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3 years ago

Someone please help me with these Geometry questions.

Mathematics

1 answer:

AnnZ [28]3 years ago

6 0

<h3>Answer: 112.5 square units</h3>

Work Shown:

A = area of the triangle

A = base*height/2

A = 9*7/2 = 63/2 = 31.5 ... see note1 below

B = area of rectangle

B = base*height

B = 9*3 = 27

C = area of parallelogram

C = base*height .... see note2 below

C = 9*6 = 54

If you're confused where I got the 6 from, check out the attached image below.

D = total area of the composite figure

D = A+B+C

D = 31.5 + 27 + 54

D = 112.5

-------------------------

note1: The vertical component of the triangle is 9 units because this is part of the rectangle. The rectangle has opposite sides that are the same length. The parallelogram's vertical sides are 9 units long as shown by the single tickmark.

note2: a rectangle is essentially a special case of a parallelogram. In other words, a rectangle is a parallelogram with 4 right angles. So this is why the formula "area = base*height" shows up identical for both rectangles and parallelograms. Keep in mind that the height is always perpendicular to the base. You will not use the segments marked with double tickmarks.

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For the function f(t) =Pe^rt , if P= 7 and r= 0.07 then what is the value of f(7) to the nearest tenth?

White raven [17]

Answer:

A. 11.4

Step-by-step explanation:

$f(t) = P e^{rt}$

Data:

P = 7

r = 0.07

Calculation:

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3 years ago

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Use the substitution method to solve the system of equations. y = -8x 4x - y = 3 O AG-2 O B. (6-1 oc c. (6.-4 D. G-4

Triss [41]

<h2>Known : </h2>

y = -8x

4x - y = 3

<h2>Asked: </h2>

Use the substitution method to solve the system of equations ?

<h2>Answered:</h2>

<h3>Substitution y</h3>

4x - y = 3

4x - (-8x) = 3

4x + 8x = 3

12x = 3

x = 3/12

x = 1/4

<h3>Substitution x</h3>

4x - y = 3

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A piece of wire of length 6363 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the

Lerok [7]

Answer:

35.2792 cm from one end (The square)

And 27.7208 cm from the other end (The circle)

b. See (b) explanation below

Step-by-step explanation:

Given

Length of Wire ,= 63cm

Let L be the length of one side of the square

Circumference of a circle = 2πr

Perimeter of a square = 4L

a. To minimise

4L + 2πr = 63 ----- make r the subject of formula

2πr = 63 - 4L

r = (63 - 4L)/2π

r = (31.5 - 2L)/π

Let X = Area of the Square. + Area of the circle

X = L² + πr²

Substitute (31.5 - 2L)/π for r

So,

X² = L² + π((31.5 - 2L)/π)²

X² = L² + π(31.5 - 2L)²/π²

X² = L² + (31.5 - 2L)²/π

X² = L² + (992.25 - 126L + 4L²)/π

X² = L² + 992.25/π - 126L/π +4L²/π ------ Collect Like Terms

X² = 992.25/π - 126L/π + 4L²/π + L²

X² = 992.25/π - 126L/π (4/π + 1)L² ---- Arrange in descending order of power

X² = (4/π + 1)L² - 126L/π + 992.25/π

The coefficient of L² is positive so this represents a parabola that opens upward, so its vertex will be at a minimum

To find the x-cordinate of the vertex, we use the vertex formula

i.e

L = -b/2a

L = - (-126/π) / (2 * (4/π + 1)

L = (126/π) / ( 2 * (4 + π)/π)

L = (126/π) /( (8 + 2π)/π)

L = 126/π * π/(8 + 2π)

L = (126)/(8 + 2π)

L = 63/(4 + π)

So, for the minimum area, the side of a square will be 63/(4 + π)

= 8.8198 cm ---- Approximated

We will need to cut the wire at 4 times the side of the square. (i.e. the four sides of the square)

I.e.

4 * (63/(4 + π)) cm

35.2792 cm from one end.

Subtract this result from 63, we'll get the other end.

i.e. 63 - 35.2792

= 27.7208 cm from the other end

b. To maximize

Now for the maximum area.

The problem is only defined for 0 ≤ L ≤ 63/4 which gives

0 ≤ L ≤ 15.75

When L=0, the square shrinks to 0 and the whole 63 cm wire is made into a circle.

Similarly, when L =15.75 cm, the whole 63 cm wire is made into a square, the circle shrinks to 0.

Since the parabola opens upward, the maximum value is at one endpoint of the interval, either when

L=0 or when L = 15.75.

It is well known that if a piece of wire is bent into a circle or a square, the circle will have more area, so we will assume that the maximum area would be when we "cut" the wire 0, or no, centimeters from the

end, and bend the whole wire into a circle. That is we don't cut the wire at

all.

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3 years ago

The equation tan(55) = 15/b can be used to find the length of line AC.what is the length of line AC round to the nearest 10th 3.

Nadusha1986 [10]

Answer:

10.5 in

Step-by-step explanation:

Given

$tan(55) = \frac{15}{b}$