The area of the figure below is 96 mm².
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The area of a shape is the amount of space occupied by a two dimensional figure.
From the diagram
Area of the triangle = (1/2) * base * height = (1/2) * (8 + 8) * 6 = 48 mm²
Area of the parallelogram = base * height = 8 * 6 = 48 mm²
Area of figure = 48 + 48 = 96 mm²
The area of the figure below is 96 mm².
Find out more on Area at: brainly.com/question/25292087
These are two questions and two answers.
1) Problem 17.
(i) Determine whether T is continuous at 6061.
For that you have to compute the value of T at 6061 and the lateral limits of T when x approaches 6061.
a) T(x) = 0.10x if 0 < x ≤ 6061
T (6061) = 0.10(6061) = 606.1
b) limit of Tx when x → 6061.
By the left the limit is the same value of T(x) calculated above.
By the right the limit is calculated using the definition of the function for the next stage: T(x) = 606.10 + 0.18 (x - 6061)
⇒ Limit of T(x) when x → 6061 from the right = 606.10 + 0.18 (6061 - 6061) = 606.10
Since both limits and the value of the function are the same, T is continuous at 6061.
(ii) Determine whether T is continuous at 32,473.
Same procedure.
a) Value at 32,473
T(32,473) = 606.10 + 0.18 (32,473 - 6061) = 5,360.26
b) Limit of T(x) when x → 32,473 from the right
Limit = 5360.26 + 0.26(x - 32,473) = 5360.26
Again, since the two limits and the value of the function have the same value the function is continuos at the x = 32,473.
(iii) If T had discontinuities, a tax payer that earns an amount very close to the discontinuity can easily approach its incomes to take andvantage of the part that results in lower tax.
2) Problem 18.
a) Statement Sk
You just need to replace n for k:
Sk = 1 + 4 + 7 + ... (3k - 2) = k(3k - 1) / 2
b) Statement S (k+1)
Replace
S(k+1) = 1 + 4 + 7 + ... (3k - 2) + [ 3 (k + 1) - 2 ] = (k+1) [ 3(k+1) - 1] / 2
Simplification:
1 + 4 + 7 + ... + 3k - 2+ 3k + 3 - 2] = (k + 1) (3k + 3 - 1)/2
k(3k - 1)/ 2 + (3k + 1) = (k + 1)(3k+2) / 2
Do the operations on the left side and you will find it can be simplified to k ( 3k +1) (3 k + 2) / 2.
With that you find that the left side equals the right side which is a proof of the validity of the statement by induction.
let those numbers be x and y
According to your question
x + y = -7
x - y =14
adding both equations
2x = 7
or x = 7/2
substitute value of x in either equation
y = -21/2
So,
x= 7/2
y=-21/2
Hope this helps!
Thanks
Answer:
1
Step-by-step explanation:
Let us consider the case of 3 numbers: x, y, and z.
Then x/x+y+z + y/x+y+z + z/x+y+z = x+y+z/x+y+z = 1
The same works also for any quantity of numbers.
The y-intercept can be used to discover the high which the ball must be to be intercepted
Step-by-step explanation:
if x represents the distance the ball traveled, y represent the height of the ball. you must use these two points in order to intercept the ball and catch it at the exact location just like a (x,y) graph.
