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kompoz [17]
2 years ago
12

4. Gloria the grasshopper is working on her hops.

Mathematics
1 answer:
aivan3 [116]2 years ago
7 0

The path that Gloria follows when she jumped is a path of parabola.

The equation of the parabola  that describes the path of her jump is \mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

The given parameters are:

\mathbf{Height = 20}

\mathbf{Length = 28}

<em>Assume she starts from the origin (0,0)</em>

The midpoint would be:

\mathbf{Mid = \frac 12 \times Length}

\mathbf{Mid = \frac 12 \times 28}

\mathbf{Mid = 14}

So, the vertex of the parabola is:

\mathbf{Vertex = (Mid,Height)}

Express properly as:

\mathbf{(h,k) = (14,20)}

A point on the graph would be:

\mathbf{(x,y) = (28,0)}

The equation of a parabola is calculated using:

\mathbf{y = a(x - h)^2 + k}

Substitute \mathbf{(h,k) = (14,20)} in \mathbf{y = a(x - h)^2 + k}

\mathbf{y = a(x - 14)^2 + 20}

Substitute \mathbf{(x,y) = (28,0)} in \mathbf{y = a(x - 14)^2 + 20}

\mathbf{0 = a(28 - 14)^2 + 20}

\mathbf{0 = a(14)^2 + 20}

Collect like terms

\mathbf{a(14)^2 =- 20}

Solve for a

\mathbf{a =- \frac{20}{14^2}}

\mathbf{a =- \frac{20}{196}}

Simplify

\mathbf{a =- \frac{5}{49}}

Substitute \mathbf{a =- \frac{5}{49}} in \mathbf{y = a(x - 14)^2 + 20}

\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

Hence, the equation of the parabola  that describes the path of her jump is \mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}

See attachment for the graph

Read more about equations of parabola at:

brainly.com/question/4074088

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<u>Answer: </u>

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<u>Explanation:</u>

Given, pizza is served in the school cafeteria every fourth school day.

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If both are served today then we have to find the number of days after which both will be served on the same day again.

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A student has four sticks of wood that measures 3 inches, 4 inches, 5 inches, and 6 inches.Can the student use any three of thes
saw5 [17]

Answer:

Yes, the student can use three of these sticks to make a right triangle.

Step-by-step explanation:

The measure of four sticks = 3 inches, 4 inches, 5 inches and 6 inches.

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Now, here among all four sticks

(3)^{2}  +(4)^{2}   = 9 + 16  = 25

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3 If f(x) = x2 and g(x) = x + 6, find g(f(0)). A. -6 B. 6 C. 12 D. 36
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Answer:

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Step-by-step explanation:

g(f(0)) means that the input of f(x) is 0 and this value of f(x) found is the input of g(x). This is known as composite functions.

Let's find the value of f(0).

f(x)= x²

f(0)= 0²

f(0)= 0

Now, we can find the value of g(f(0)).

g(x)= x +6

g(f(0))

= g(0)

= 0 +6

= 6

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-3y - 2z = -3 → -6y - 4z = -6
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          -2    -2
            z = 0

    -2x + 2y + 3z = 0
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              (x, y, z) = (1, 1, 0)
8 0
3 years ago
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