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ki77a [65]
1 year ago
7

How much of the initial mass remains after 80 years? (Round your answer to three decimal places.)

Mathematics
1 answer:
aleksandr82 [10.1K]1 year ago
4 0

Given

y=11(\frac{1}{2})^{\frac{t}{30}}

When t = 80

We substitute for t

y=11(\frac{1}{2})\frac{}{}^{\frac{80}{30}}

Simplify

y=11(\frac{1}{2})^{\frac{8}{3}}

Simplify further

y=1.732g

The final answer

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The some of two consecutive even integers is 170. find the two integers.
Tatiana [17]
2 consecutive even integers : x and x + 2

x + x + 2 = 170
2x + 2 = 170
2x = 170 - 2
2x = 168
x = 168/2
x = 84

x + 2 = 84 + 2 = 86

so ur 2 numbers are 84 and 86
8 0
3 years ago
A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y=ax 2 about the y-
Setler79 [48]

Answer:

a = \frac{1}{2}. Surface Area = \frac{4}{3}ft^{2}. and area of the Dish = \frac{4}{3}ft^{2}+pi4^{2} = \frac{4}{3}ft^{2}+50.27=51.6ft^{2}

Step-by-step explanation:

(1) Constant. y(x) = ax^{2} that is the curve that we need to rotate around the y axis to get the parabola with diameter of 8 feet and 2 meter depth that statement is translated in mathematics as x = -4 to 4 and y = 0 to 2.

y max = 2, x max = 4 setting up a equation with a unknown gives

2=a4 and  a = \frac{1}{2}.

so we have now.

y(x) = \frac{1}{2}x^{2} (Done with solving for a Constant).

(2) Surface Area.

Setting Up surface integral.

(i) range in x = 0 to 4.

(ii) range in y = 0 to 2.

integral is.

Integral(0-2)[{integral[(0-4)\frac{1}{32}x^{2}]}]dy

Evaluating this integral gives. \frac{4}{3}ft^{2}.

and area is surface area + area of the circle with 8ft diameter.

= \frac{4}{3}ft^{2}+pi4^{2} = \frac{4}{3}ft^{2}+50.27=51.6ft^{2}...

Note the Difference between area and aurface area.!

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