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Makovka662 [10]
3 years ago
13

Here's a question ~

Mathematics
1 answer:
Gre4nikov [31]3 years ago
3 0

Answer:

  • (0, 5√3/2 + 2)

Step-by-step explanation:

Given is the absolute value function.

<u>Observations:</u>

  • It has a slope of ±√3 and the y- intercept of 2.
  • There is no horizontal shift, so the the y-axis is the line of symmetry.
  • The y-axis is also an angle bisector of the two lines.
  • The foot P₁P₂ is parallel to the x-axis since it's perpendicular to the y- axis.

We need to find the coordinates of intersection of the line P₁P₂ with the y- axis (the point Y in the picture).

Consider the triangle AYP₂.

We know AP₂ = 5.

<u>The angle YAP₂ is:</u>

  • arctan (1/√3) = 30°

<u>The distance AY is:</u>

  • AY = AP₂ cos 30° = 5*√3/2

<u>The distance from the x-axis to the point Y is:</u>

  • 5√3/2 + 2, added the y- intercept of the graphed lines

<u>The coordinates of the point Y:</u>

  • (0, 5√3/2 + 2)

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olga2289 [7]

Answer:

a) 2.5 pounds of candy

b) 2.5 pounds of candy

    \frac{0.5}{1} :\frac{y}{5}

    y × 1 = 0.5 × 5

    y = 2.5

Step-by-step explanation:

1 = 5

1/2 = y or 0.5 = y

\frac{0.5}{1} :\frac{y}{5}

y × 1 = 0.5 × 5

y = 2.5

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3 years ago
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Mademuasel [1]

Answer:

USE BODMAS

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Maurice and Johanna have appreciated the help you have provided them and their company Pythgo-grass. They have decided to let yo
Colt1911 [192]
<span><span>1.A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.
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The Law of Cosines is always preferable when there's a choice.  There will be two triangle angles (between 0 and 180 degrees) that share the same sine (supplementary angles) but the value of the cosine uniquely determines a triangle angle.

To find a missing side, we use the Law of Cosines when we know two sides and their included angle.   We use the Law of Sines when we know another side and all the triangle angles.  (We only need to know two of three to know all three, because they add to 180.  There are only two degrees of freedom, to answer a different question I just did.

<span>2.An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
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We'll use the standard parabola, oriented in the usual way.  In that case the directrix is a line y=k and the focus is a point (p,q).

The points (x,y) on the parabola are equidistant from the line to the point.  Since the distances are equal so are the squared distances.

The squared distance from (x,y) to the line y=k is </span>(y-k)^2
<span>
The squared distance from (x,y) to (p,q) is </span>(x-p)^2+(y-q)^2.<span>
These are equal in a parabola:

</span>
(y-k)^2 =(x-p)^2+(y-q)^2<span>

</span>y^2-2ky + k^2 =(x-p)^2+y^2-2qy + q^2

y^2-2ky + k^2 =(x-p)^2 + y^2 - 2qy+ q^2

2(q-k)y =(x-p)^2+ q^2-k^2

y = \dfrac{1}{2(q-k)} ( (x-p)^2+ q^2-k^2)

Gotta go; more later if I can.

<span>3.There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.

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What happens when the two addends have opposite signs and the number with the larger magnitude (size) is positive?
zimovet [89]

Answer:

The smaller addend is subtracted from the bigger addend

Step-by-step explanation:

Represent the two numbers with a and b such that a > b

So, the mathematical representation will be

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Open the bracket

+a -b

<em>This implies that the smaller addend (b) is subtracted from the bigger addend (b)</em>

<em></em>

<em>Take for instance; a = 6 and b = 4</em>

<em>This gives</em>

<em></em>+6 + (-4)<em></em>

<em></em>

<em>Open the bracket</em>

<em></em>= +6 - 4<em></em>

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Answer:

A. a line segment

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