First method: by the rule of three:
126 miles---------------------3 hours
x---------------------------------7 hours
x=(126 miles * 7 hours) / 3 hours=294 miles.
Answer: 294 miles.
Second method:
Speed=distance/ time ⇒distance=speed x time
We calculate the speed of the car:
Speed=126 miles/3 hours= 42 miles/hour.
Data:
Speed=42 miles/hour
time=7 hours
Distance=speed x time
Distance=(42 miles/hour)(7 hours)=294 miles
answer: 294 miles.
The dimensions of a cylinder which has this maximum volume are equal to 1.83 units and 3 units.
<u>Given the following data:</u>
- Height of cylinder, h = 5.5 units.
- Radius of cylinder, r = 4.5 units.
<h3>How to calculate the volume of this cylinder?</h3>
Mathematically, the volume of a cylinder can be calculated by using this formula:
V = πr²h
Next, we would convert the above multi-variable function into a single-variable function by applying the properties of 2 similar triangles:
H/H - h = R/r
H - h = r(H/R)
h = H/R(R - r)
V = πHr²/R(R - r)
In order to maximize the volume of this cylinder, we would determine the critical points of the function by differentiating wrt r:
dV/dr = πH/R(2rR - 2r² - r²)
(2rR - 3r²) = 0
r = 2R/3
r = (2 × 4.5)/3
Maximum radius, r = 3 units.
For the max. height, we have:
h = H/R(R - r)
h = H/R(R - 2R/3)
h = H/3
h = 5.5/3
Maximum height, h = 1.83 units.
Read more on cylinder here: brainly.com/question/315709
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15% = 0.15
0.15 x 20 = 3
15% of 20 is 3.
7 5 35
-- x -- = ---
8 1 8
Therefore 35/8 = 4 3/8
Your answer is 4 3/8, Hope this helped! :)
Answer:
3(x + 2)(2x - 5)
Step-by-step explanation:
Given
6x² - 3x - 30 ← factor out 3 from each term
= 3(2x² - x - 10) ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 10 = - 20 and sum = - 1
The factors are + 4 and - 5
Use these factors to split the x- term
2x² + 4x - 5x - 10 ( factor the first/second and third/fourth terms )
= 2x(x + 2) - 5(x + 2) ← factor out (x + 2) from each term
= (x + 2)(2x - 5), thus
2x² - x - 10 = (x + 2)(2x - 5) and
6x² - 3x - 30
= 3(x + 2)(2x - 5) ← in factored form