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3 years ago

Find the surface area Sphere: area of the great circle ~ 28.6 in2

1 answer:

6 0

Area of a circle is πr².

Therefore we can get the radius of the great circle (and thus the sphere) by doing √(A / π).

√(28.6 / π) = 3.017 to 3DP.


Surface area of a sphere is 4πr².

4π(3.017)² = 114.4 to 1DP

You might be interested in

Find the x-intercepts of the parabola with vertex (5,-4) and y-intercept (0,96). Write your answer in this form: (x1,y1),(x2,y2)

lesya692 [45]

Answer:

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

Step-by-step explanation:

we know that

The equation of the given parabola is

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

we have

the vertex is the point (5,-4)

substitute

$(y+4)=a(x-5)^{2}$

The y-intercept is the point (0,96)

substitute and solve for a

$(96+4)=a(0-5)^{2}$

$100=a(25)$

$a=100/25=4$

The equation of the vertical parabola is equal to

$(y+4)=4(x-5)^{2}$

Find the x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero

For y=0

$4=4(x-5)^{2}$

Simplify

$1=(x-5)^{2}$

Rewrite

$(x-5)^{2}=1$

square root both sides

$(x-5)=(+/-)1$

$x=(+/-)1+5$

$x=(+)1+5=6$

$x=(-)1+5=4$

therefore

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

4 0

3 years ago

Find the midpoint of PQ P(4 1/3, 3 1/6), Q(-2 1/5, 3 2/3)

Paha777 [63]

Answer:

$(1\frac{1}{15},3\frac{5}{12})$

Step-by-step explanation:

To find the midpoint, you must average the x's then average the y's.

So the x's are $4 \frac{1}{3}$ and $-2\frac{1}{5}$ .

The y's are $3\frac{1}{6}$ and $3\frac{2}{3}$ .

To find an average of a data with 2 elements you must add the two elements then take that sum and divide it by 2.

So this is what we will do with the x's then the y's.

So first x:

$\frac{4\frac{1}{3}+-2\frac{1}{5}}{2}$

Write as improper fractions:

$\frac{\frac{13}{3}+\frac{-11}{5}}{2}$

Division by 2 is the same as multiplying by 1/2:

$\frac{13}{6}+\frac{-11}{10}$

The least common multiple of 6 and 10 is 30. We will multiply first fraction by 5/5 and 3/3 for the second so we can have the same denominator.

$\frac{65}{30}+\frac{-33}{30}$

Now that the bottoms are the same we can write as one fraction:

$\frac{65+-33}{30}$

Simplify:

$\frac{32}{30}$

If you want the answer as a mix fraction like your question began as we can do that by first figuring out how many 30's are in 32 and what is the remainder of that division.

There is one 30 and 32 and so 32-30=2 is the remainder.

$1\frac{2}{30}$

Reduce by dividing top and bottom by 2:

$1\frac{1}{15}$

Now for y:

$\frac{3\frac{1}{6}+3\frac{2}{3}}{2}$

Write the mix fractions as improper fractions:

$\frac{\frac{19}{6}+\frac{11}{3}}{2}$

Dividing by 2 is the same as multiplying by 1/2:

$\frac{19}{12}+\frac{11}{6}$

The least common multiple of 12 and 6 is 12 so I'm going to multiply the second fraction by 2/2 so the denominators will be the same:

$\frac{19}{12}+\frac{22}{12}$

Since the denominators are the same we can write as a single fraction:

$\frac{41}{12}$

How many 12's are in 41? 3 and so the remainder is 41-3(12)=41-36=5.

$3\frac{5}{12}$

So the midpoint is:

$(1\frac{1}{15},3\frac{5}{12})$ .

6 0

3 years ago

Read 2 more answers

What is 3/4-(-2/9) I need hekppp

Sonbull [250]

Answer:

35/36

Step-by-step explanation:

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3 0

3 years ago

Factor 125x^3-1000. Show your work.

Salsk061 [2.6K]

The left term is (5x)³.

The right term is 10³.

So, you can use the formula for the factorization of the difference of cubes.

... a³ - b³ = (a-b)(a² +ab +b²)

Here, you have a=5x, b=10, so the factorization is

... 125x³ -1000 = (5x-10)(25x² +50x +100)

4 0

2 years ago

miguel walked 3/4 miles to the library and then 3/8 miles to the post office. Which statement is true?

Paraphin [41]

Answer:

Post office is true because 3/4 miles is 1320 yards and 3/8 is only 660 yards. So basically it will take A LONG TIME for him to get there at the library. But you know I am not always accurate /:

6 0

2 years ago