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Sergio039 [100]
3 years ago
12

Consider the graph the following exponential, y= 3(2)^x, Is the graph increasing or decreasing? What’s the y intercept? What’s t

he x intercept?
Mathematics
1 answer:
Norma-Jean [14]3 years ago
7 0
Because the base (2) is positive and greater than 1, the function / graph is increasing.  To find the y-intercept, let x= 0 and find y:  y = 3(2)^0 = 6, so the y-intercept is (0,6).  There is no x-ntercept because the graph and the function are always positive / above the x-axis.
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The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute. At the instant when the volume of
Inessa05 [86]

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere -2201.293 square centimeters per second.

<h3>What is the volume of a sphere?</h3>
  • The volume of a sphere, of radius r, is given by:

V = \frac{4\pi r^3}{3}

<h3>What is the surface area of a sphere?</h3>
  • The surface area of a sphere, of radius r, is given by:

S = 4\pi r^2

<h3>What is the rate of change?</h3>

Applying <em>implicit differentiation</em>, the rate of change of both the volume and the surface area can be found, as follows:

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}

\frac{dS}{dt} = 8\pi r\frac{dr}{dt}

Volume of 3131 cubic centimeters, hence:

V = \frac{4\pi r^3}{3}

\frac{4\pi r^3}{3} = 3131

4\pi r^3 = 3(3131)

r = \sqrt[3]{\frac{3(3131)}{4\pi}}

r = 9.0754

The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute, hence:

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}

-9988 = 4\pi (9.0754)^2\frac{dr}{dt}

\frac{dr}{dt} = -\frac{9988}{4\pi (9.0754)^2}

\frac{dr}{dt} = -9.651

Then, the <u>rate of change of the surface area</u> of the sphere is given by:

\frac{dS}{dt} = 8\pi (9.0754)(-9.651) = -2201.293

The rate of change of the surface area of the sphere -2201.293 square centimeters per second.

To learn more about implicit differentiation, you can take a look at brainly.com/question/25608353

4 0
3 years ago
If you have a balance of 1,000 on your edit card and the interest rate is 17 3/4% a year in order to pay off the $100 in 5 years
ankoles [38]

Answer:

$2,263.63

Step-by-step explanation:

You start with "if" but don't end with what your goal is.  I will assume that you want to know how much you'll have to pay after 5 years to pay off this $1,000 loan.  

Use the compound amount formula A = P(1 + r)^5.  Replacing P with $1,000, r with 0.1775 and t with 5 years, we get the payoff balance

A = $1,000(1 + 0.1775)^5 = $2,263.63

6 0
3 years ago
The sum of two natural numbers is 474. One has the digit 1 as its rightmost digit. If this digit is removed from the number, the
Olenka [21]

Answer:

431 and 43

Step-by-step explanation:

Two numbers: y1 and y

Number one: y1 = 10 * y + 1

(10 * y + 1) + y = 474

11y = 473

y = 43

Two numbers: 431 and 43

check: 431 remove 1 (digit) -> 43

431+43=474

8 0
3 years ago
Find the unknown size <br>please I really need answers ​
katen-ka-za [31]

Answer:

z=80°<em><u>(</u></em><em><u>corresponding</u></em><em><u> </u></em><em><u>angles)</u></em>

<em><u>x+z=180°(linear \: pair \: ) \\ 80°  + x = 180°  \\ x= 100°</u></em>

<em><u>y=</u></em><em><u>100 </u></em><em><u>° </u></em><em><u>(</u></em><em><u>alternate</u></em><em><u> </u></em><em><u>angles</u></em><em><u>)</u></em>

<h2><em><u>Hope </u></em><em><u>it </u></em><em><u>helps</u></em><em><u> you</u></em><em><u><</u></em><em><u>3</u></em></h2>
8 0
2 years ago
Which transformation does not always produce a figure that is congruent to the original figure?
natta225 [31]

Answer:dilation

Step-by-step explanation:

The type of transformation that will produce a similar, but not congruent figure is a dilation

7 0
3 years ago
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