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3 years ago

If diameter of a circle is twice as large as the diameter of a smaller circle, What

Mathematics

1 answer:

Leona [35]3 years ago

3 0

The area of a circle uses the radius of a circle, which is 1/2 the diameter.

In the calculation the radius is squared.

Since the diameter of the larger circle is twice as large the radius would be 2 times.

2 squared would be: 2^2 = 4

This means the area of the larger circle is 4 times larger which would make the ratio 4:1

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Two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other.

Makovka662 [10]

An isosceles triangle is a type of triangle where 2 sides are equal.

Picture out 2 triangles with the same base length.
On the first triangle, its legs are twice the length of the legs of the second triangle.

To put it into variables, let:
B = the same base length of the two triangles
A = the length of one leg the smaller triangle
2A = the length of one leg of the bigger triangle

Given: Perimeter of smaller triangle = 23cm
Perimeter of bigger triangle = 43cm

Recall the formula for solving the perimeter of a triangle:
Perimeter = A + B + C

where, A, B, and C are the legs of the triangle

Since the triangle involved is an isosceles triangle, therefore, we can say that
Perimeter = 2A + B , 2 legs are equal ( A=C )

Substituting the given perimeter value to the formula.

23cm = 2A + B ⇒ equation 1 (smaller triangle)
43cm = 2(2A) + B ⇒ equation 2 (bigger triangle)

Simplifying equation 2.
43cm = 4A + B
(rearranging) B = 43cm - 4A ⇒ equation 3

Substituting equation 3 to equation 1:
(equation 1) 23cm = 2A + B
23cm = 2A + (43cm - 4A)
23cm = -2A + 43cm
2A = 43cm - 23cm
2A = 20cm ⇒ length of the leg of the bigger triangle
A = 10cm ⇒ length of the leg of the smaller triangle

To solve for the base length, just substitute the value of A to equation 3
(equation 3) B = 43cm - 4A
B = 43cm - 4(10cm)
B = 3 cm

Final Answer:

• For the smaller triangle, the length of the sides are 10cm, 10cm, and 3cm
• For the bigger triangle, the length of the sides are 20cm, 20cm, and 3cm

8 0

3 years ago

In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

erica [24]

In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?

Answer:

$BD = c*sin(A)$

$BD = c*cos(B)$

$BD = b*tan(A)$

Step-by-step explanation:

∆ABD is a right triangle.

Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.

SOH => sin(θ) = opposite/hypotenuse

CAH => Cos(θ) = adjacent/hypotenuse

TOA = tan(θ) = opposite/adjacent

Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:

Let BD = x

AB = c

AD = b

=>The sine ratio for the length of line segment BD = x, using SOH.

θ = A

Opposite = DB = x

hypotenuse = AB = c

$sin(A) = \frac{x}{c}$

Make x the subject of formula.

$c*sin(A) = x$

$BD = x = c*sin(A)$

=>The Cosine ratio for the length of line segment BD = x, using CAH

θ = B

Adjacent = DB = x

hypotenuse = AB = c

$cos(B) = \frac{x}{c}$

Make x the subject of formula.

$c*cos(B) = x$

$BD = x = c*cos(B)$

=>The Tangent ratio for the length of line segment BD = x, using TOA

θ = A

Adjacent = DB = x

hypotenuse = AD = b

$tan(A) = \frac{x}{b}$

Make x the subject of formula.

$b*tan(A) = x$

$BD = x = b*tan(A)$

5 0

4 years ago

Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 4 to

Troyanec [42]

Answer:

40 to 20

Step-by-step explanation:

If you have more work on ratios I'd go to this site https://goodcalculators.com/ratio-calculator/

3 0

3 years ago

the formula s=sqrt sa/6 gives the lenth of the side , s, of a cube with a surface area,SA. how much longer is the side of a cube

nasty-shy [4]

Using the given formula, replace sa with the given surface areas and solve for s:

Surface area = 1200

s = √1200/6

s = √200

s = 14.142

Surface area = 768

s = √768/6

s = √128

s = 11.313

Difference:

14.142 - 11.313 = 2.829 inches

Round answer as needed.

7 0

3 years ago

Read 2 more answers

Not good with word problems please help

Zepler [3.9K]

Let a and b be the respective rates in bricks per minute for Alex and Bob separately.

Alex lays 4 bricks per minute more than Bob

a = b + 4

Working together, their rates scale by 3/4 and they achieve 15 bricks per minutes.

(3/4)(a + b) = 15

Two equations, two unknowns, we solve:

b = a - 4

(3/4)(a + a - 4) = 15

2a - 4 = (4/3) 15 = 20

2a = 24

a = 12

b = a - 4 = 8

Answer: Alex alone does 12 bricks per minute, Bob alone 8 bricks per minute

Check: a=b+4, good

(3/4)(12 +8)=(3/4)(20)=15, good

5 0

3 years ago