What is 1/4 times 2/4

A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the

ira [324]

Answer:

7 1/17

Step-by-step explanation:

A figure can be helpful.

The inscribed semicircle has its center at the midpoint of th base. It is tangent to the side of the isosceles triangle, so a radius makes a 90° angle there.

The long side of the isosceles triangle can be found from the Pythagorean theorem to be ...

BC² = BD² +CD²

BC² = 8² +15² = 289

BC = √289 = 17

The radius mentioned (DE) creates right triangles that are similar to ∆BCD. In particular, we have ...

(long side)/(hypotenuse) = DE/BD = CD/BC

DE = BD·CD/BC = 8·15/17

DE = 7 1/17 ≈ 7.059

8 0

2 years ago

5 + 1 7/8 and explain answer

anzhelika [568]

Answer:

6 7/8

Step-by-step explanation:

To evaluate 5 + 1 7/8 we combine the integers 5 and 1 and to this sum add the fraction 7/8:

5 + 1 + 7/8 = 6 7/8 (six and seven eighths)

8 0

2 years ago

A spray irrigation system waters a section of a farmer’s field. If the water shoots a distance of 85 feet, what is the area that

gtnhenbr [62]

Answer:

3,781

Step-by-step explanation:

To solve this problem, we will find the area of the whole circle and use that to find teh area of the 60º section.

First, recognize the formula for the area of a circle:

A = 3.14 $r^{2}$

In this scenario, the radius (r) is 85 feet:

A = 3.14(85 $)^{2}$

A circle is 360º and we only require the area of 60º. 360º / 60º = 6 so we will divide by 6:

A = $\frac{3.14(85)^{2} }{6}$

Finally, we will simplify and round:

A = 3,781

7 0

2 years ago

Please answer the question below (ABOUT VECTORS AND MAGNITUDE)

coldgirl [10]

(a) v appears to have a fixed direction along the positive x-axis. If ||u|| = 150 N, ||v|| = 220 N, then when θ = 30°, you have

u = (150 N) (cos(30°) i + sin(30°) j ) ≈ (129.904 i + 75 j ) N

v = (220 N) (cos(0°) i + sin(0°) j ) = (220 i ) N

(i and j are the unit vectors in the positive x and y directions)

and their sum is

u + v ≈ (349.904 i + 75 j ) N

with magnitude

||u + v|| ≈ √((349.904)² + (75)²) N ≈ 357.851 N ≈ 357.9 N

and at angle φ made with the positive x-axis such that

tan(φ) ≈ (75 N) / (349.904 N) → φ ≈ 12.098° ≈ 12.1°

(b) Letting θ vary from 0° to 180° would make v a function of θ :

u = (150 N) (cos(θ) i + sin(θ) j ) = (150 cos(θ) i + 150 sin(θ) j ) N

Then

u + v = ((220 + 150 cos(θ)) i + (150 sin(θ)) j ) N

→ M = ||u + v|| = √((220 + 150 cos(θ))² + (150 sin(θ))²) N

M = √(48,400 + 66,000 cos(θ) + 22,500 cos²(θ) + 22,500 sin²(θ)) N

M = 10 √(709 + 660 cos(θ)) N

(c) As a function of θ, u + v makes an angle α with the positive x-axis such that

tan(α) = (150 sin(θ) / (220 + 150 cos(θ))

→ α = tan⁻¹((15 sin(θ) / (22 + 15 cos(θ)))

(d) Filling in the table is just a matter of evaluating M and α for each of the given angles θ. For example, when θ = 0°,

M = 10 √(709 + 660 cos(0°)) N = 370 N

α = tan⁻¹((15 sin(0°) / (22 + 15 cos(0°))) = 0°

When θ = 30°, you get the same result as in part (a).

When θ = 60°,

M = 10 √(709 + 660 cos(60°)) N ≈ 323.3 N

α = tan⁻¹((15 sin(60°) / (22 + 15 cos(60°))) = 23.8°

and so on.

4 0

3 years ago

In the figure below, BE || CD . AC is a line. Using the figure for the following questions, select the best answer from the choi

Assoli18 [71]

Because BE and CD are parallel angle DBE = BDC

BDC is given as 36

The answer is 36 degrees

4 0

2 years ago