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s344n2d4d5 [400]
3 years ago
14

1. Isiah wants to bring cupcakes for 54 of his friends. One box of cupcakes is

Mathematics
1 answer:
AleksandrR [38]3 years ago
6 0

Answer:

6 boxes.

Step-by-step explanation:

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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant
nirvana33 [79]

Answer:

The instantaneous rate of change of y with respect to x at the value x = 3 is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of y with respect to x over the interval by definition of secant line:

r = \frac{y(b) -y(a)}{b-a} (1)

Where:

a, b - Lower and upper bounds of the interval.

y(a), y(b) - Function exaluated at lower and upper bounds of the interval.

If we know that y = 3\cdot x^{2}, a = 3 and b = 6, then the average rate of change of y with respect to x over the interval is:

r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}

r = 27

The average rate of change of y with respect to x over the interval [3,6] is 27.

b) The instantaneous rate of change can be determined by the following definition:

y' =  \lim_{h \to 0}\frac{y(x+h)-y(x)}{h} (2)

Where:

h - Change rate.

y(x), y(x+h) - Function evaluated at x and x+h.

If we know that x = 3 and y = 3\cdot x^{2}, then the instantaneous rate of change of y with respect to x is:

y' =  \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}

y' =  3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}

y' = 3\cdot  \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}

y' = 6\cdot  \lim_{h \to 0} x +3\cdot  \lim_{h \to 0} h

y' = 6\cdot x

y' = 6\cdot (3)

y' = 18

The instantaneous rate of change of y with respect to x at the value x = 3 is 18.

5 0
2 years ago
Y= -27(x+4)³+1 the real zero(s) is (are)
rjkz [21]
\bf y=-27(x+4)^3+1\implies 0=-27(x+4)^3+1
\\\\\\
-1=-27(x+4)^3\implies \cfrac{-1}{-27}=(x+4)^3\implies \cfrac{1}{27}=(x+4)^3
\\\\\\
\sqrt[3]{\cfrac{1}{27}}=x+4\implies \cfrac{\sqrt[3]{1}}{\sqrt[3]{27}}=x+4\implies \cfrac{1}{3}=x+4\implies \cfrac{1}{3}-4=x
\\\\\\
-\cfrac{11}{3}=x
4 0
3 years ago
Answers please! I’m a bit confused
scoray [572]

Answer:

all work is shown and pictured

5 0
2 years ago
Read 2 more answers
Please help me! I really need someone to explain how to find the perimeter also. Thank you in advance!
andrezito [222]
You add all the sides together and divide by the number of side so in your case it would be 6 sides and you should get your perimeter i think thats how you do it i could be wrong 

5 0
3 years ago
Read 2 more answers
The yearly sales of candles decreased from 560 to 476. By what percentage did the candle sales decrease?
Korvikt [17]

The candle sales decreases to - 15 percentage.

<u>Step-by-step explanation:</u>

(476 - 560) : 560 x 100

= (476 : 560 - 1)100

= 85 - 100 = - 15

Therefore, - 15% did the candle sales decrease.

4 0
3 years ago
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