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2 years ago

11

If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=8/17and cos b=1

2/13
1) -220/221

2) -140/221

3) 140/221

4) 220/221

1 answer:

n200080 [17]2 years ago

6 0

Recall the sum identity for cosine:

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

so that

cos(a + b) = 12/13 cos(a) - 8/17 sin(b)

Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,

cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17

cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13

Then

cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221

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Karolina [17]

The answer is letter c. If we talked about arithmetic sequence it has the explicit formula: A(n)= a+(n-1)d. So it showed in the choices that letter c has the correct formula for arithmetic sequence. It is the only formula if you are going to find nth term of an arithmetic sequence.

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3 years ago

How much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $14,0

Free_Kalibri [48]

Answer:

The amount of money to be deposited today is $11,725

Step-by-step explanation:

In this question , we are concerned with calculating the amount of money that should be deposited presently to have $14,000 in three years.

To get this, we have to use the compound interest formula

A = P( 1+ r/n)^nt

where A is the amount to be earned after the end of the compounding period which is $14,000 according to this question

P is the initial amount to be deposited which is what we are looking for

r is the rate of compounding which is 6% or simply 6/100 = 0.06

n is the number of times interest is compounded yearly which is semiannually according to the question and this means 2

t is the number of years which is 3 according to the question

Now, plugging all these values, we have;

14,000 = P( 1 + 0.06/2)^(3 * 2)

14,000 = P(1+0.03)^6

14,000 = P(1.03)^6

14,000 = 1.194P

P = 14,000/1.194

P = 11,724.77 which is approximately $11,725

8 0

2 years ago

I need help with 14 and 15!?

Levart [38]

Answer:

15

Step-by-step explanation:

Pythagorean theorem states that the hypogenous of a right triangle is $c=\sqrt{a^{2}+b^{2}}$ . The hypogenous is the longest part of the triangle which is directly across from the 90 degree angle.

a = 9

b = 12

so,

$c = \sqrt{9^{2}+12^{2} } = 15$

7 0

2 years ago

without building the graph, find the coordinates of the point of intersection of the lines given by the equation y=3x-1 and 3x+y

DaniilM [7]

<h2><u>1. Determining the value of x and y:</u></h2>

Given equation(s):

$y = 3x - 1$
$3x + y = -7$

To determine the point of intersection given by the two equations, it is required to know the x-value and the y-value of both equations. We can solve for the x and y variables through two methods.

<h3 /><h3><u>Method-1: Substitution method</u></h3>

Given value of the y-variable: 3x - 1

Substitute the given value of the y-variable into the second equation to determine the value of the x-variable.

$\implies 3x + y = -7$

$\implies3x + (3x - 1) = -7$

$\implies3x + 3x - 1 = -7$

Combine like terms as needed;

$\implies 3x + 3x - 1 = -7$

$\implies 6x - 1 = -7$

Add 1 to both sides of the equation;

$\implies 6x - 1 + 1 = -7 + 1$

$\implies 6x = -6$

Divide 6 to both sides of the equation;

$\implies \dfrac{6x}{6} = \dfrac{-6}{6}$

$\implies x = -1$

Now, substitute the value of the x-variable into the expression that is equivalent to the y-variable.

$\implies y = 3(-1) - 1$

$\implies$ $\ \ = -3 - 1$

$\implies$ $= -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h3 /><h3><u>Method 2: System of equations</u></h3>

Convert the equations into slope intercept form;

$\implies\left \{ {{y = 3x - 1} \atop {3x + y = -7}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {y = -3x - 7}} \right.$

Clearly, we can see that "y" is isolated in both equations. Therefore, we can subtract the second equation from the first equation.

$\implies \left \{ {{y = 3x - 1 } \atop {- (y = -3x - 7)}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

Now, we can cancel the "y-variable" as y - y is 0 and combine the equations into one equation by adding 3x to 3x and 7 to -1.

$\implies\left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

$\implies 0 = (6x) + (6)$

$\implies0 = 6x + 6$

This problem is now an algebraic problem. Isolate "x" to determine its value.

$\implies 0 - 6 = 6x + 6 - 6$

$\implies -6 = 6x$

$\implies -1 = x$

Like done in method 1, substitute the value of x into the first equation to determine the value of y.

$\implies y = 3(-1) - 1$

$\implies y = -3 - 1$

$\implies y = -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h2><u>2. Determining the intersection point;</u></h2>

The point on a coordinate plane is expressed as (x, y). Simply substitute the values of x and y to determine the intersection point given by the equations.

⇒ (x, y) ⇒ (-1, -4)

Therefore, the point of intersection is (-1, -4).

<h3>Graph:</h3>

5 0

1 year ago

Please help! Will mark the brainliest!

dimaraw [331]

(f+g)(5)=33 is the answer

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3 years ago