1. Observe that the f(t) is change by 4 per time t => there's a acceleration of 4 => f''(t) = 4; Take the derivative of it we can get a velocity function. f'(t) = 4t + c. Since the velocity from 100 to 80 is -20 (average), this means at t = 0, f'(0) = -22 => f'(t) = 4t - 22; Take the derivative again to get the position function: f(t) = 2t^2 - 22t + d, here d = 100 should be trivial. So, the function that models the relationship is f(t) = 2t^2 - 22t + 100.
2. By the compound interest formula:
A = P (1 + r/n)^(nt) , since it's yearly, so n = 1;
results A(t) = 100 (1+0.12)^t.
3. The average rate of change is basically finding the slope, m = y1 - y2 / x1 - x2.
The solutions of the equations are -1.3 and -7.7
Step-by-step explanation:
The quadratic formula of solving the quadratic equation
ax² + bx + c = 0, where a, b and c are constant is:
To solve the quadratic equation by using the quadratic formula
1. Find the values of a , b and c from the equation
2. Substitute the values of a , b and c in the quadratic formula
3. Find the two values of x
∵ x² + 9x + 10 = 0
∴ a = 1 , b = 9 and c = 10
∵ 
∴ 
∴ 
∴ x = -1.3
∵ 
∴ 
∴ 
∴ x = -7.7
The solutions of the equations are -1.3 and -7.7
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Answer:
a = 5
Remainder when p(x) is divided by x+2 = 62
Step-by-step explanation:
Given:
P(x) = x⁴-2x³+3x²-ax+3a-7
When x+1 divides the polynomial p(x) the ramainder is 19.
Applying remainder theorem,
x = -1
p(-1) = 19
Substitute the x = -1 into the polynomial expression
p(-1) = (-1)⁴-2(-1)³+3(-1)²-a(-1)+3a-7 = 19
1+2+3+a+3a-7 = 19
6-7+4a = 19
4a-1 = 19
4a = 19+1
4a = 20
a = 20/4
a = 5.
Hence, a = 5
p(x) = x⁴-2x³+3x²-5x+8
If p(x) is divided by x+2,
Then the remainder is p(-2)
p(-2) = (-2)⁴-2(-2)³+3(-2)²-5(-2)+8
p(-2) = 16+16+12+10+8
p(-2) = 62
Hence the remaider when p(x) is divided by x+2 is 62
function rule describes the amount of profit that will be made by the student council on the shirt sales is
.
<u>Step-by-step explanation:</u>
Here we have , student council at Smith Valley High School is planning to sell t-shirts as part of a fundraiser using company A, the shirts cost $4.50 each. The student council has to pay the shirt company a design fee of $45. the shirts will be sold for $12 each. We need to find a function rule describes the amount of profit that will be made by the student council on the shirt sales . Let's find out:
Each shirt cost $4.50 . The student council has to pay the shirt company a design fee of $45. the shirts will be sold for $12 each , So the total amount of t shirt he sell is :
⇒
, where x is the number of t shirts !
Now , expenses is given by :
⇒
, where x is the number of t shirts !
So , Profit made is :
⇒ 
⇒ 
Therefore , function rule describes the amount of profit that will be made by the student council on the shirt sales is
.
Answer:
C. 10 sq. units
Step-by-step explanation:
Area of a pentagon = 1/2 * apothem * perimeter
1/2*(1.62)(2.36*5)=0.81*11.8=9.558
Therefore, about 10 sq. units, or option C.
I hope this helped and have a good rest of your day!