MATHEMATICS COLLEGE

Use a half-angle identity to fifd the exact value of sin 75º

Answers

Answer 1

Answer:

Answer:sin75=√(2+√3)/2

Step-by-step explanation:

Cosx=1-2sin^2(x/2) let x=150

Cos150=1-2sin^2(150/2) cos150=-√3/2

-(√3)/2=1-2sin^2(75)

2sin^2(75)=1+(√3)/2

2sin^2(75)=(2+√3)/2

Cross multiply

2x2sin^2(75)=2+√3

4sin^2(75)=2+√3

sin^2(75)=(2+√3)/4

Take square root of both sides

sin75=√(2+√3)/√4

sin75=√(2+√3)/2

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Please help me with this homework equation I don’t understand and need help someone please do step by step

What is the equation of the line through (-6,-5) and (-4,-4) in slope-intercept form?

Answers

Answer:

y = 1/2x − 2

Which statement describes this system of equations?
9x – 6y = 15,
3x – 2y = 5

Answers

This system of equation has an infinite number of solutions.

You can tell this because multiplying one equation by a constant gives you exactly the other equation. You can multiply the second equation by 3.

9x - 6y = 15

5(3x - 2y = 5) = 9x - 6y = 15

When this happens, you can assume that there are an infinite number of solutions.

Answer:

1) The equations in the system are equivalent equations.

2) There is no solution to the system of equations.

3) The system of equations has one solution at (3, 2).

4) The system of equations has one solution at (5, 5).

Answer = 1

Step-by-step explanation:

I just did the assignment

Find the slope of the line that asses through the pair of oints (17,11) and (21,19)

Answers

Answer:

The slope of the two points is 2. (8/4)

Answer:

The slope of the two points is 2. (8/4)

Step-by-step explanation:

thats it

If f(x)=8x then what is the area enclosed by the graph of the function, the horizontal axis, and vertical lines at x=2 and x=6

Answers

Answer:

$A=128$

Step-by-step explanation:

First of all we need to graph f(x)=8x, (First picture)

Now we have to calculate the area enclosed by the graph of the function, the horizontal axis, and vertical lines at $x_(1)=2$ and $x_(2)=6$ ,

The area that we have to calculate is in pink (second picture).

The function is positive and the domain is $[2,6]$ then we can calculate the area with this formula:

$A=\int\limits^b_a {f(x)} \, dx$ ,

In this case $b=x_(2) , a=x_(1)$

$A=\int\limits^6_2 {8x} \, dx = 8\int\limits^6_2 {x} \, dx$

The result of the integral is,

$A=8(x^(2))/(2)$ , but the integral is defined in [2,6] so we have to apply Barrow's rule,

Barrow's rule:

If f is continuous in [a,b] and F is a primitive of f in [a,b], then:

$\int\limits^b_a {f(x)} \, dx =F(b)-F(a)$

Applying Barrow's rule the result is:

$A=8.(6^(2) )/(2)-8.(2^(2) )/(2)$

$A=8.(36)/(2) -8.(4)/(2)$

$A=144-16$

$A=128$

AJ, Blaze, Laurence, and Jack pick oranges. Blaze picks three times as many as Laurence. Jack picks twice as many as Blaze. Aj picks three times as many as Laurence. The total weight of the oranges is 1092 pounds. How many pounds does AJ pick?

Answers

Answer: 252 pounds.

Step-by-step explanation:

Let be "b" the amount of pounds Blaze picks, "j" the amount of pounds Jack picks, "l" the amount of pounds Laurence picks and "a" the amount of pounds AJ picks.

Based on the information provided, we know that:

$b=3l\n\n j=2b\n\n a=3l$