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Tresset [83]
2 years ago
11

Use the function below to find F(3). F(x) = 3x

Mathematics
1 answer:
Vikki [24]2 years ago
7 0

The value of F(3) = 27.

Step-by-step explanation:

Step 1:

F(x) is dependent on the value of x.

So x is independent while F(x) is dependent on x i.e. the value of F(x) depends on the value of x.

Step 2:

F(x) = 3^{x}, if we have the x's value we can calculate the F(x)'s value.

Here the value of x is given as 3 so F(x) when x equals 3 can be calculated.

F(x) = 3^{x} , F(3) = 3^{3} = 27.

So F(3) = 27.

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70 miles

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2 years ago
Lightning strikes earth 1000 times in 10 sec. how many times does lightning strike per sec?
atroni [7]
Simple division:

The amount/number of seconds=amount per second.

1000/10=100

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6 0
2 years ago
Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y
Yuri [45]

Let the curve C be the intersection of the cylinder  



16x^2+y^2=16



and the plane



x+y+z=1



The projection of C on to the x-y plane is the ellipse



16x^2+y^2=16



To see clearly that this is an ellipse, le us divide through by 16, to get



\frac{x^2}{1}+ \frac{y^2}{16}=1



or  



\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1,



We can write the following parametric equations,



x=cos(t), y=4sin(t)



for  



0\le t \le 2\pi



Since C lies on the plane,



x+y+z=1



it must satisfy its equation.



Let us make z the subject first,  



z=1-x-y



This implies that,



z=1-sin(t)-4cos(t)



We can now write the vector equation of C, to obtain,



r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))



The length of the curve of the intersection of the cylinder and the plane is now given by,



\int\limits^{2\pi}_0 {|r'(t)|} \, dt



But  



r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))



|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}



\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184



Therefore the length of the curve of the intersection  intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0
2 years ago
A trapezoid has an area of 20 cm2 and a height z cm. The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm. Find the
andriy [413]
Check the picture below.

\bf A=\cfrac{h(a+b)}{2}\quad 
\begin{cases}
A=20\\
a=6z-1\\
b=2z+3\\
h=z
\end{cases}\implies 20=\cfrac{z[(6z-1)~+~(2z+3)]}{2}
\\\\\\
20=\cfrac{z(8z+2)}{2}\implies 20=\cfrac{2z(4z+1)}{2}\implies 20=z(4z+1)
\\\\\\
20=4z^2+z\implies 0=4z^2+z-20

\bf \qquad \qquad \textit{quadratic formula}\\\\
\begin{array}{llccll}
0=&{{ 4}}z^2&{{ +1}}x&{{ -20}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
z= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}
\\\\\\
z=\cfrac{-1\pm\sqrt{1+320}}{8}\implies z=\cfrac{-1\pm\sqrt{321}}{8}\implies z\approx 
\begin{cases}
\boxed{2.1146}\\
-2.3646
\end{cases}

since the height is just a length unit, it can't be -2.3646.

4 0
2 years ago
Read 2 more answers
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Ostrovityanka [42]
22-[(87-32)/5]x2
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22-22
0
Answer is 0
4 0
2 years ago
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