Determine the amplitude of the function y = 2 cos x from the graph shown below:

A 9.85 m ladder is placed against a wall. The height to the top of the ladder is 5 m more than the distance between the wall and

Dafna1 [17]

Given:

Length of the ladder = 9.85 m

The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.

To find:

The height to the top and the distance between the wall and the foot of the ladder.

Solution:

let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).

Pythagoras theorem: In a right angle triangle,

$Hypotenuse^2=Base^2+Perpendicular^2$

In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.

Using the Pythagoras theorem, we get

$(9.85)^2=x^2+(x+5)^2$

$97.0225=x^2+x^2+10x+25$

$0=2x^2+10x+25-97.0225$

$0=2x^2+10x-72.0225$

Here, $a=2, b=10,c=-72.0225$ . Using the quadratic formula, we get

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}$

$x=\dfrac{-10\pm \sqrt{676.18}}{4}$

Approximating the value, we get

$x=\dfrac{-10\pm 26}{4}$

$x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}$

$x=\dfrac{16}{4},\dfrac{-36}{4}$

$x=4,-9$

Distance cannot be negative so $x\neq -9.$

Now we have $x=4$

$x+5=4+5$

$x+5=9$

Therefore, the base is 4 m and the height is 9 m.

5 0

3 years ago

Choose all the polynomials that are in standard form?

Allisa [31]

<h3>2 Answers: Choice B and Choice D</h3>

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Explanation:

Standard form will always have the largest exponents listed first on the left side. Then as you move to the right, the exponents will decrease. Choice B shows this with the exponents counting down (3,2). Choice D is a similar story with the exponents counting down (9,2,1,0). Think of -6x as -6x^1, and also think of the 10 as 10x^0.

Something like choice A is a non-answer because the term with the largest exponent 3 is buried in the middle, and not at the left side. The exponents are not in decreasing order. Choice C can be ruled out for similar reasons.

Side note: the largest exponent is the degree of the polynomial. This only applies to single variable polynomials.

6 0

3 years ago

Read 2 more answers

Solve the system by substitution.<br> -2y - 10 = x<br> - 10x - y = -14

masya89 [10]

Answer:

x=2 and y=−6

sorry this is pretty long, I did not know if you needed the steps or not

Step-by-step explanation:

−2y−10=x;−10x−y=−14

Solve−2y−10=x for x

−2y−10=x

−2y−10+−x=x+−x

−x−2y−10=0

−x−2y−10+2y=0+2y

−x−10=2y

−x−10+10=2y+10

−x=2y+10

-x/-1=2y+10/-1

x=−2y−10

Substitute−2y−10 for x in−10x−y=−14

−10x−y=−14

−10(−2y−10)−y=−14

19y+100=−14

19y+100+−100=−14+−100

19y=−114

19y/19=-114/19

y=-6

Substitute−6 for y in x=−2y−10

x=−2y−10

x=(−2)(−6)−10

x= 2

x=2 and y=−6

6 0

2 years ago

Related subtraction fact for 7+6=13

Svet_ta [14]

13-6=7 or 13-7=6 Hope this helps you

4 0

3 years ago

Read 2 more answers

The price of a video game was reduced from $70.00 to $40.00. By what percentage was the price of the

Sauron [17]

Answer:

43%

Step-by-step explanation:

(40-70) ÷ 70 = -30 ÷ 70 = -0.43 or -43%

Answer: The video game was reduced by 43%.

3 0

3 years ago