r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

(a) The tangent vector to r(t) is parallel to this line, so you can use

v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

3 0

2 years ago

Simply 15 to the 18 power divide by 15 to the 3 power

andrew11 [14]

The property of exponents says that when you divide two exponents with the same base, you can keep the base and subtract the exponents. So you can do 18-3, which is 15, so it would be 15 to the 15th power

6 0

3 years ago

Calculate the angle of depression from the

s344n2d4d5 [400]

Answer:

angle of depression ≈ 53.8°

Step-by-step explanation:

the angle of depression is the measure of the angle from the horizontal downwards from the top of the flag pole.

this angle is alternate to ∠ A and is congruent to ∠ A

using the sine ratio in the right triangle

sin A = $\frac{opposite}{hypotenuse}$ = $\frac{25}{31}$ , then

∠ A = $sin^{-1}$ ( $\frac{25}{31}$ ) ≈ 53.8° ( to 1 d.p )

Angle of depression ≈ 53.8°

6 0

2 years ago

Calculate this reflection of the triangle:

Mice21 [21]

Answer:

a = 3, b = 0, c = 0, d = -2

Step-by-step explanation:

To find the reflection Multiply the matrices

∵ The dimension of the first matrix is 2 × 2

∵ The dimension of the second matrix is 2 × 3

1. Multiply the first row of the 1st matrix by each column in the second matrix add the products of each column to get the first row in the 3rd matrix.

2. Multiply the second row of the 1st matrix by each column in the second matrix add the products of each column to get the second row of the 3rd matrix

$\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right]$ × $\left[\begin{array}{ccc}0&3&0\\0&0&2\end{array}\right]$ = $\left[\begin{array}{ccc}(1*0+0*0)&(1*3+0*0)&(1*0+0*2)\\(0*0+-1*0)&(0*3+-1*0)&(0*0+-1*2)\end{array}\right]=\left[\begin{array}{ccc}0&3&0\\0&0&-2\end{array}\right]$