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3 years ago

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A rectangle is inscribed in a circle of radius 4 inches. if the length of the rectangle is decreasing at the rate of 2 inches pe

r second, how fast is the area changing at the instant when the length is 5 inches?

1 answer:

evablogger [386]3 years ago

8 0

Awnser is on mathaway.com :)

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9x^2+30x+25=0 graphed

pogonyaev

The graphical representation is give in image

8 0

3 years ago

Graph each absolute value function. State the domain, range, and y-intercept.

Inessa05 [86]

Answer:

i. D:All real numbers

ii.R: $y\le-2$

iii. Y-int: $b=-2.5$

Step-by-step explanation:

The given function is

$y=-\frac{1}{2} |x-1|-2$

The domain of this function are the values of x that makes the function defined.

The absolute value function is defined for all real values.

The domain is all real numbers.

ii. The range refers to the values of y for which x is defined.

$y=-\frac{1}{2} |x-1|-2$

The vertex of this function is

$(1,-2)$

The function is reflected in the x-axis.

The vertex is therefore the maximum point on the graph of the function.

The range is therefore;

$y\le-2$

Or

$(-\infty,2]$

iii. To find the y-intercept, we substitute $x=0$ into the funtion.

$y=-\frac{1}{2} |0-1|-2$

$y=-\frac{1}{2} (1)-2$

$y=-2.5$

The y-intercept is $b=-2.5$

The graph is shown in the attachment.

3 0

3 years ago

Which function can be used to find the number of cells of bacteria in the population at time t

Nonamiya [84]

Answer:

db / dt = kb

this becomes b(t) = Ce^(kt)

C = 100, the initial population

P(1) = 420 = 100 e^(1k)

4.2 = e^k

ln 4.2 = k

a) thus, b(t) = 100 e^(t ln 4.2)

b) b(3) = 100 e^(3 ln 4.2)

c) growth constant will still be ln 4.2 (constant percentage of populatioin)

d) 10000 = 100 e^(t ln 4.2)

100 = e^(t ln 4.2)

ln 100 = t ln 4.2

t = ln 100 / ln 4.2

Step-by-step explanation:

6 0

3 years ago

Write a multiplication sentence to show how 10 gallons and 300 miles are related. How are 5 gallons ad 150 miles related? How ar

RUDIKE [14]

Answer:

It shows for each gallon consumed, we multiply by 30 to get the amount of miles

This applies for the three questions

Step-by-step explanation:

10 gallons and 300 miles are related in such a way that you divide the number if miles by number of gallons.

300/10 = 30 miles per gallon.

It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.

5 gallons ad 150 miles related in such a way that you divide the number if miles by number of gallons.

150/5 = 30 miles per gallon.

It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.

1 gallon and 30 miles related in such a way that you divide the number if miles by number of gallons.

30/1= 30 miles per gallon.

It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.

7 0

3 years ago

Pls give an explanation w your answer

Shalnov [3]

$a^{\frac{1}{n}}=\sqrt[n]{a}\\\\\left(a^n\right)^m=a^{n\cdot m}\\\\a^n\cdot a^m=a^{n+m}$
therefore
$64^\frac{1}{4}=\left(2^6\right)^\frac{1}{4}=2^{6\cdot\frac{1}{4}}\\\\=2^\frac{6}{4}=2^{1\frac{2}{4}}=2^{1+\frac{2}{4}}=2\cdot2^\frac{2}{4}\\\\=2\sqrt[4]{2^2}=2\sqrt[4]4$
Other method:
$64^\frac{1}{4}=\sqrt[4]{64}=\sqrt[4]{16\cdot4}=\sqrt[4]{16}\cdot\sqrt[4]4=2\sqrt[4]4$

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4 0

3 years ago

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