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Dahasolnce [82]
3 years ago
5

Which of the following expressions are polynomials

Mathematics
1 answer:
harkovskaia [24]3 years ago
3 0
Its A. B. and C.............
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If tan 0=5/4, calculate the value of cos 0
emmasim [6.3K]
 
                     5
If  tan θ  =  —— , calculate the value of  cos θ:
                     4


Recall the definition of the tangent function:

                 sin θ
tan θ  =  ————
                cos θ
 
  5           sin θ
——  =  ————
  4          cos θ

Cross multiply:

5 · cos θ = 4 · sin θ

Square both sides:

(5 · cos θ)² = (4 · sin θ)²

5² · cos² θ = 4² · sin² θ

25 · cos² θ = 16 · sin² θ

But  sin² θ = 1 – cos² θ.  Substitute that for  sin² θ  into the equation above, then you get

25 · cos² θ = 16 · (1 – cos² θ)

25 · cos² θ = 16 – 16 · cos² θ

Isolate  cos² θ:

25 · cos² θ + 16 · cos² θ = 16

(25 + 16) · cos² θ = 16

41 · cos² θ = 16
 
                    16
cos² θ  =  ———
                    41

                      4²
cos² θ  =  ————
                  (√41)²

Take square root of both sides:
 
                       4
cos θ  =  ±  ———
                    √41

                       4                                    4
cos θ  =  –  ———     or     cos θ  =  ———          ✔
                     √41                               √41


The sign of  cos θ  depends on which quadrant  θ  lies. Since you first have a positive value for  tan θ, then that means  θ  lies either in the  1st  or the  3rd quadrant.

•  If  θ  is a  1st  quadrant angle, then

cos θ > 0
 
                   4
cos θ  =  ———          ✔
                 √41

•  If  θ  is a  3rd  quadrant angle, then

cos θ < 0
 
                       4
cos θ  =  –  ———          ✔
                     √41


I hope this helps. =)

3 0
3 years ago
Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool.
Sergio039 [100]
For this case we can model the problem as a rectangle triangle.
 We know:
 Length of the sides of the triangle
 We want to know:
 Length of the hypotenuse
 Using the Pythagorean theorem we have:
 d =  \sqrt{3^2 + 3^2}
 Rewriting the expression we have:
 d = \sqrt{2(3^2)}
 d = 3\sqrt{2}
 d = 4.2 miles
 Then, the distance that he would have saved if he travels directly is:
 3 + 3 - 4.2 = 1.8 miles&#10;
 Answer:
 
he would have saved:
 
1.8 miles

3 0
3 years ago
Read 2 more answers
If the mean of 4 and x is the same as the mean of 4,10, and x what is the value of x?
storchak [24]
A. (4+16)/2 = (4+10+16)/3 =10
8 0
3 years ago
3[5x - 4] - [-30 - 45x]
Nimfa-mama [501]
3(5x - 4) - (-30-45x)
= 15x - 12 + 30 + 45x <- Distributive Property
=60x + 18 <- Combine Like Terms

If you're trying to solve for 0:

0 = 60 x + 18
-18 = 60x <- Subtracted 18 from both sides
x = \frac{-18}{60} = \frac{-9}{30} <- Divided both sides by 60 and then simplified.

x = \frac{-9}{30} <- Fraction Form
x = -0.3 <- Decimal Form

Give Brainliest for simple answer plz :P
3 0
3 years ago
Read 2 more answers
Reggie cuts 2 feet from a 9​-foot length of rope. Then he cuts 14 inches from the rope. How many inches of rope are​ left?
babunello [35]

Answer:

He is left with 5 feet and 10 inches.

4 0
2 years ago
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