Find the radius of a sphere with a volume of 180 cubic feet. Round your answer to the nearest tenth.

Answer:

[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

Step-by-step explanation:

Since the required hyperbola has its vertex at (5,0), its transverse axis is on the x-axis and center at (0,0).

So, we use the equation in standard form

[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1[/tex]

Also, since the path of the space probe gets closer to y = -x, this is the asymptote to the hyperbola.

Our standard asymptote equation is y = ±bx/a taking the negative sign and comparing with y = -x,

-bx/a = -x ⇒ b/a = 1 ⇒ a = b

Also, the coordinate of the vertex (c, 0) = (5, 0) and c² = a² + b²

substituting c = 5 and a = b into the equation, we have

c² = a² + b²

5² = a² + a²

25 = 2a²

a² = 25/2

a = √(25/2)

a = ±5/√2

rationalizing, we have

a = ±5/√2 × √2/√2

a = ±5√2/2

Since a = b, b = ±5√2/2

Inserting a and b into the equation for the hyperbola, we have

[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1\\\frac{x^{2} }{(\frac{5\sqrt{2} }{2} )^{2} } + \frac{y^{2} }{\frac{5\sqrt{2} }{2} ^{2} } = 1\\\frac{x^{2} }{\frac{25 X 2 }{4} } + \frac{y^{2} }{\frac{25X2 }{4} } = 1\\\frac{x^{2} }{\frac{25}{2} } + \frac{y^{2} }{\frac{25}{2} } = 1\\\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

So, the required equation is

[tex]\frac{2x^{2} }{{25} } + \frac{2y^{2}}{{25} } = 1[/tex]

Answer:

-5/4+1/4=-4/4=-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

m∠ 1  =  180 - 117

m∠ 1  = 63

m∠2 = the same as m∠ 1

m∠2 = 63

m∠3 is also the same b/c of the same length of the "legs" of the triangle

m∠3 = 63

Answer:

343

Step-by-step explanation:

[tex]\frac{(7^4)^2}{7^5}[/tex]

[tex]=\frac{7^4^*^2}{7^5}[/tex]

[tex]=\frac{7^8}{7^5}[/tex]

[tex]=7^8^-^5[/tex]

[tex]=7^3[/tex]

[tex]=7*7*7[/tex]

[tex]=343[/tex]

Answer:

5

Step-by-step explanation:

divide the figure as a triangle and a rectangle first.

take away the rectangle part and if you just look at the triangle part,

you can get x using Pythagorean theorem.

Pythagorean theorem is a^2 + b^2 = c^2,

so 3^2 + 4^2 = x^2.

If you calculate it, x should be root 25, which equals 5.

So, the answer is 5.

Answer:

512

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

1)  [tex]2^{3} * \frac{4^{3} }{5^{0}}[/tex]

2)  [tex]8 * \frac{4^{3} }{5^{0}}[/tex]

3)  [tex]8 * \frac{64 }{1}[/tex]

4)  [tex]\frac{512 }{1}[/tex]

5)  [tex]512[/tex]  

Answer:

$340

Step-by-step explanation:

Let $p be the price yesterday.

(1 - 15%)p = 289

85%p = 289

p = 340

∴ The price yesterday is $340.

Answer:

y=-2(x+8)²-7

Step-by-step explanation:

Given: y=-2x²+5

After transformations: y=-2(x+8)²-7

Vertex would be (h,k) -> (-8,-7) instead of (0,5)

Answer:

Parametric Equation of a Line

Step-by-step explanation:

A line, parallel to vector (a,b,c) passing through point P (x1,y1,z1) is represented by parametric equations

x = x1+ at

y = y1 + bt

z = z1 + ct

Answer

15

Step-by-step explanation:

12-3²+6÷(10÷5)x2²

12-9+6÷2x4

12-9+3x4

12-9+12

3+12

15

This is the only one I saw wrong. you added wrong

Answer:

There is no x, so I’ll find y

Step-by-step explanation:

-4(y-2)=12

Multiply -4 with y and -2

-4y+8=12

Then subtract 8 with its self and 12

-4y = 4

now divide both numbers with 4

y= -1

Answer:

the answer is option (A) . (-4) + 8

Answer:

First of all, is it the ratio cats to dogs or dogs to cats?

Step-by-step explanation:

?????

Answer:

100.0

Step-by-step explanation:

because if you round divide that you get

Answer:

Both volumes are the same

Step-by-step explanation:

Volume of cylinder = [tex]\pi[/tex][tex]r^{2} h[/tex]

r = radius

h = height

Since area of the circle is given on top,

Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

We know the area is 12

12 = [tex]\pi[/tex][tex]r^{2}[/tex] (we need to find r)

r = [tex]\sqrt{\frac{12}{\pi} }[/tex]

r = 1.954

Now we can find the cylinder's volume:

Volume of cylinder = [tex]\pi[/tex][tex](1.954)^{2}[/tex] (6)

Volume of cylinder = 72

To find the volume of the cuboid, we use

Volume of cuboid = lwh

l = length

w = width

h = height

Volume of cuboid = 6 x 4 x 3

Volume of cuboid =  72

This proves that both the volumes are the same.

Answer:

Because they are both using (g units rates).

Step-by-step explanation:

Answer:

Uh i think its a uhhh carrot

Step-by-step explanation:

Step-by-step explanation:

false I think this only answer

Answer:

8.62

Step-by-step explanation:

Use the Pythagorean theorem.

b= [tex]\sqrt{c^{2}-a^{2} }[/tex]

b=[tex]\sqrt{10.5^{2}-6^{2} }[/tex]

b= [tex]\sqrt{110.25-36[/tex]

b=[tex]\sqrt{74.25}[/tex]

b= 8.62

Answer:

b

Step-by-step explanation:

Answer:

20 + 0.10t

Step-by-step explanation:

The 20 is the flat rate, the .10 is the per minuet rate meaning the answer is 20 + 0.10t. plz 5 str and thx, and brailiest.

Consider we need to find f(n).

Given:

Achilles ordered a pizza with 16 slices.

Every hour, he ate half of the remaining slices.

To find:

The function f(n) that is the number of slices Achilles ate in the hour since he got home.

Solution:

Initial number of slices = 16

Every hour, he ate half of the remaining slices. So, the number slices Achilles ate in the hour since he got home are:

8, 4, 2, 1, ...

It is a geometric sequence with first term 8 and common ratio [tex]\dfrac{1}{2}[/tex].

The explicit formula for a geometric sequence is:

[tex]f(n)=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Substituting [tex]a=8,r=\dfrac{1}{2}[/tex], we get

[tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex]

Therefore, the  function f(n) that is the number of slices Achilles ate in the hour since he got home is [tex]f(n)=8\left(\dfrac{1}{2}\right)^{n-1}[/tex].

Answer:

the answer is D

Step-by-step explanation:

The Dot plot for Alia's Sample is plot D.

Based on the values of each point, a dot plot visually groups the number of data points in a data set. Similar to a histogram or probability distribution function, this provides a visual representation of the data distribution.

Tasneem has a sample of 12 bags of candy.

Now, the median for Tasneem sample space is

= (47.1 + 47.2)/ 2

= 47. 15

As, the median mass in A is 47.05, B is 47.1, in C is 47.1 and in D is 47.4.

Also, we know that the median mass for Alia's Sample is greater than Tasneem.

Thus, the correct plot is D.

Learn more about Dot plot here:

https://brainly.com/question/22746300

#SPJ3

Answer:

1.) rectangle and triangle

2.)4 because 2 for each rectangle

3.)yes and a rectangle has 4 vertics and 4 sides and 2 equal lengths

Answer:

True, since 1 is 1/1, which is 100%

Hope that helps! :)

Step-by-step explanation:

9514 1404 393

Answer:

  (c)  Perpendicular

Step-by-step explanation:

The slope is the coefficient of x in this slope-intercept form.

The slope of the first line is +1.

The slope of the second line is -1.

The product of the slopes is (1)(-1) = -1. When the product of slopes is -1 for two lines, those lines are perpendicular.

Answer:

B. 84 students

Step-by-step explanation:

12% of students

700 students in all

700 * 0.12 = 84

Answer:

Trinity can withdraw $25 from her bank account for 13 weeks.

Step-by-step explanation:

If she wants to have at least $200 by the end of summer you need to subtract that much from what she has now. Which would be $325.38. Now you have to divide that number into 25, which should give you the number of week that money would last. That number is 13.0152, you don't need all those extra numbers so just use 13. No to check you work multiply 25 and 13. You get 325.

28ft

dkdkdk

dkdkdkdkdkdkd

ddjdjddddddddddddddddddddddddddddddddddddddddd