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2 years ago

What is the length of the diagonal of a square whose perimeter is 6rad6

Mathematics

1 answer:

andre [41]2 years ago

3 0

Answer:

d = 2.12

Step-by-step explanation:

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4. Gloria the grasshopper is working on her hops.

aivan3 [116]

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

7 0

2 years ago

At thw movies,Aaron buys popcorn for $5.25 and a bottle of water for $2.50. He pays with a $10 dollar bill. How much change shou

4vir4ik [10]

Answer:

5.25 + 2.50 = 7.75. 10 - 7.75 =2.25

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

If x = 8 units, y = 3 units, and h = 9 units, find the area of the trapezoid shown above using decomposition.

lys-0071 [83]

Answer:

Step-by-step explanation:

because you do 8x9 and its 72

4 0

2 years ago

A circle with a 10 inch diameter is cut from a square piece of tin with 10 inch sides. To the nearest tenth of a square inch, fi

saveliy_v [14]

The area of the circle is

... A = (π/4)d² . . . . where d=10 in

The area of the square is

... A = d² . . . . . . . . where d=10 in

The amount of the square that is not in the circle is

... (1 -π/4)d² = 0.2146018d² ≈ 21.5 in² . . . for d=10 in

5 0

2 years ago

It cost 32 dollars for 8 cookies. What is the price of one cookie?

Sonbull [250]

So 32 dollars for 8 cookies.

To find the price of one item, you take the amount of items, and divide it by the price:

32 / 8 = 4 dollars for the price of 1 cookie.

5 0

3 years ago

Read 2 more answers