Ughhh...the limit formula...this should be thrown in the trash the minute you start doing derivatives :P
(-8-9(t+d)-(-8-9t))/(t+d-t)
(-8-9t-9d+8+9t)/d
-9d/d (which is -9 for any value of d as well as when d approaches zero)
-9
So the instantaneous velocity is regardless of t or delta t
(a) The employees must sell 66 pizzas to receive bonus.
(b) There was a 27.27% decrease in sales today.
Step-by-step explanation:
Given,
Pizzas sold yesterday = 55
(a) The owner offers the employees a bonus if the number of pizzas sold increases by 20% today. How many pizzas must the pizzeria sell for employees to receive the bonus?
Pizzas to be sold = 20% of pizzas sold yesterday
Pizzas to be sold = ![\frac{20}{100}*55 = \frac{1100}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B100%7D%2A55%20%3D%20%5Cfrac%7B1100%7D%7B100%7D)
Pizzas to be sold = 11
Total pizzas to be sold today = Yesterday's + 20% more
Total pizzas to be sold today = 55+11 = 66 pizzas
The employees must sell 66 pizzas to receive bonus.
(b) Suppose the actual number of pizzas sold today was 40. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth.
Old value = 55
New value = 40
Change = New value - Old value
Change = 40 - 55 = -15
The negative sign indicates the decrease in sales.
Decrease percent = ![\frac{Change}{Old\ value}*100\\](https://tex.z-dn.net/?f=%5Cfrac%7BChange%7D%7BOld%5C%20value%7D%2A100%5C%5C)
![Decrease\ percent=\frac{15}{55}*100\\Decrease\ percent=27.27%](https://tex.z-dn.net/?f=Decrease%5C%20percent%3D%5Cfrac%7B15%7D%7B55%7D%2A100%5C%5CDecrease%5C%20percent%3D27.27%25)
There was a 27.27% decrease in sales today.
Keywords: percentage, decrease
Learn more about percentages at:
#LearnwithBrainly
Answer:
-5 ; 1/2
Step-by-step explanation:
<u>GIVEN :-</u>
- A quadratic polynomial f(x) = 2x² + 9x - 5
<u>TO FIND :-</u>
- Zeroes of f(x) = 2x² + 9x - 5
<u>GENERAL CONCEPTS TO BE USED IN THIS QUESTION :-</u>
Lets say there's a quadratic polynomial f(x) = ax² + bx + c , whose factors are (x - α) & (x - β). To find the values of x for which f(x) will be zero , equate the factors of f(x) with 0.
⇒ (x - α) = 0 & (x - β) = 0
⇒ x = α & x = β
Hence, it can be concluded that if (x - α) & (x - β) are factors of f(x) , then α & β are the roots of f(x).
<u>SOLUTION :-</u>
Factorise f(x) = 2x² + 9x - 5.
![=> 2x^2 + 10x - x - 5](https://tex.z-dn.net/?f=%3D%3E%202x%5E2%20%2B%2010x%20-%20x%20-%205)
- Take '2x' common from first two terms & '-1' from last two terms.
![=> 2x(x + 5) - 1(x + 5)](https://tex.z-dn.net/?f=%3D%3E%202x%28x%20%2B%205%29%20-%201%28x%20%2B%205%29)
- Take (x + 5) common from the whole expression.
![=> (x + 5)(2x - 1)](https://tex.z-dn.net/?f=%3D%3E%20%28x%20%2B%205%29%282x%20-%201%29)
So , the factors of f(x) are (x + 5) & (2x - 1). Now equate the factors with zero.
⇒ (x + 5) = 0 & (2x - 1) = 0
⇒ x = -5 & x = 1/2
∴ The zeroes of f(x) = 2x² + 9x - 5 are (-5) & (1/2)
<u>VERIFICATION :-</u>
1) Put x = -5 in f(x) = 2x² + 9x - 5
⇒ f(-5) = 2(-5)² + 9×(-5) - 5
= 50 - 45 - 5
= 50 - 50
= 0
2) Put x = 1/2 in f(x) = 2x² + 9x - 5
![f(\frac{1}{2} ) = 2 \times (\frac{1}{2} )^2 + 9 \times \frac{1}{2} - 5](https://tex.z-dn.net/?f=f%28%5Cfrac%7B1%7D%7B2%7D%20%29%20%3D%202%20%5Ctimes%20%28%5Cfrac%7B1%7D%7B2%7D%20%29%5E2%20%2B%209%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%20-%205)
![= \frac{1}{2} + \frac{9}{2} - 5](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Cfrac%7B9%7D%7B2%7D%20-%205)
![= \frac{ 1 + 9 - 10}{2}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%201%20%2B%209%20-%2010%7D%7B2%7D)
![= \frac{0}{2}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B0%7D%7B2%7D)
![= 0](https://tex.z-dn.net/?f=%3D%200)
Answer:
1
Hope this helps sorry I'm not really good at explaining math, cause when I do nobody understands.
Answer:
1.8 years
Step-by-step explanation:
Step one:
given data
P= $2000
Rate= 5%
Final amount A= $3800
Step two
A= P(1+rt)
substitute
3800=2000(1+0.05*t)
solve for t
3800=2000(1.05t)
3800=2100t
divide both sides by 2100
t= 3800/2100
t=1.8 years
it will take 1.8 years