MATHEMATICS COLLEGE

An architect uses a scale of 2/3inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?

Answers

Answer 1

Answer:

Length of the wall on blueprint will be 16 inches.

Use of scale to calculate the distances or length,

Scale used by an architect on a blueprint,

$(2)/(3)\text{ inch}= 1\text{ foot}$

Scale represents the ratio of the length of the wall on blueprint and actual length,

$\frac{\text{Length on the blueprint}}{\text{Actual length}} =\frac{(2)/(3)\text{ inches}}{1\text{ feet}}$

$\frac{\text{Length on the blueprint}}{\text{Actual length}} =(2)/(3)$

If actual length of the east wall of the building = 24 feet

Substitute the value in the expression representing the ratio,

$\frac{\text{Length on the blueprint}}{24} =(2)/(3)$

Length of the blueprint = $(2)/(3)* 24$

= $16$ inches

Therefore, length of the wall on blueprint will be 16 inches.

Learn more about the use of scale to calculate the distances on map.

brainly.com/question/11276271?referrer=searchResults

Answer 2

Answer:

Answer:

16 in.

Step-by-step explanation:

We have the ratio

$(in.)/(ft): ((2)/(3) )/(1)$

How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of

$(in.)/(ft):(2)/(3)$

Now we need to know how many inches there would be if the number of feet is 24:

$(in.)/(ft):(2)/(3) =(x)/(24)$

Cross multiply to get

3x = 48 so

x = 16 in.

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Which inequality is equivalent to |x-4|<9?

HELP ASAP WILL MARK BRAINLY

Answers

Answer:

$(61)/(99)$

Step-by-step explanation:

let x = 0.616161 (etc.)

make a second equation because you multiply by 100:

100x = 61.616161 (etc.)

subtract from each other

100x = 61.616161

x = 0.616161

you get

99x = 61

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Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?

Answers

Answer:

q = 0.105uC

Step-by-step explanation:

We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.

Considering the horizontal and vertical components.

First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:

E=kq/r²

Where r = 20cm

= 20/100

= 0.2m

K = 9.0×10^9

9.0×10^9 × q /0.2²

9.0×10^9/0.04

2.25×10^11 q

These are vector fields of course

Sum the horizontal components

Ecos0 + Ecos300 = E+0.5E

= 1.5E

Sum the vertical components

Esin0 + Esin300 = -E√3/2

Resultant = √3E at -30° or 330°

So the force on q at the lower right corner is q√3×E

The balls have two forces, horizontal = √3×E×q

and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg

mg×tanθ = q√3E.

..1

Then θ will be...

Since the hypotenuse = 80cm

80cm/100

= 0.8m

The distance from the centroid to the lower right vertex is 0.1/cos30 =

0.1/0.866

= 0.1155m

Hence,

0.8×sinθ = 0.1155

Sinθ = 0.1155/0.8

Sin θ = 0.144375

θ = arch sin 0.144375

θ = 8.3°

From equation 1

mg×tanθ = q√3E

g = 9.8m/s^2

m = 3.0g = 0.003kg

0.003×9.8×tan(8.3)

0.00428 = q√3E

0.00428 = q×1.7320×E

Where E=kq/r²

Where r = 0.2m

0.0428 = kq^2/r² × 1.7320

K = 9.0×10^9

0.0428/1.7320 = 9.0×10^9 × q² / 0.2²

0.02471×0.04 = 9.0×10^9 × q²

0.0009884 = 9.0×10^9 × q²

0.0009884/9.0×10^9 = q²

q² = 109822.223

q = √109822.223

q = 0.105uC

The orange shape is a dilation of the black shape. What is the scale factor of the dilation?1/10 1/2 10 2

Answers

Answer:

Scale = ¼

Step-by-step explanation:

See attachment for complete question.

In the attached, we have.

Width = 4 units. ----- Orange

Width = 16 units ------- Black

Required

Determine the scale of dilation

The scale of dilation can be calculated as:

Scale = Width(orange)/Width (black)

Scale = 4/16

Scale = ¼

Hence, the scale of dilation is ¼

Find the surface area of the cube shown below. units 2 2 squared

Answers

The surface area of the cube with a side length of 2 units is 24 units squared

How to determine the surface area?

The side length of the cube is given as:

l = 2

The surface area is calculated as:

Surface area = 6l^2

This gives

Surface area = 6 *2^2

Evaluate

Surface area = 24

Hence, the surface area of the cube is 24 unit squared

Answers

Answer:

Perimeter = 126 cm, area = 972 cm2

Step-by-step explanation:

Rectangle perimeter:

P = 2(w + l)

Rectangle area:

A = wl

When scaled, the perimeter will change by same factor but the area by the square of same factor.

Applying to the given rectangle

Perimeter:

P = 2(6 + 8)(4.5) = 126 cm

Area:

A = 6*8*4.5² = 972 cm²

Correct choice is B

Answer:

Perimeter = 126cm

Area = 972cm^2

Step-by-step explanation:

6*4.5 = 27

8*4.5 = 36

Perimeter = 27*2+36*2= 126 cm

Area = 27*36 = 972 cm^2

Hope this helped!

The table below shows the linear function f.x: -6,-5,-4,-3,-2
f(x): 22,19,16,13,10
Determine the average rate of change of the given function over an interval [-5, -2].
A. -1/3
b.1/3
c.-3
D.3