1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Deffense [45]
4 years ago
14

For the angles α and β in the figures, find cos(α + β)?

Mathematics
2 answers:
Blizzard [7]4 years ago
4 0

Answer:

cos(\alpha + \beta)=cos(68.4\°) \approx 0.37

Step-by-step explanation:

<h3>Little triangle.</h3>

We know both legs, we can use the tangent trigonometric reason to find the angle.

tan\alpha =\frac{2}{4}\\ tan \alpha=\frac{1}{2}\\ \alpha=tan^{-1}(\frac{1}{2} )\\ \alpha \approx 26.6\°

<h3>Larger triangle.</h3>

We know the hypothenuse and the opposite leg. We can use the sin trigonometric reason to find the angle

sin\beta =\frac{4}{6}\\ sin\beta=\frac{2}{3}\\ \beta=sin^{-1} (\frac{2}{3} )\\\beta= 41.8\°

So, the sum of them is

\alpha + \beta = 26.6+41.8= 68.4\°

Then,

cos(\alpha + \beta)=cos(68.4\°) \approx 0.37

Therefore,

cos(\alpha + \beta)=cos(68.4\°) \approx 0.37

Blababa [14]4 years ago
3 0

Answer:

\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})

Step-by-step explanation:

Let the hypotenuse of the smaller triangle be h units.

Then; from the Pythagoras Theorem.

h^2=4^2+2^2

h^2=16+4

h^2=20

h=\sqrt{20}

h=2\sqrt{5}

From the smaller triangle;

\cos (\alpha)=\frac{4}{2\sqrt{5} }=\frac{2}{\sqrt{5} } and \sin(\alpha)=\frac{2}{2\sqrt{5} }=\frac{1}{\sqrt{5} }

From the second triangle, let the other other shorter leg of the second triangle be s units.

Then;

s^2+4^2=6^2

s^2+16=36

s^2=36-16

s^2=20

s=\sqrt{20}

s=2\sqrt{5}

\cos(\beta)=\frac{2\sqrt{5} }{6}=\frac{\sqrt{5} }{3}

and

\sin(\beta)=\frac{4}{6}=\frac{2}{3}

We now use the double angle property;

\cos(\alpha +\beta)=\cos(\alpha)\cos(\beta) -\sin(\alpha)\sin(\beta)

we plug in the values to obtain;

\cos(\alpha +\beta)=\frac{2}{\sqrt{5} }\times \frac{\sqrt{5} }{3}-\frac{1}{\sqrt{5} }\times \frac{2}{3}

\cos(\alpha +\beta)=\frac{2}{3}(1-\frac{\sqrt{5}}{5})

You might be interested in
Your younger sibling runs up to you and excitedly exclaims, "I'm thinking of a number. If I add it to the number 2 ten times, th
erik [133]

Answer:

x = 0

Step-by-step explanation:

Given

Represent the number with x.

So:

2 + x + x + x + x + x + x  + x + x + x + x = 2

or

2 + 10x = 2

We want to solve for x

Subtract both sides by 2

2 - 2 + 10x = 2 - 2

10x = 0

Solve for x

x = \frac{0}{10}

x = 0

No other number aside 0, satisfy the property.

4 0
3 years ago
A circular flower bed in a botanical garden with a radius of 4 feet
n200080 [17]
First you have to know the formula, which is a=p*r^2.
next you have to fill in the info which is 3.14*16 or A=50.24
so the answer for the area is 50.24 Ft
hope this helps have a great day
pls give brainliest

5 0
3 years ago
Find the sum of three consecutive numbers if the number in the middle is 32.
Sav [38]

Answer:

96

Step-by-step explanation:

x + (x + 1 ) + (x + 2)

x + 32 + x + 1

31 + 32 + 33

96

4 0
4 years ago
∆ABC rotates 90° clockwise about point P to form ∆A′B′C′.
OlgaM077 [116]
Assume P(xp,yp), A(xa,ya), etc.
We know that rotation rule of 90<span>° clockwise about the origin is
R_-90(x,y) -> (y,-x)
For example, rotating A about the origin 90</span><span>° clockwise is
(xa,ya) -> (ya, -xa)
or for a point at H(5,2), after rotation, H'(2,-5), etc.

To rotate about P, we need to translate the point to the origin, rotate, then translate back.  The rule for translation is
T_(dx,dy) (x,y) -> (x+dx, y+dy)

So with the translation set at the coordinates of P, and combining the rotation with the translations, the complete rule is:
T_(xp,yp)  R_(-90)  T_(-xp,-yp) (x,y) 
-> </span>T_(xp,yp)  R_(-90)  (x-xp, y-yp)
-> T_(xp,yp)  (y-yp, -(x-xp))
-> (y-yp+xp, -x+xp+yp)

Example: rotate point A(7,3) about point P(4,2)
=> x=7, y=3, xp=4, yp=2
=> A'(3-2+4, -7+4+2) => A'(5,-1)

6 0
4 years ago
A rice merchant purchased 50 bags of rice at rupees 300 per back he spent 500 rupees towards transportation due to lack of deman
Alex777 [14]

Answer:

10500 rupees

Step-by-step explanation:

So 50 bags 300 per pack so

300*50= 15000

15000 is what he spent on the 50 bags of rice

So he spent 500 rupees on transportation

15000 + 500 = 15500 total spent which is not needed but extra information

30% loss is 30% of 15000 so

30% of 15000 = 4500

15000 - 4500 = 10500 rupees

8 0
3 years ago
Other questions:
  • A particular fruit's weights are normally distributed, with a mean of 446 grams and a standard deviation of 17 grams. If a fruit
    14·2 answers
  • Solve for y
    15·1 answer
  • The domain of f(x) = 2x 2 + 4x - 1 is . The range of f(x) = 2x 2 + 4x - 1 is
    15·2 answers
  • Find their perimeter and the area of trapezoid EFGH. Show all work needed to complete this problem. A=1/2(b1+b2)•h
    9·1 answer
  • Which operation? is it dividing
    15·1 answer
  • How do you find the angle between 2 vectors
    14·1 answer
  • If f || g, then find the value of x. The diagram is not to scale.
    11·1 answer
  • The 68-95-99.7 Rule
    15·1 answer
  • Please :/ 38 in scientific notation
    15·2 answers
  • WILL MAKE BRAINLIEST!!! Find the correct angle measure for angle b in each figure.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!