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2 years ago

A circular picture is 8 inches in diameter what is the area of the picture in square inches

Mathematics

2 answers:

barxatty [35]2 years ago

6 0

area = PI x r^2

radius = 1/2 diameter

1/2 of 8 = 4

3.14 x 4^2 = 3.14 x 16 = 50.24 square inches ( answer may vary depending on what you use for PI. 3.14 is common)

Lemur [1.5K]2 years ago

3 0

The formula for the area of a circle is:
A=3.14r^2
To find the radius you divide the diameter by 2 so:
8/2=4
Then plug in 4 for the radius and solve.
A=3.14x4^2
A=3.14x16
A= 50.24
So the answer is 50.24 square inches

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The base of a triangle is 9 inches more than 3 times the height. if the area of the triangle is 105 square inches, find the base

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2 years ago

Find the derivative.

Aleksandr [31]

Answer:

Using either method, we obtain: $t^\frac{3}{8}$

Step-by-step explanation:

a) By evaluating the integral:

$\frac{d}{dt} \int\limits^t_0 {\sqrt[8]{u^3} } \, du$

The integral itself can be evaluated by writing the root and exponent of the variable u as: $\sqrt[8]{u^3} =u^{\frac{3}{8}$

Then, an antiderivative of this is: $\frac{8}{11} u^\frac{3+8}{8} =\frac{8}{11} u^\frac{11}{8}$

which evaluated between the limits of integration gives:

$\frac{8}{11} t^\frac{11}{8}-\frac{8}{11} 0^\frac{11}{8}=\frac{8}{11} t^\frac{11}{8}$

and now the derivative of this expression with respect to "t" is:

$\frac{d}{dt} (\frac{8}{11} t^\frac{11}{8})=\frac{8}{11}\,*\,\frac{11}{8}\,t^\frac{3}{8}=t^\frac{3}{8}$

b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:

"If f is continuous on [a,b] then

$g(x)=\int\limits^x_a {f(t)} \, dt$

is continuous on [a,b], differentiable on (a,b) and $g'(x)=f(x)$

Since this this function $u^{\frac{3}{8}$ is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means:

$\frac{d}{dt} \int\limits^t_0 {u^\frac{3}{8} } } \, du=t^\frac{3}{8}$

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2 years ago

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IceJOKER [234]

The answer is 36.25.

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2 years ago

Read 2 more answers

If x / 2y = 0.4 , A / 5B = 0.25 Then A + y / 5 =…....

shusha [124]

Answer:

$\frac{x}{2y} = \frac{4}{10} \\ 8y = 10x \\ y = \frac{10x}{8} - - - - - 1 \\ \\ \frac{a}{5b} = \frac{25}{100} \\ \frac{a}{5b} = \frac{1}{4} \\ 4a = 5b \\ a = \frac{5b}{4} - - - 2 \\ \\ so \: \: \frac{a + y}{5} \\ = (a + y) \times \frac{1}{5} \\ = ( \frac{5b}{4} + \frac{5x}{4} ) \times \frac{1}{5} \\ = \frac{5b + 5x}{4} \times \frac{1}{5} \\ = \frac{5(b + x)}{4} \times \frac{1}{5} \\ = \frac{b + x}{4} \\ \\ so \: \: \: \frac{a + y}{5} = \frac{b + x}{4}$

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2 years ago