3 sinx + 4 cosx = 5

Answers

Answer 1

Answer: 3sinx+4cosx=5
=> 3/5 sinx +4/5 cosx = 1
let cosA=3/5 => sinA=4/5
=> cosAsinx + sinAcosx = 1
=> sin(x+A) = 1
Now,
4sinx - 3cosx
= 5(4/5sinx - 3/5 cosx) [multipying numerator and denominator by 5]
= 5(sinAsinx - cosAcosx)
= -5{cos(x+A)} = -5[root{1-(sin(x+A)^2)}] = -5 x 0 = 0 Ans 0

TRICK: if asinx+bcosx is given then multiply numerator and denominator by root(a^2 +b^2)
this method is useful in many questions

Related Questions

A car has 444 wheels while an autorickshaw has just 333. Complete the blank. An autorickshaw has \%%percent fewer wheels than a car. Show Calculator
Can you guys please help me solve these
Not so good with mathematics
How do I write 4(3x+2)-9 in written form?
PLEASE ANSWER QUICKLY... Liam and Michelle split the cost of supplies to build some trebuchets. The expression for the cost that each must pay to make t (trebuchets) is (2.5t+2)+(1.8t+3) as the numerator and 2 as the denominator. What is the cost for each person if t=2

An experiment requires that each student use an 8.5 cm length of magnesium ribbon. How many students can do the experiment if there is a 570 cm length of magnesium ribbon available?

Answers

Just divide 570 cm by 8.5 cm to get number of students.

Find the approximate value of the circumference of a circle with the given radius. Use = 3.14. Round your answer to the nearest hundredth.5.1 cm

how do you now what to mutliply by like 5.1 x 5.1 the multiply by 3.14

Answers

In solving for the value of the circumference of the circle we will just the formula c = πr². From that we will substitute the value c = (3.14)(5.1)², which is equal to c = 3.14 (26.01), which will be then c = 81.6714. In presenting the answer to nearest hundredth it would be 81.67 cm

If 3t − 7 = 5t , then 6t = how do you solve this

Answers

$3t-7=5t \ \ \ |\hbox{subtract 3t} \n -7=5t-3t \n -7=2t \ \ \ |\hbox{multiply by 3} \n \boxed{6t=-21}}$

$3t-7=5t\n5t-3t=-7\n2t=-7|\cdot3\n\boxed{6t=-21}$

What is 23.791 rounded to the nearest tenth?

Answers

The nearest tenth would be the first decimal place, so the answer would be 23.8

how many solutions does the graph above show?
a. one
b. none
c. Infinite

Answers

Answer:

None

Step-by-step explanation:

I said this because i usually don't find any solutions for graphs until i find out that there are infinite or one

b. no solution

explain: if they are parallel, there are no solutions

Solve for x and y simultaneously:
X-2y=3
4xsquared-5xy+6y=3

Answers

x - 2y = 3
4x^2 - 5xy + 6y = 3
lets solve for x the first and substitute in the second:
x = 3 + 2y
4(3 + 2y)^2 - 5(3 + 2y)y + 6y = 3
4(9 + 12y + 4y^2) - 15y - 10y^2 = 3
36 + 48y +16y^2 - 15y - 10y^2 = 3
6y^2 + 33y + 33 = 0
we can solve using the general quadratic formula:
y = (-33 +- √(33^2 - 4*6*33))/12
y = (-33 +- √(297))/12
so there are 2 solutions for y:
y1 = (-33 + √(297))/12
y2 = (-33 - √(297))/12
pick one and then substitute the y value in the first equation to find x

x = 3 + 2y

4(3+2y)^2 - 5(3+2y)y + 6y = 3
4(4y^2 + 12y + 9) - 5(3y + 2y^2) + 6y - 3 = 0
16y^2 + 48y + 36 - 15y - 10y^2 + 6y - 3 = 0
6y^2 + 39y + 33 = 0
6y^2 + 6y + 33y + 33 = 0
6y(y+1) + 33(y+1) = 0
(y+1)(6y+33) = 0
y = -1, -11/2

x = 3 + 2y
x = 3 + 2(-1)
x = 3 + 2(-11/2)
x = 1, -8

Other Questions

Solve for y: 3/4(5x-y)<3

Fast as possible, 100 pointWrite an expression for the Product of (x+5)(x-3)

The coordinates of the vertices of ANGLE PQR are P(-3,3), Q(2,3), and R(-3,-4). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.

Ms. Luna is waterproofing the top of a rectangular wood deck. The width of the deck is 3 m less that the length. The length is 8m. What is the area to be waterproofed?