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gogolik [260]
3 years ago
12

The roof of a barn rises vertically 2.5 meters through the horizontal distance of 10 meters. What is the pitch (slope) of the ro

of?
Mathematics
1 answer:
vodomira [7]3 years ago
4 0

Answer:

The pitch (slope) of the roof is 0.25   or 25\%

Step-by-step explanation:

we know that

The formula to calculate the slope  is equal to

m=\frac{y2-y1}{x2-x1}

where

{y2-y1}=2.5\ m  -----> is the vertical distance (rise)

{x2-x1}=10\ m  -----> is the horizontal distance (run)

therefore

m=\frac{2.5}{10}=0.25

convert to percentage

0.25*100=25\%

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Diamonds have a density of 3.5 LaTeX: \frac{g}{cm^3}g c m 3. How big is a diamond that has a mass of 0.10 g?
liubo4ka [24]

For this case we have that by definition, the density is given by:

d = \frac {M} {V}

Where:

M: It is the mass of the diamond

V: It is the volume of the diamond

According to the data of the statement we have:

d = 3.5 \frac {g} {cm ^ 3}\\M = 0.10 \ g

So the volume is:

V = \frac {M} {d}\\V = \frac {0.10 \ g} {3.5 \frac {g} {cm ^ 3}}\\V = 0.02857\\V = 0.03 \ cm^3

Thus, the volume of the diamond is approximately 0.03 \ cm ^ 3

Answer:

0.03 \ cm ^ 3

3 0
3 years ago
Write as a sum, difference or<br> multiple of logarithms.<br> In(8x) = [ ? ]8+ [ ]x
deff fn [24]

Answer:

In(8x)=[In]8 + [In]x

Step-by-step explanation:

By product rule:

In(8x)=[In]8 + [In]x

8 0
2 years ago
In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.
OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

<u>s</u>inθ = <u>o</u>pposite/<u>h</u>ypotenuse           Soh

<u>c</u>osθ = <u>a</u>djacent/<u>h</u>ypotenuse          Cah

<u>t</u>anθ = <u>o</u>pposite/<u>a</u>djacent                Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the <u>hypotenuse</u>. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the <u>adjacent</u> side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has <u>hypotenuse</u> and <u>adjacent</u>: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = d*\frac{41ft}{d}     Multiply both sides by "d"

dcos77° = 41 ft                          

dcos77° / cos77° = 41 ft / cos77°        Divide both sides by cos77°

d = 41 ft / cos77°                      Input into calculator

d = 182.261874....... ft           Unrounded answer

d ≈ 182 ft                       Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

8 0
3 years ago
What is the angle of DBC
Licemer1 [7]
When added, these two angles are supplementary, meaning that their sum is 180. This means that we can do the following to find x, and eventually DBC:

3x+67+4x+50=180
Simplifies to:
7x+117=180
Then by the Subtraction Prop. of Equality:
7x=63
Then divide by 7 on both sides to get that x=9.

We then substitute 9 into angle DBC.
4(9)+50
=36+50
DBC=86

:)

8 0
3 years ago
7)
yuradex [85]

Answer:

9 blue marbles

Step-by-step explanation:

12 divided by 4 = 3

3x3=9

7 0
3 years ago
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