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2 years ago

Given: The

Mathematics

1 answer:

AlekseyPX2 years ago

7 0

Answer:

Step-by-step explanation:

We can calculate for a using sine rule.

For angle A,

A + 27° + 82° = 180 ( sum of angles in a triangle).

A + 109 = 180

A = 180 - 109 = 71°

Therefore,

A = 71°

calculating for side a

$\frac{sin \: 27}{12} = \frac{sin71}{a} \\ a = \frac{12 \times sin71}{sin27} \\ a \: = \frac{11.346}{0.454} \\ a = 25$

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Find all solutions in the interval [0,2pi). cos 2x + sqrt(2) sinx=1

kykrilka [37]

cos 2x + sqrt(2) sinx=1

Note that: cos 2x = cos^2x - sin^2x = (1-sin^2x) - sin^2x = 1 - 2sin^2x.
So, when alternatively written, you have the following equation:

- 2sin^2x + sqrt(2)sinx + 1 = 1
- 2sin^2x + sqrt(2)sinx = 0

Then, let z=sin(x). So you get,

- 2z^2 + sqrt(2)z = 0
z(- 2z + sqrt(2)) = 0

Either z=0, or - 2z + sqrt(2) = 0 ---> z=sqrt(2)/2.
Then, since z=0 or z=sqrt(2)/2, therefore sin(x)=0, or sin(x)=sqrt(2)/2.

Then, for you remains just to list the angles. (Let me know if this is not fair or if you got questions.)

6 0

3 years ago

What are the next three terms of the sequence below?

vichka [17]

Answer:

64, 256, 1024 (D)

Step-by-step Explanation:

The sequence is following some rule. And the rule is: Multiplying the term with 4 to get the next term. Like:

$1 × 4 = 4$
$4 \times 4 = 16$

Similarly, the next terms are:

$16 \times 4 = 64$
$64 \times 4 = 256$
$256 \times 4 = 1024$

The terms are 64, 256, 1024 which matches with Option D. And that's the correct answer

4 0

3 years ago

Read 2 more answers

A fisherman casts his bait toward the river at an angle of 25° above the horizontal. The bait and hook reach a maximum height of

weeeeeb [17]

the vertical component of the casting velocity will be reduce to zero at point h by the force of gravity.

If we use the kinematic equation

vf² = vi² +2as

and realize that the final vertical velocity is zero

and the initial vertical velocity is vsinθ

where θ is the angle of cast above the horizon

0 = vsin25 + 2(-9.8)h

h = 0.423v / 19.6

h = 0.02156v

so the missing potential heights and the associated answer velocities are

v = 19 m/s...h = 0.410 m

v = 8.3 m/s...h = 0.179 m

v = 6.9 m/s...h = 0.149 m

v = 8.4 m/s...h = 0.181 m

choose the one that fits the question

or use the method to find the correct velocity based on the actual height reference frame.

4 0

3 years ago

a quadrilateral ABCD in which angle DAB is a right angle. AB is 3.3cm, BC is 3.9cm, CD is 5.2cm and DA is 5.6cm. Find the length

Greeley [361]

Answer:

Part A) BD = 6.5 cm

Part B) see explanation

Step-by-step explanation:

See the attached figure

Part A) Find the length of BD

ΔDAB is a right triangle at A, AB is 3.3cm , DA is 5.6cm

So, DB is the hypotenuse

Using Pythagorean equation:

DB = √(AD² + AB²) = √(3.3² + 5.6²) = √42.25 = 6.5 cm

===================================================

Part B) Show that angle BCD is 90°

Given: CD is 5.2cm , BC is 3.9cm and DB = 6.5 cm

So, CD² = 5.2² = 27.04

BC² = 3.9² = 15.21

DB² = 6.5² = 42.25

So, CD² + BC² = 27.04 + 15.21 = 42.25 = DB²

So, DB represent a hypotenuse at ΔBCD

So, the apposite angle of BD is a right angle

So, ∠BCD = 90°

5 0

3 years ago

the larger of two numbers is 1 more than 3 times the smaller. the diffrence is between 8 time the smaller and 2 tmies the larger

neonofarm [45]

Let the two numbers be x and y, with y being larger than x.
Then y=3x+1.
Also, 8x-2y= 10.

The first equation has already been solved for y. Substitute 3x+1 for y in the second equation:

8x-2(3x+1)=10, or 8x - 6x - 2 = 10, or 2x = 12 and x = 6.

If x = 6, then by the first equation y must be 3(6)+1, or 19.

The numbers are 6 and 19.

8 0

3 years ago