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3 years ago

What is the correct answer..

Mathematics

1 answer:

solong [7]3 years ago

3 0

Answer:

64 feet

Step-by-step explanation:

To find the height of the kite we use sin trigonometric ratio.

Let the height of the kite from the ground be x feet.

$\therefore \: \sin 40 \degree = \frac{x}{100} \\ \\ \therefore \: 0.6427876097= \frac{x}{100} \\ \\ \therefore \: 0.6427876097 \times 100= x \\ \\ \therefore \:x = 64.29 \\ \\ \therefore \:x = 64 \: feet$

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Rate of change for 71, 62,53,44

Vladimir79 [104]

Answer:-9

Step-by-step explanation:

71-62=9

62-53=9

53-44=9

It is negative because the numbers are decreasing

3 0

3 years ago

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

3 years ago

Bobby wants to go on a school trip that will cost him $250. He comes up with an equation that represents how much he needs to sa

monitta

Yes, Bobby will have enough money if he saves for 9 weeks. You can find this through either substituting w for 9 in the equation, or solving the equation itself.

Substituting:

$25(9)+30$
Substitute w for 9.

$225+30$
Simplify.

$225+30=255$
Solve.

255 is greater than 250, so yes, he will have enough money saved.

Solving the equation:

$25w+30=250$
Original Equation

$25w=220$
Subtract 30 from both sides.

$w=8.8$
Divide both sides by 25.

The number of weeks he needs is 8.8. When rounding it up, you get 9.

4 0

3 years ago

55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555

Mazyrski [523]

Answer:

Step-by-step explanation:

7 0

2 years ago

What is the square root of -6.76

mojhsa [17]

Answer:

2.6i

Step-by-step explanation:

undo the - by making it: √-6.76= √6.76 x √-1

then, √-1 would be converted to imaginary number -> i

now rewrite it as √6.76 x i or i√6.76 which is the same as the squareroot of 6.76 which is 2.6 times i.

Then just write your final answer as 2.6i

5 0

3 years ago

Read 2 more answers