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Hoochie [10]
3 years ago
13

1. Graph the function f(x)=4cos(x). (Be sure to label your x-axis.)

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
6 0

ANSWER

To graph the function


y=4cos(x) we need to plot some few points within one period. Since the interval is not given, we shall use [0,2 \pi]'


\left \begin{array}{cc}x&y=4cos(x)\\0 &4\\\frac{\pi}{2}&0 \\ \pi&-4\\\frac{3\pi}{2} &0\\2\pi&4\end{array}\right.


We plot the above points to obtain the graph as shown in the attachment.



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Simplify (2/5÷3/8)÷(-3/5)
liberstina [14]

Answer:

\pink{ - 1 \frac{7}{9} }

Step-by-step explanation:

( \frac{2}{5}  \div  \frac{3}{8} ) \div ( -  \frac{3}{5} ) \\ (\frac{2}{5}  \times  \frac{8}{3} ) \times ( -  \frac{5}{3} ) \\  \frac{16}{15}  \times  -  \frac{5}{3}  \\ -   \frac{80}{45}

As the answer can be more simplified, divide both numerator and denominator by 5.

-  \frac{16}{9}  =   - 1 \frac{7}{9}

3 0
1 year ago
Use the information frompart a to write an equation representing the number of colories burned each minute while bowling. Let m
Fofino [41]

Answer:

To find the number of calories burned:

Find the Metabolic Equivalent of Task (MET) value of the task.

Calculate the number of calories burned per minute. (MET x body weight in kg x 3.5) / 200.

Multiply the calories burned per minute by the number of minutes of activity.

Now, as per the question, weight is 125 pounds (lb), we will convert the weight in kilogram (kg) which is 1 lb = 0.453 kg, it means 125 lb = 56.7

Now we have to find the MET,

A metabolic equivalent (MET) value is a measurement of the energy cost of a specific physical activity for a specific period of time.

For example. A MET of 1 would be roughly equivalent to a person's energy expenditure from sitting still in a room temperature and not actively digesting food.

As per the Calorie guide value of MET for bowling is 3.9

Now the overall formula is

Calorie Burn (x) = ((MET * body weight in kg * 3.5) / 200) * (Number of minutes) m

x = ((3.9*56.7*3.5)/200) * m

Finally, x = 3.87 m represents the number of calorie burned (x) while bowling m minutes.

8 0
3 years ago
Can u proof it pls indeed help<br>ΑΔΒ = ΒΔΑ.​
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6 0
3 years ago
A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la
SOVA2 [1]

Answer:

8\pi\text{ square cm}

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

S=2\pi rh

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

4^2 = (2r)^2 + h^2   ( see in the below diagram ),

16 = 4r^2 + h^2

16 - 4r^2 = h^2

\implies h=\sqrt{16-4r^2}

Thus, the surface area of the cylinder,

S=2\pi r(\sqrt{16-4r^2})

Differentiating with respect to r,

\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})

=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})

=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})

Again differentiating with respect to r,

\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})

For maximum or minimum,

\frac{dS}{dt}=0

2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0

-8r^2 + 16 = 0

8r^2 = 16

r^2 = 2

\implies r = \sqrt{2}

Since, for r = √2,

\frac{d^2S}{dt^2}=negative

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

S = 2\pi (\sqrt{2})(\sqrt{16-8})

=2\pi (\sqrt{2})(\sqrt{8})

=2\pi \sqrt{16}

=8\pi\text{ square cm}

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