Answer:
£31
Step-by-step explanation:
25 = 800
x = 992
x = 992 x 25 / 800 = 31
To check for continuity at the edges of each piece, you need to consider the limit as
approaches the edges. For example,

has two pieces,
and
, both of which are continuous by themselves on the provided intervals. In order for
to be continuous everywhere, we need to have

By definition of
, we have
, and the limits are


The limits match, so
is continuous.
For the others: Each of the individual pieces of
are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.
The image is missing, so i have attached it.
Answer:
x = 56.44°
Step-by-step explanation:
From the attached image, we can see that this is a right angle triangle which has opposite, adjacent and hypotenuse as sides. Since we want to find the angle x, thus, we can make use of trigonometric ratios.
From the attached image, the side opposite to angle x is 10ft and the hypotenuse is 12 ft.
From trigonometric ratios, we know that, sin x = opposite/hypotenuse
So, sin x = 10/12
x = sin^(-1) (10/12)
x = sin^(-1) 0.8333
x = 56.44°
Answer:
√23
Step-by-step explanation:
When you are given two side lengths of a right triangle, you use the Pythagorean theorem to find the third side: a² + b² = c², where c is the hypotenuse (the longest side).
All you have to do is plug the given information in:
Remember, 13 is the hypotenuse for this triangle.
12² + b² = 13²
Simplify:
144 + b² = 169
Subtract 144 from both sides:
b² = 169-144
b² = 23
Square root both sides:
b = √23
And that's your answer!