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2 years ago

6

Joanna recorded the number of laps she swam during practice in one week. Freestyle 100 Breaststroke 50 Backstroke 60 Butterfly 2

5 What is the value of the breaststroke to backstroke ratio? Type your answer as a fraction in simplest form. Ratio Value:

1 answer:

Y_Kistochka [10]2 years ago

3 0

What is the answer choices ?

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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

2 years ago

$800 deposit over 10 years with an interest rate of 2%

TiliK225 [7]

Answer:

the interest is 960.

Step-by-step explanation:

the formula: I=prt i=interest p= pricipal [the money you start with]

r= rate t= time

I=? I= 800 (0.02) (10)

P= $800 I= 160+ 800 {because $160 is added}

R= 2% --> 0.02 [as a decimal] I= $960

T= 10 years

8 0

2 years ago

Mrs. Burnham has a 1 cup measure that has no other markings. Can she make 6 of molding clay using only 1 cup measure? Describe t

AURORKA [14]

Yes she can. two ways to find the answer is to measure with an actual cup

7 0

2 years ago

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A teacher always arranged the content0 of each lessons to Year 10 as teaching and practising learnt skills in the ratio 2:3. α I

Paraphin [41]

I'd say (a) = 52.5 minutes or 52 minutes and 30 second

(b) = 45 minutes

3 0

2 years ago

Rachel has $10.00. She wants to buy a book that costs $6.79. Will she have enough

prisoha [69]

Answer:

No

Step-by-step explanation:

Because 10 - 6.79 = 3.21

8 0

2 years ago

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