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3 years ago

Can anyone help me out? Steps would be useful but not needed. Its Trig-Missing Sides.

Mathematics

1 answer:

Hitman42 [59]3 years ago

5 0

Answer:

10.3 units

Step-by-step explanation:

Recall: SOHCAHTOA

Reference angle = 69°

Side length Opposite to reference angle = x

Hypotenuse length = 11

Thus, apply the trigonometric ratio, SOH:

Sin 69 = Opp/Hyp

Substitute

Sin 69 = x/11

11 × Sin 69 = x

10.2693847 = x

x = 10.3 units (nearest tenth)

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Question 8 (1 point)

ra1l [238]

Probly the first one it looks right

6 0

3 years ago

Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6

Alla [95]

Given:

The expression is:

$2x^3+mx^2+nx+c$

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

$m+n=-6$

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

$P(x)=2x^3+mx^2+nx+c$

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

$P(2)=P(-1)$ ...(i)

Substituting $x=-1$ in the given polynomial.

$P(-1)=2(-1)^3+m(-1)^2+n(-1)+c$

$P(-1)=-2+m-n+c$

Substituting $x=2$ in the given polynomial.

$P(2)=2(2)^3+m(2)^2+n(2)+c$

$P(2)=2(8)+m(4)+2n+c$

$P(2)=16+4m+2n+c$

Now, substitute the values of P(2) and P(-1) in (i), we get

$16+4m+2n+c=-2+m-n+c$

$16+4m+2n+c+2-m+n-c=0$

$18+3m+3n=0$

$3m+3n=-18$

Divide both sides by 3.

$\dfrac{3m+3n}{3}=\dfrac{-18}{3}$

$m+n=-6$

Hence proved.

7 0

3 years ago

What is the value of n in the equation 2.3 × 10 9power = (1 × 10 3power)(2.3 × 10n)

Amanda [17]

Hello,

2.3 x 10^9 = ( 1 x 10^3) ( 2.3 x 10^n)

Solution:

Take the logarithm of both sides of the equation to remove the variable from the exponent.

n=6

Faith xoxo

7 0

3 years ago

Solve X/3+5=9 pls give me answer

dalvyx [7]

The answer is x= 12.

5 0

2 years ago

Let u = <-4, 3>. Find the unit vector in the direction of u, and write your answer in component form. (2 points)

lana66690 [7]

Answer: < -4/5, 3/5>

This is equivalent to writing < -0.8, 0.6 >

======================================================

Explanation:

Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.

We have a right triangle with legs of 4 and 3. The hypotenuse is $\sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5$ through use of the pythagorean theorem.

We have a 3-4-5 right triangle.

Therefore, the vector is 5 units long. This is the magnitude of the vector.

Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.

Therefore, we go from < -4, 3 > to < -4/5, 3/5 >

This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6

Side note: Unit vectors are useful in computer graphics.

6 0

2 years ago