What expressions equal to 19

Brianne's town is building a pool based on a scale drawing that is 20 centimeters by 10 centimeters and uses the scale 1 cm:250

kiruha [24]

Answer:

$A=1250m^2$

Step-by-step explanation:

From the question we are told that

Dimension of drawing

20 centimetres by 10 centimetres

Scale of drawing

1 cm:250 cm

Generally the the Main dimension of the pool is mathematically given as

$L=length\ of\ scaled\ pool*250 cm\\B=length\ of\ scaled\ pool*250 cm\\L=20*250=5000 cm=50m\\B=10*250=2500 cm=25m$

Therefore Area Aof main pool is mathematically given as

$A=50m*25m=1250 m^2$

$A=1250m^2$

4 0

3 years ago

Find the length of the curve given by ~r(t) = 1 2 cos(t 2 )~i + 1 2 sin(t 2 ) ~j + 2 5 t 5/2 ~k between t = 0 and t = 1. Simplif

xxMikexx [17]

Answer:

The length of the curve is

L ≈ 0.59501

Step-by-step explanation:

The length of a curve on an interval a ≤ t ≤ b is given as

L = Integral from a to b of √[(x')² + (y' )² + (z')²]

Where x' = dx/dt

y' = dy/dt

z' = dz/dt

Given the function r(t) = (1/2)cos(t²)i + (1/2)sin(t²)j + (2/5)t^(5/2)

We can write

x = (1/2)cos(t²)

y = (1/2)sin(t²)

z = (2/5)t^(5/2)

x' = -tsin(t²)

y' = tcos(t²)

z' = t^(3/2)

(x')² + (y')² + (z')² = [-tsin(t²)]² + [tcos(t²)]² + [t^(3/2)]²

= t²(-sin²(t²) + cos²(t²) + 1 )

................................................

But cos²(t²) + sin²(t²) = 1

=> cos²(t²) = 1 - sin²(t²)

................................................

So, we have

(x')² + (y')² + (z')² = t²[2cos²(t²)]

√[(x')² + (y')² + (z')²] = √[2t²cos²(t²)]

= (√2)tcos(t²)

Now,

L = integral of (√2)tcos(t²) from 0 to 1

= (1/√2)sin(t²) from 0 to 1

= (1/√2)[sin(1) - sin(0)]

= (1/√2)sin(1)

≈ 0.59501

8 0

3 years ago

Triangle ABC contains side lengths b=3 inches and c= 5 inches in two or more sentences describe whether or not it is possible fo

Scrat [10]

Answer:

Since sine of all angles are always less than one, this shows there is no possible way to have an angle C. Thus it is impossible to have a triangle ABC with the given properties of side lengths b=3 inches and c= 5 inches to have angle B =45 degrees.

Step-by-step explanation:

In the attached drawing, each of the tic-marks are equal and

represent 1 inch each. The angle B has measure 45. We can

see by the arc that the line AC, which equals 3 inches, is

not long enough to reach the slanted side of the 45 angle.

Therefore triangle ABC is not possible. We can also show

by the law of sines that no triangle ABC with the given

properties in possible.

5 0

3 years ago

A baby outfit uses 2/9 square yard of fabric for the hat and 5/9 square yards of fabric for the bib. A tailor has 5 4/9 square y

Ludmilka [50]

Answer:

She can make<u> 7 </u>baby outfits.

Step-by-step explanation:

Given:

A baby outfit uses 2/9 square yard of fabric for the hat and 5/9 square yards of fabric for the bib.

A tailor has 5 4/9 square yards of fabric.

Now, to find the outfits she can make.

So, we add to get the total fabric used for baby outfits hat and bib:

$\frac{2}{9} +\frac{5}{9}\ square\ yards.$

$=\frac{2+5}{9}\ square\ yards.$

$=\frac{7}{9}\ square\ yards.$

Total fabric used for outfit = $=\frac{7}{9}\ square\ yards.$

Total fabric tailor has = $5\frac{4}{9} =\frac{49}{9}\ square\ yards$

Now, to get the number of outfits from the fabric tailor has we divide by total fabric used for outfit:

Number of outfits = Total fabric tailor has ÷ Total fabric used for outfit.

$Number\ of\ outfits = \frac{49}{9} \div\frac{7}{9}$

<em>Thus, on dividing we get:</em>

$Number\ of\ outfits = 7\ outfits.$

Therefore, she can make 7 baby outfits.

6 0

4 years ago

Please help and fast

kirza4 [7]

A the slope of the line is 1

to calculate the slope m , use the ' gradient formula '

m = ( y₂ - y₁ ) /( x₂ - x₁ )

where (x₁, y₁ ) = 6, 3) and (x₂, y₂ ) = (9, 6)

m = $\frac{6 - 3}{9 - 6}$ = $\frac{3}{3}$ = 1

5 0

3 years ago