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mariarad [96]
3 years ago
12

ABCD is a rectangle. The length of BD is 8 units, and m angle ABD is 67°. The length of AC is units, and m angle CDB is °.

Mathematics
2 answers:
Mekhanik [1.2K]3 years ago
7 0

Answer:

AC = 8 units

Angle CDB = 67°

Step-by-step explanation:

The given figure represents the data given.

From figure we can see that BD = AC

Length of AC =  8 units

We also have

      ∠ABD = ∠CDB

Angle CDB = 67°

Marina86 [1]3 years ago
5 0
See the attached picture to better understand the problem
we know that
in rectangle ABCD 
AB=CD
and 
AD=BC
therefore
the triangle ACD and triangle ABC are congruent
so
BD=AC
BD=8 units

the answer part a) is
BD= 8 units

Part b) Find angle CBD

we know that
∠ABD+∠CBD=90°---------> by complementary angles
so
∠CBD=90-∠ABD-----> 90-67----> 23°
∠CBD=23°

the answer Part b) is
∠CBD=23 degrees

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3 years ago
Find a parametric representation for the part of the cylinder y2 + z2 = 49 that lies between the planes x = 0 and x = 1. x = u y
sweet-ann [11.9K]

Answer:

The equation for z for the parametric representation is  z = 7 \sin (v) and the interval for u is 0\le u\le 1.

Step-by-step explanation:

You have the full question but due lack of spacing it looks incomplete, thus the full question with spacing is:

Find a parametric representation for the part of the cylinder y^2+z^2 = 49, that lies between the places x = 0 and x = 1.

x=u\\ y= 7 \cos(v)\\z=? \\ 0\le v\le 2\pi \\ ?\le u\le ?

Thus the goal of the exercise is to complete the parameterization and find the equation for z and complete the interval for u

Interval for u

Since x goes from 0 to 1, and if x = u, we can write the interval as

0\le u\le 1

Equation for z.

Replacing the given equation for the parameterization y = 7 \cos(v) on the given equation for the cylinder give us

(7 \cos(v))^2 +z^2 = 49 \\ 49 \cos^2 (v)+z^2 = 49

Solving for z, by moving 49 \cos^2 (v) to the other side

z^2 = 49-49 \cos^2 (v)

Factoring

z^2 = 49(1- \cos^2 (v))

So then we can apply Pythagorean Theorem:

\sin^2(v)+\cos^2(v) =1

And solving for sine from the theorem.

\sin^2(v) = 1-\cos^2(v)

Thus replacing on the exercise we get

z^2 = 49\sin^2 (v)

So we can take the square root of both sides and we get

z = 7 \sin (v)

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Step-by-step explanation:

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timofeeve [1]

Answer:

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Step-by-step explanation:

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