X=cubic root 2/27
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Yes, because it is continuous on [0,2] and differentiable on (0,2), the theorem states that there must exist some value c where a line tangent to c is parallel to the secant line through 0 and 2.
Answer:
BC ≈ 4.85 m
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos26° = 
= 
= 
( cross- multiply )
5.4 × cos26° = BC , then
BC ≈ 4.85 m ( to 3 s f )
Answer:
8
Step-by-step explanation:
Let's just call the number x for simplicity.
So, 7x is 8 less than x².
Putting this into an equation would look like this
x² - 8 = 7x
It looks like we'll have to factor this to solve. Before we do that we need to move the 7x to the left side so that everything is together.
x² - 7x -8 = 0
Now, we can proceed. To factor we first need to find the factors of -8.
The factors of -8 are
-2 ⋅ 4, -4 ⋅ 2, -1 ⋅ 8, 1 ⋅ -8.
We need to find the pair of factors that adds up to -7. The only ones that do are -1 and 8.
So now that we have these we can create a pair of binomials using them. This will give us the factored form of this equation.
( x + 1 ) ( x - 8 )
To find the solutions we will have to set them to 0 and solve each of these binomials individually.
x - 1 = 0
x = 1
So, one of the solutions is 1. It's not the one we want, since it's positive.
x - 8 = 0
x = 8
This is the one we want since it is positive.
Answer:
In year 2030 the population is predicted to be 71.75 million
Step-by-step explanation:
* <em>Lets explain how to solve the problem</em>
- Using data from 2010 and projected to 2020, the population of
the United Kingdom (y, in millions) can be approximated by the
equation 10.0 y − 4.55 x = 581
- x is the number of years after 2000
- We need to know in what year the population is predicted to be
71.75 million
* <em>Lets substitute the value of y in the equation by 71,75</em>
∵ The equation of the population is 10.0 y - 4.55 x = 581
∵ y = 71.75
∴ 10.0(71.75) - 4.55 x = 581
∴ 717.5 - 4.55 x = 581
- Subtract 717.5 from both sides
∴ - 4.55 x = - 136.5
- Divide both sides by - 4.55
∴ x = 30
∵ x represents the number of years after 2000
∵ 2000 + 30 = 2030
∴ In year 2030 the population is predicted to be 71.75 million
