Answer:
Step-by-step explanation:
The objective is to combine the terms to make one radical, so therefore we know that we will have to take a 
out of the second radical 
.
If we divide 180 by 5, we will get 36, so now we have
×
can be simplied into just 6.
So now the expression becomes
Then we can further simplify by moving the 
into the radical to get two common terms with 
.
, so we now have
So then we can combine the two radicals to get the expression to
We now see that we have two terms with a common radical, and coefficients of -1, and 48.
That allows us to simplify further to
Here, we can take out 
, which is 
, and get the final simplied form to be
Hope this helped.
Answer:
The force that must be applied on the small piston has a magnitude of 500 newtons.
Step-by-step explanation:
By Pascal's Principle, we know that pressure within any point of a closed hydraulic system is the same. Hence, the hydraulic machine can be described by the following model:
(1)
Where:
- Forces applied on the small and large pistons, in newtons.
- Areas of the small and large pistons, in square meters.
If we know that 
, 
and 
, then the force to be applied on the small piston is:
The force that must be applied on the small piston has a magnitude of 500 newtons.
Answer:
4.2 × 10⁻⁵
Step-by-step explanation:
The decimal point must be after the first non-zero digit.
⇒ 4.2
Multiply 4.2 by a number that results in 0.000042. That number is 0.00001 or 10⁻⁵.
⇒ 4.2 × 10⁻⁵
Answer:
√7 / 4
Step-by-step explanation:
Trigonometrical identity are used to show the relationship between the sides and angles of a right angled triangle. Some trigonometric identities are:
sinΘ = opposite / hypotenuse, cosΘ = adjacent / hypotenuse, tanΘ = opposite / adjacent.
Given that cosΘ = 3 / 4
Therefore, cosΘ = adjacent / hypotenuse = 3 / 4
adjacent = 3, hypotenuse = 4. Let x be the opposite side, to get the opposite side, we use Pythagoras theorem:
opposite² + adjacent² = hypotenuse²
x² + 3² = 4²
x² + 9 = 16
x² = 7
x = √7
sinΘ = opposite/hypotenuse = √7 / 4
15, 35, 55, 75, 95, 115, <u>135</u>.
Step-by-step explanation:
From what I'm seeing you're adding 20 to each term. So you can count from 15 to whatever term you're looking for; which in this case, the 7th term is <u>1</u><u>3</u><u>5</u>.
