This is an arithmetic sequence.
The numbers differ by a constant.
The general form of an arithmetic sequence is:
Where
a is first term
n is nth term
d is the common difference
Looking at the sequence, we can say the common difference is -3 [since 3 is subtracted from a term to get the next term]
Also, first term is 13
Now, we plug into formula:
Answer:
A
B
Vertex=(6,576)
Step-by-step explanation:
The problem gives us the following data:
A.
Thus the function is
The graph of h has the shape of an inverted parabola. Recall if the coefficient of the quadratic term is negative, the parabola is concave down, so it has a maximum value.
Part B
Let's take the function of h
Factoring by -16
Completing squares
Factoring
Rearranging
We can get the coordinates of the vertex from this standard form of the parabola.
Vertex=(6,576)
The maximum value means that at t=6 seconds, the firework will be 576 feet high and then it will start falling back to the ground.
Answer:
Sin O =
Cos O =
Cot O =
Csc O =
Sec O =
Step-by-step explanation:
Do you know the definitions of all the trig functions? If not, you need to memorize them. Also, you need to memorize which functions are positive in each quadrant. All functions are positive in quad I, sine and reciprocal are positive in quad II, tan and reciprocal are positive in quad III, and cos and reciprocal are positive in quad IV. OK?
Tan of an angle is opposite side/adjacent side of a right triangle
If the tan O = - 2. let the opp. side = 2 and adjacent side = 1. Then the hypotenuse =
Sine is positve and equals opp/hyp =
Cos is negative and equals adj/hyp =
Cot is negative and is the reciprocal of the tan or adj/opp =
Csc is positive and is the reciprocal of the sine or hyp/opp =
Sec is negative and is the reciprocal of the cos or hyp/adj =
Answer:
x = y = 22
Step-by-step explanation:
It would help to know your math course. Do you know any calculus? I'll assume not.
Equations
x + y = 44
Max = xy
Solution
y = 44 - x
Max = x (44 - x) Remove the brackets
Max = 44x - x^2 Use the distributive property to take out - 1 on the right.
Max = - (x^2 - 44x ) Complete the square inside the brackets.
Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.
Max = -(x - 22)^2 + 484
The maximum occurs when x = 22. That's because - (x - 22) becomes 0.
If it is not zero it will be minus and that will subtract from 484
x + y = 44
xy = 484
When you solve this, you find that x = y = 22 If you need more detail, let me know.
Answer:
324 cm²
Step-by-step explanation:
→ Work out perimeter of square
72 + 72 + 72 + 72 = 288
→ Work out the width of the rectangle
288 - (90 × 2) = 108
108 ÷ 2 = 54
→ Work out area of square
72 × 72 = 5184 cm²
→ Work out area of rectangle
90 × 54 = 4860 cm²
→ Minus the areas from each other
5184 cm² - 4860 cm² = 324 cm²