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Math Help - 4 word problems on functions, please help.

  1. #1
    Newbie Twilight's Avatar
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    4 word problems on functions, please help.

    I'm sorry for having to ask like this. I've never been good at word problems.
    1. As a weather balloon is inflated, its radius increases at the rate of 4 cm per second. Express the volume of the balloon as a function of time, and determine the volume of the balloon after 4 seconds.
    2. Express the surface area of the weather balloon in the above problem as a function of time.
    3. (this one has a picture, I tried to get the basics) Brandon, who is 6 feet tall, walks away from a streetlight that is 15 ft high at a rate of 5 feet per second, as shown in the figure. Express the length s of Brandon's shadow as a function of time.
    4. (This one has a picture, too) A water-filled balloon is dropped from a window 120 ft above the ground. Its height above the ground after t seconds is 120-16t(squared) ft. Laura is standing on the ground 40 ft from the point where the balloon will hit the ground, as shown in the figure. (A) Express the distance d between Laura and the balloon as a function of time. (B) When is the balloon exactly 90 ft from Laura?]
    I'm sorry for the poor quality of the pictures, I had to use a picture editor instead of something like paint. Also, if it helps, we have only done number patterns and equations and inequalities before this.
    Attached Thumbnails Attached Thumbnails 4 word problems on functions, please help.-problem.jpg   4 word problems on functions, please help.-problem-2.jpg  
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  2. #2
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    Quote Originally Posted by Twilight View Post
    I'm sorry for having to ask like this. I've never been good at word problems.
    1. As a weather balloon is inflated, its radius increases at the rate of 4 cm per second. Express the volume of the balloon as a function of time, and determine the volume of the balloon after 4 seconds.
    2. Express the surface area of the weather balloon in the above problem as a function of time.

    ...
    Hello,

    to 1.: I assume that the balloon has the shape of a sphere. Let t be the variable for the time. Then r = 4t.

    You know the formula for the volume of a sphere:

    V(r) = \frac43 \pi r^3 . Plug in the term for r: V(t) = \frac43 \pi (4t)^3~\implies~V(t) = \frac{256}{3} \cdot \pi t^3

    to 2.:
    You know the formula for the surface of a sphere:

    A(r) = 4 \pi r^2 . Plug in the term for r: A(t) = 4 \pi (4t)^2~\implies~A(t)=64 \pi t^2
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  3. #3
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    Quote Originally Posted by Twilight View Post
    I'm sorry for having to ask like this. I've never been good at word problems.
    1. ...
    2. ...
    3. (this one has a picture, I tried to get the basics) Brandon, who is 6 feet tall, walks away from a streetlight that is 15 ft high at a rate of 5 feet per second, as shown in the figure. Express the length s of Brandon's shadow as a function of time.
    4. (This one has a picture, too) A water-filled balloon is dropped from a window 120 ft above the ground. Its height above the ground after t seconds is 120-16t(squared) ft. Laura is standing on the ground 40 ft from the point where the balloon will hit the ground, as shown in the figure. (A) Express the distance d between Laura and the balloon as a function of time. (B) When is the balloon exactly 90 ft from Laura?]

    ...
    Hello,

    to 3.:

    Set up the proportion

    \frac{s}{s+d}=\frac{6}{15}=\frac25 . Solve for s.

    s=\frac23 d Now plug in the term for d: d = 5t . So you have now:

    s=\frac23 \cdot 5t ~\implies~s=\frac{10}{3} t

    to 4.:

    Use Pythagorean theorem:

    d^2=40^2+(120-16t^2)^2

    Set up the equation with the given distance:

    90^2=40^2+(120-16t^2)^2 . If the balloon falls down the complete distance of 120' it will take approximately 2.7 seconds until it hits the ground. Therefore the solution of this equation can only be between zero and 2.7 s. Substitute y = t^2 and solve for y. Afterwards calculate t. Because it was asked for the exact solution you should get:

    t=\frac14 \cdot \sqrt{120-10 \cdot \sqrt{65}}
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