Answer:
x³ + 7x² - 6x - 72
Step-by-step explanation:
Given
(x + 6)(x + 4)(x - 3) ← expand the second and third factor, that is
(x + 4)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) + 4(x - 3) ← distribute both parenthesis
= x² - 3x + 4x - 12 ← collect like terms
= x² + x - 12
Now multiply this by (x + 6) in the same way
(x + 6)(x² + x - 12)
= x(x² + x - 12) + 6(x² + x - 12) ← distribute both parenthesis
= x³ + x² - 12x + 6x² + 6x - 72 ← collect like terms
= x³ + 7x² - 6x - 72
Answer:
AC = 8√3 AC = 7.65
A = 43.17° AB = 16.8
B = 46.83° B = 27°
Step-by-step explanation:
FIRST TRIANGLE
by using pythagorus theorem:
Hypo² = Base² + height²
19² = 13² + AC²
AC² = 19² - 13²
AC² = 192
AC = √192
AC = 8√3
sinФ =base/hypo
sin A = 13/19
A = sin^-1 (13/19)
A = 43.17°
43.17°+ B + 90° =180 (sum of angles of triangle)
B = 180° - 133.17°
= 46.83°
<h3>SECOND TRIANGLE</h3>
TanФ = base/height
Tan 63° = 15 / AC
1.96 = 15/AC
AC = 15/1.96
AC = 7.65
AB² = AC² + BC²
AB² = 7.65² + 15²
AB² = 283.5
AB = √283.5
AB = 16.8
tan B = AC /BC
tanФ = 7.65/15
tanФ = 0.51
Ф = tan^-1(0.51)
B = 27°
Answer:
d. If your sample size is very large, the distribution of the sample averages will look more like distribution.
Step-by-step explanation:
The central limit Theorem states that for population distribution if you repeatedly take samples from the distribution, then the normal thing for it to happen would be that the distribution means of the samples will be normally distributed, this is what it states, the option that comes closer to that statement would be d. If your sample size is very large, the distribution of the sample averages will look more like distribution, because they large sample will create for a normally distributed means distribution.
The area covered by the canal in 30 mins is 562500 sq m
Step-by-step explanation:
Step 1 :
Given,
The canal's width = 6 meter
The canal's Depth is given as 1.5 meter
Speed of the water flowing = 10 kilometer per hour
We need to determine the area which will be irrigated in 30 mins
Step 2 :
In one hour the canal flows 10 kilometer , therefore in 30 minutes it covers 5 kilometer = 5 × 
meter
Hence the volume of the water irrigated per 30 minutes = 6 × 1.5 × 5 ×
= 45 × cubic meter
The standing water is 8 centimeter = 8 × 
meter
Hence the area covered in 30 min = Volume ÷ the height of the standing water
= (45 × ) ÷ 8 × meter
= 562500 square meter
Step 3 :
The area covered by the canal in 30 mins is 562500 square meter
