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3 years ago

What is the area of a circle whose diameter is 22?

Mathematics

1 answer:

Rina8888 [55]3 years ago

7 0

diameter 22 equals radius of 11

Area = PI * radius^2 = PI * 11 * 11

Area = 380.1327110844

You might be interested in

How many liters each of a 25% acid solution and a 50% acid solution must be used to produce 80 liters of a 40% acid solution?

alina1380 [7]

Answer:

32 and 48 liters

Step-by-step explanation:

Let 25% solution is x liters, then 50% solution is (80 - x) liters.

<u>Acid content is going to be same:</u>

0.25x + 0.5(80 - x) = 80*0.4
0.25x - 0.5x + 40 = 32
0.25x = 8
x = 8/0.25
x = 32 liters

So 32 liters of 25% solution and 80 - 32 = 48 liters of 50% solution

4 0

3 years ago

The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after

Olenka [21]

To solve this we are going to use the half life equation $N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) }$
Where:
$N_{0}$ is the initial sample
$t$ is the time in years
$t_{1/2}$ is the half life of the substance
$N(t)$ is the remainder quantity after $t$ years

From the problem we know that:
$N_{0} =100$
$t=200$
$t_{1/2} =1600$

Lets replace those values in our equation to find $N(t)$ :
$N(200) =100e^{( \frac{(-0.693)(200)}{1600}) }$
$N(200)=100e^{( \frac{-138.6}{1600} )}$
$N(200)=100e^{-0.086625}$
$N(200)=91.7$

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.

8 0

3 years ago

Find an equation of a line that is tangent to the graph of f and parallel to the given line. Please see picture

ivanzaharov [21]

Answer:

y = 3x - 2 (smaller y-intercept)

y = 3x + 2 (larger y-intercept)

Step-by-step explanation:

First let's write the generic equation of a line:

y = ax + b

This line needs to be parallel to the line 3x - y + 5 = 0, so it needs to have the same slope of this line.

The line 3x - y + 5 = 0 has a slope of 3, so our line has a = 3:

y = 3x + b

Now we need to find the values of b that make this line tangent to the function f(x) = x^3

Let's first find the derivative of f(x) in relation to x:

df(x)/dx = 3x^2

This derivative is the slope of the tangent line to the function for any value of x. We need a slope of 3, so:

3x^2 = 3

x^2 = 1

x = ±1

Now, to find the y-values, we have:

f(1) = 1^3 = 1

f(-1) = (-1)^3 = -1

So, using the points (1,1) and (-1,-1) in our parallel line, we have:

first line using (1,1) : 1 = 3*1 + b

b = -2

second line using (-1,-1) : -1 = -3*1 + b

b = 2

The value of b is the y-intercept of the line, so the line with smaller y-intercept is y = 3x - 2, and the line with larger y-intercept is y = 3x + 2

8 0

2 years ago

A survey was done that asked students to indicate whether they enjoy reading or playing video games.

Xelga [282]

8:1 because it's just and 8 to a 1

5 0

3 years ago

ranslate the sentence into an equation using n as the unknown number. Then solve the equation for n. Two times a number increase

joja [24]

Hi there!

Let's break this down:
Two times a number = 2n
Increased by 5 = + 5
is 15 - = 15

Total equation:
2n + 5 = 15

Solving:
2n + 5 = 15
2n = 10
n = 5

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

4 0

3 years ago