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3 years ago

5. Jake ordered a pizza with a 14 inch diameter. He wants to add more cheese on the

Mathematics

1 answer:

Naily [24]3 years ago

3 0

Answer:

A=πr^2

=3.142×(0.168)^2

=3.142×0.028224

=0.088679808

=0.0887m^2

=8.87×10^-2m^2

Step-by-step explanation:

This question is asking the area on which has to add more cheese. A pizza usually has the shape of a circle and the are of a circle is πr^2 . You'd have to multiply the value of π by the radius of the pizza (7 inches=0.168 metres)

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Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A

Vlad [161]

Answer:

$y(x)=sin(2x)+2cos(2x)$

Step-by-step explanation:

$y''+4y=0$

This is a homogeneous linear equation. So, assume a solution will be proportional to:

$e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda$

Now, substitute $y(x)=e^{\lambda x}$ into the differential equation:

$\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0$

Using the characteristic equation:

$\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0$

Factor out $e^{\lambda x}$

$e^{\lambda x}(\lambda ^2 +4) =0$

Where:

$e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda$

Therefore the zeros must come from the polynomial:

$\lambda^2+4 =0$

Solving for $\lambda$ :

$\lambda =\pm2i$

These roots give the next solutions:

$y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}$

Where $c_1$ and $c_2$ are arbitrary constants. Now, the general solution is the sum of the previous solutions:

$y(x)=c_1 e^{2ix} +c_2 e^{-2ix}$

Using Euler's identity:

$e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)$

$y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\$

Redefine:

$i(c_1-c_2)=c_1\\\\c_1+c_2=c_2$

Since these are arbitrary constants

$y(x)=c_1sin(2x)+c_2cos(2x)$

Now, let's find its derivative in order to find $c_1$ and $c_2$

$y'(x)=2c_1 cos(2x)-2c_2sin(2x)$

Evaluating $y(0)=2$ :

$y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2$

Evaluating $y'(0)=2$ :

$y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1$

Finally, the solution is given by:

$y(x)=sin(2x)+2cos(2x)$

5 0

3 years ago

Us<br> Find the area shaded in yellow.<br> [ ? ] square units

ira [324]

Answer:

45 square units

Step-by-step explanation:

You can cut the yellow figure into a triangle (4 by 5) and a rectangle (7 by 5).

Using the formula $\frac{1}{2} *b*h$ and $l*w$ area formulas, we get:

$\frac{1}{2} *4*5+7*5=\\2*5+7*5=\\10+35=\\45$

The area shaded in yellow is 45 square units

6 0

3 years ago

Suppose f(x) = x2 and g(x) = 2x − 3. What is the value of g(4) + f(−3)?

MAVERICK [17]

In order to find the value of g(4)+f(-3), we must substitute those values into the functions first.

Substitute -3 into f(x).

f(x)=x²

f(-3)=(-3)²

f(-3)=9

Substitute 4 into g(x).

g(x)=2x-3

g(4)=2(4)-3

Using the rules of PEMDAS, multiply first then subtract.

g(4)=8-3

g(4)=5

Therefore, if f(-3) is 9 and g(4) is 5, we must add the two values together.

5+9=14

<u>The value of g(4)+f(-3) is 14.</u>

8 0

3 years ago

Can anybody help me please

slega [8]

Answer:

i dont know give me points

Step-by-step explanation:

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4 0

2 years ago

Read 2 more answers

A tree 4.7 m tall casts a shadow 8.2 m long. Calculate the angle of elevation of the sun.

EleoNora [17]

Answer:

9.45

Step-by-step explanation:

A^2 + B^2 = C^2

4.7^2 + 8.2^2 = C^2

22.09 + 67.24 = C^2

89.33 = C^2

Square Root It

C = 9.45

3 0

2 years ago