A soft drink has a diameter of 6 cm and a height of 11.5 cm. What is the surface area?

You have two circles, one with radius r and the other with radius R. You wish for the difference in the areas of these two circl

gtnhenbr [62]

Answer:

maximum difference of radii = $(r-R)=\frac{1}{2\pi ^{2}}$

Step-by-step explanation:

We know that area of circle is given by

$A=\pi \times (radius)^{2}$

For circle with radius 'r' we have

$A_{1}=\pi \times (r)^{2}$

For circle with radius 'R' we have

$A_{2}=\pi \times (R)^{2}$

Now according to given condition we have

$A_{1}-A_{2}\leq \frac{5}{\pi }$

$\Rightarrow \pi r^{2}-\pi R^{2}\leq \frac{5}{\pi }\\\\\Rightarrow (r^{2}-R^{2})\leq \frac{5}{\pi ^{2}}\\\\(r+R)(r-R)\leq \frac{5}{\pi ^{2}}\\\\\because (a^{2}-b^{2})=(a+b)(a-b)\\\\(r+R)=10(Given)\\\\\Rightarrow(r-R)\leq \frac{5}{10\pi ^{2}}\\\\\therefore (r-R)\leq\frac{1}{2\pi ^{2}}$

Thus maximum difference of radii = $(r-R)=\frac{1}{2\pi ^{2}}$

6 0

2 years ago

The hypotenuse of a 45°-45°-90° triangle measures 10 StartRoot 5 EndRoot in. A right triangle is shown. The hypotenuse has a len

suter [353]

Answer:

$5\sqrt{10}\ units$

5 StartRoot 10 EndRoot

Step-by-step explanation:

we know that

The legs of a 45°-45°-90° triangle are congruent

Let

x ----> the length of one leg of the triangle

Applying the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse

a and b are the legs

we have

$c=10\sqrt{5}\ units$

$a=b=x\ units$

substitute

$(10\sqrt{5})^2=x^2+x^2$

$500=2x^2\\x^2=250\\x=\sqrt{250}\ units$

Simplify

$x=5\sqrt{10}\ units$

5 StartRoot 10 EndRoot

4 0

2 years ago

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Assume that x is a char variable has been declared and already given a value. Write an expression whose value is true if and onl

Lorico [155]

Answer:

bool b = isupper(x);

Step-by-step explanation:

I have written the expression for a char variable x.The isupper(x) will return true if the character x is upper case and false if the character x is lower case.

I have stored the returned value to a bool variable b .So the value of variable b will be true only when the x is in uppercase and false when b is lower case.

4 0

2 years ago

Which expression is an equivalent expression of 12x + 10 + 4y?

Nutka1998 [239]

-3x-2.5=y would be an equivalent to that equation

6 0

2 years ago

L = loudness, in decibels (dB); I = sound intensity, in watts/m2; I0 = 10−12 watts/m2

irina [24]

The sound intensity of the Pile Driver is 39.5
or nearly 40 times the sound intensity of the jackhammer.

Given with Loudness in dB for pile driver = 112 dB
We have to convert it in terms of sound intensity.
First,
112dB/10 = 11.2

Then we'll use this as exponent of 10
(10)^(11.2) = 1.5849 * 10 ^ 11

Then use the equation of Watts per square meter to find the intensity:
I / (10^-12 W/m^2) =1.5849 * 10 ^ 11
I = sound intensity = 0.158

Then compare:

Sound intensity of Pile Driver/ Sound intensity of Jackhammer
(0.158) / (0.004)
= 39.5
or nearly 40 times the jackhammer.

3 0

2 years ago

Read 2 more answers