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3 years ago

What is the surface area of a rectangular prism that has these dimensions? 14m x 8m x 6m

1 answer:

4 0

The surface area is 488m2:)

(keep in mind every side has an opposite...)

14 x 8 x 2 = 224

14 x 6 x 2 = 168

6 x 8 x 2 = 96

224 + 168 + 96 = 488

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is $\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$
The focus is $\mathbf{Focus = (80, -1760)}$
The directrix is $\mathbf{y = \frac{1}{640}}$
The axis of the symmetry of parabola is: $\mathbf{x = 80}$

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

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

Substitute the values of origin and vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

Substitute the values of a and the vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

Substitute the values of a and the vertex in $\mathbf{Focus = (h, \frac{k+1}{4a})}$

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

$\mathbf{x = -\frac{b}{2a}}$

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

$\mathbf{x = -\frac{b}{2a}}$

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

Read more about parabola at:

brainly.com/question/21685473

6 0

3 years ago

A flat-screen television was marked down by 35 percent, which reduced its price by $115.65. What was the original cost of the te

Vera_Pavlovna [14]

Marked down by 35% this decreased it by 115.65 thhat means that 115.65 is 35% of original find original 35%=35/100=7/20 'of' means multiply 115.65=7/20 times original multiply both sides by 20/7 to clear fraction (20/7 times 7/20=140/140=1) 2313/7=original 330.428=original round 330.43 original price=$330.43

3 0

3 years ago

Read 2 more answers

Round 492.3069 to the nearest thousandth

Llana [10]

The answer is 492.307
The number after the thousandths is 9 - greater than 5 - so we round 6 up to 7.

4 0

4 years ago

18 times what is 504

schepotkina [342]

Answer:

Step-by-step explanation:

3 0

4 years ago

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Find the complex conjugate of the given number -1+4i

adell [148]

With every imaginary term, there are 2 complex conjugates with opposing signs. So if I had the term a+bi, the complex conjugate would be a-bi. So given your example of -1+4i, the complex conjugate would just be the opposite sign, now negative, to get -1-4i.

3 0

3 years ago