All categories

2 years ago

If 4 sec a _ 5 = 0, evaluate 2 cos a + 5 sin a ÷ 2 sin a + 5 cos a

Mathematics

2 answers:

Effectus [21]2 years ago

8 0

Answer:

sorry but I don't know the answer for this

Sever21 [200]2 years ago

4 0

Answer:

23/26 = 0.8846=0.88 [ to the nearest hundredth]

Step-by-step explanation:

4 sec a-5 = 0; seca=1/cos a

Therefore;

4 sec a-5 = 0=>4/cos a - 5 = 0

Multiplying through by cos a, we have;

4-5cosa= 0=>4= 5cosa

4/5 = cosa

a = cos^{-1}0.8

=36.88

Alternatively Cos a =4/5

Sina = 3/5; {note Cos a = adjacent / hypothesis and from Pythagoras rule we can derive the value of the opposite side which is;

5^2 -4^2 = 25-16 = 9; hence the opposite side is √9 = 3;sin a = opposite/ hypothenus = 3/5}

Substituting the value of Cosa and Sina into the expression below;

2 cos a + 5 sin a ÷ 2 sin a + 5 cos a

We have ;

[2×4/5 + 5× 3/5 ]/ [2 × 3/5 + 5× 4/5]

[8/5 + 15/5 ]/ [6/5 + 20/5]

[23/5]/[26/5] = 23/5 × 5/26 = 23/26

You might be interested in

a cone and a sphere have the same volume. the height of the cone is 96 units. what would be the values for the radius of the con

jolli1 [7]

The volume $V_c$ of a cone with base radius $r_c$ and height $h_c$ is

$V_c = \dfrac{1}{3}\pi r_c^2 h_c$

Similarly, the volume $V_s$ of a sphere with radius $r_s$ is

$V_s = \dfrac{4}{3}\pi r_s^3$

We know that $V_c=V_s$ and that $h_c=96$

So, we can set up the following equation:

$\dfrac{96}{3}\pi r_c^2=\dfrac{4}{3}\pi r_s^3$

We can simplify the common denominator 3, and pi appearing on both sides:

$96r_c^2=4r_s^3$

We can divide both sides by 4:

$24r_c^2=r_s^3$

Without further information, this is all we can say: the cubed radius of the sphere is the same as 24 times the squared radius of the cone.

3 0

3 years ago

2. Given a directed line segment with endpoints A(3, 2) and B(6, 11), what is the point that

KATRIN_1 [288]

Answer:

The point of division is (5 , 8)

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divides the line whose endpoints are $(x_{1},y_{1})$

and $(x_{2},y_{2})$ at ratio $m_{1}:m_{2}$ , then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

- The directed line segment with endpoints A (3 , 2) and B (6 , 11)

- There is a point divides AB two-thirds from A to B

∵ The coordinates of the endpoints of the directed line segments

are A = (3 , 2) and B = (6 , 11)

∴ $(x_{1},y_{1})$ is (3 , 2)

∴ $(x_{2},y_{2})$ is (6 , 11)

∵ Point (x , y) divides AB two-thirds from A to B

- That means the distance from A to the point (x , y) is 2/3 from

the distance of the line AB, and the distance from the point (x , y)

to point B is 1/3 from the distance of the line AB

∴ $m_{1}:m_{2}$ = 2 : 1

∵ $x=\frac{(3)(1)+(6)(2)}{2+1}=\frac{3+12}{3}=\frac{15}{3}=5$

∴ The x-coordinate of the point of division is 5

∵ $y=\frac{(2)(1)+(11)(2)}{2+1}=\frac{2+22}{3}=\frac{24}{3}=8$

∴ The y-coordinate of the point of division is 8

∴ The point of division is (5 , 8)

6 0

3 years ago

Craig just finished reading 120 pages of his history assignment if the assignment is 125 Pages what percent has Craig read so fa

diamong [38]

96% is the answer 100%/x%=125/120
(100/x)*x=(125/120)*x - we multiply both sides of the equation by x
100=1.04166666667*x - we divide both sides of the equation by (1.04166666667) to get x
100/1.04166666667=x
96=x
x=96

7 0

3 years ago

6. Mrs. Martinez graphed the transformation shown below. Which algebraic representation shows the effect of the transformation o

iragen [17]

Answer:

Step-by-step explanation:

3 0

2 years ago

The graph of y=f(x) is above. If f(−4)=k, what is the value of f(k)?

cupoosta [38]

Answer:

The answer is B, which is -1.5.

3 0

3 years ago

If 4 sec a _ 5 = 0, evaluate 2 cos a + 5 sin a ÷ 2 sin a + 5 cos a​

If 4 sec a _ 5 = 0, evaluate 2 cos a + 5 sin a ÷ 2 sin a + 5 cos a