Extra Credit:
8 congruent spheres are packed into a cube with
edge length x so that each sphere is tangent to 3
faces of the cube and 3 other spheres as shown.
what is the ratio of the total volume of the
spheres of the volume of the cube?
Answer:
Ratio of the volumes of the spheres and cube = 0.523
Step-by-step explanation:
From the figure attached,
Diameter of one sphere = Half of the measure of one side of the cube
= [tex]\frac{x}{2}[/tex]
Radius of the sphere = [tex]\frac{\frac{x}{2}}{2}[/tex]
= [tex]\frac{x}{4}[/tex]
Volume of a cube is given by the formula,
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
Therefore, volume of one sphere = [tex]\frac{4}{3}\pi (\frac{x}{4})^{3}[/tex]
= [tex]\frac{x^3\pi}{48}[/tex]
Volume of 8 spheres = [tex]8\times \frac{x^3\pi}{48}[/tex]
= [tex]\frac{x^3\pi}{6}[/tex]
Volume of a cube = (side)³
= [tex]x^3[/tex]
Ratio of the volumes of the sphere and cube = [tex]\frac{\frac{\pi x^3}{6} }{x^3}[/tex]
= [tex]\frac{\pi}{6}[/tex]
≈ 0.523
I need to know what X solves for
Answer:
x= 30
Step-by-step explanation:
triangle is equal to 180 n we know c=90 so now we're just looking for the other 90 so 3x=90 n solve for x
sorry im bad at explaining
Answer:
X = 30
Step-by-step explanation:
Tan C=
Help help help
Answer:
I believe the ans is (B) 40/9
Answer:
The answer is B. 40/9.
Step-by-step explanation:
We know, tan= opposite/adjacent
so, tan C = 40/9
A bird flying at an altitude of 50 feet spies a worm in the ground up ahead. How far must the bird travel to the worm if the angle of depression from the bird to the worm is 56°?
Answer:
33.7 ft
Step-by-step explanation:
We solve the above question using Trigonometric function of Tangent
tan θ = opposite/adjacent
θ = 56°
Opposite = 50 ft
Adjacent = x
Cross Multiply
tan 56 = 50 ft/x
Cross Mulitiply
tan 56 × x = 50ft
x = 50ft/tan 56
x = 33.725425842 ft
Approximately = 33.7 ft
The bird must travel 33.7 ft to meet the worm
asap please !
Suppose that an insurance company has broken down yearly automobile claims for drivers from age 16 through 21 as shown in the following table. How much should the company charge as its average premium in order to break even on costs for claims?
Answer:
?
Step-by-step explanation:
PLEASE I NEED SOME HELP WITH MATH
Answer:
28 cm area
Step-by-step explanation:
PLEASE HELP!
Prove that the diagonals of a parallelogram bisect each other. The midpoints are the same point, so the diagonals ___
A. are perpendicular to each other
B. are parallel to each other
C. bisect each other
D. have the same slope
Answer:
C
Step-by-step explanation:
they bisect each other if all diagonals have the same midpoint!!!
3. Solve triangle ABC if a = 4, b = 6, and c = 5.
Show work
Answer:
4 x 6 x 5= 120 divided by 2 equals 60 because 4 x 6 = 24 x 5 = 120 and u divide by 2 when its a triangle. :) hope this helps
Step-by-step explanation:
https://socratic.org/questions/in-triangle-abc-a-4-b-6-c-8-how-do-you-find-the-cosine-of-each-of-the-angles
Find the volume.
5cm
10 cm
15 cm
Answer:
750
Step-by-step explanation:
10x15x5=750
Hope this helps!
Have a lovely day!
Answer:
The volume is 5x5x5 or 125cm ^3
Step-by-step explanation:
The basic formula for the area of a rectangluar shape is lenghx, width x, and high
whats the answers??????????????
the arrows pointing to 36
Name two pairs of adjacent angles and two pairs of vertical angles in
the figure.
Answer:
choice 2
Step-by-step explanation:
If the equation of a circle is (x + 4)2 + (y - 612 = 25, its center point is
(4,6)
(4,6)
(4,-6)
Answer:
Center point: [tex](-4,6)[/tex]
Radius: [tex]r=5[/tex]
Step-by-step explanation:
The equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center point of the circle and [tex]r[/tex] is the radius of the circle.
Given our equation [tex](x+4)^2+(y-6)^2=25[/tex], we can see that [tex](h,k)[/tex] is [tex](-4,6)[/tex] and since [tex]r^2=25[/tex], our radius is [tex]r=\sqrt{r^{2} } =\sqrt{25} = 5[/tex]
Therefore, the center point is [tex](-4,6)[/tex] and the radius is [tex]r=5[/tex]
A figure has 4 sides with two sets of parallel sides
Answer:
It can be a square!
Step-by-step explanation:
Answer:Parallelogram
Step-by-step explanation: Parallelogram: A quadrilateral with 2 pairs of parallel sides
8. The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to
cover the block entirely with paper. How much paper do you need? Show ALL steps to find the
amount of paper. Do not use units in your answer. Enter the number only.
7 cm
5 cm
<
6 cm
6 cm
(The figure is not to scale)
Amount of paper:
Answer:
Amount of paper need = 140 cm²
Step-by-step explanation:
Given:
Length of rectangular prism = 5 cm
Width of rectangular prism = 5 cm
Height of rectangular prism = 4 cm
Base of triangular side = 5cm
Height of triangular side = 6 cm
Find:
Amount of paper need
Computation:
Amount of paper need = Curved surface area of rectangular prism + Curved surface area of square pyramid
Amount of paper need = 2h(l + b) + 4[Area of triangle]
Amount of paper need = 2h(l + b) + 4[(1/2)(b)(h)]
Amount of paper need = (2)(4)(5 + 5) + 2[(5)(6)]
Amount of paper need = (8)(10) + 2[30]
Amount of paper need = 80 + 60
Amount of paper need = 140 cm²
Use the vertical line test to determine whether y is a function of x
Answer:
Not a function of x
Step-by-step explanation:
A vertical line intersects the graph twice, which immediately tells us that y is not a function of x here. If y were a function, the vertical line would intersect the graph in only one place.
No, A vertical line intersects the graph doubled, which instantly tells us that y exists not a function of x here. If y existed a function, the vertical line would intersect the graph in just one area.
What is Vertical line test?If a vertical line can be drawn to connect the graph of a function in more than one place, then stands NOT a function. If it exists not feasible to draw a vertical line to touch the graph of a function in more than one place, then y exists as a function of x.
No, A vertical line intersects the graph doubled, which instantly tells us that y exists not a function of x here. If y existed a function, the vertical line would intersect the graph in just one area.
Therefore, the correct answer is option B. No.
To learn more about vertical line test
https://brainly.com/question/1821791
#SPJ2
What is missing from the graph?
HELP I WILL GIVE BRAINIEST
Answer:
I think the title is missing from the graph
Answer:
Y-intercept maybe? since the given function doesn't have a point where x = 0
Or it could also be the x and y-axis are not labeled
I'm so sorry if this is wrong but i hope this helps!
ASAP
(AND HOW DID YOU GET THE ANSWER)
- Will mark brianist
its c
Step-by-step explanation:
Answer:
A) The mean would increase
Step-by-step explanation:
What is the volume of a sphere with a diameter of 49.3cm, rounded to the nearest tenth of a cubic centimeter?
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms.
f(x) = 6x2 + x − 12
A. quadratic function; quadratic term: −12x2; linear term: −6x; constant term: −12
B. linear function; linear term: x; constant term: −12
C. linear function; linear term: 6x2; constant term: −12
D. quadratic function; quadratic term: 6x2; linear term: x; constant term: −12
Answer:
D
Step-by-step explanation:
The function f(x) = 6x2 +x -12 is a quadratic since the highest degree polynomial term is 2. So that eliminates B and C. Option A is incorrect because the quadratic term is 6 not double the constant. There for the correct choice is D because the function is a quadratic and the quadratic term is 6x2, the linear term is x and the constant term is -12.
Need help ASAP please
Answer:
C
Step-by-step explanation:
Given
x² - 36 = 0 ( add 36 to both sides )
x² = 36 ( take the square root of both sides )
x = ± [tex]\sqrt{36}[/tex] = ± 6
That is x = - 6, x = 6 → C
What is the correct answer?
Answer:
yellow
Step-by-step explanation:
this is how I solved it....
have a great day!
Before rock climbing, Michelle wants to know how
high she will climb. She places a mirror on the
ground and walks backward until she can see the
top of the cliff in the mirror. She drew a sketch of
the situation. What is the height of the cliff?
Answer:
22 feets
Step-by-step explanation:
From the diagram attached :
We have two similar triangles which can be related proportionally :
Hence ;
Mitchell's height / distance from mirror = cliff height / cliff distance
Michelle's height = 5.5
Michell's distance from mirror = 4
Cliff height = h
Cliff distance from mirror = 16
We have ;
5.5 / 4 = h / 16
Cross multiply :
4 * h = 5.5 * 16
h = 88 / 4
h = 22 feets
Find the area of the circle. Use 3.14
42 mm
Answer:
A = 5538.96mm
Step-by-step explanation:
A = πr2
A = π × 422
A = 1764π
A = 5538.96
Please mark as brainliest if answer is right
Have a great day, be safe and healthy
Thank u
XD
Can someone help me? Don’t put a link I will report links
Answer:
3.5
Step-by-step explanation:
Solve.
-7 2/3+ (-5 1/2) +8 3/4= _
6 7/12
-4 2/3
-21 11/12
-4 5/12
An automobile's velocity, starting from a complete stop, is v(t) =140t/5t - 6 where v is
measured in feet per second. After what elapsed time would the automobile reach a
velocity of 44 Feet per second?
Answer:
3.3 seconds
Step-by-step explanation:
v(t) =140t/5t - 6 where v is velocity
The time, t when, v = 44 ft/s
Put v = 44 ft/s in the equation :
44 = 140t / 5t - 6
44(5t - 6) = 140t
220t - 264 = 140t
-264 = 140t - 220t
-264 = - 80t
Divide both sides by 80
264 / 80 = 80t/80
3.3 = t
Hence, automobile will reach a velocity of 44 ft /s after 3.3 seconds
The elapsed time would the automobile reach a velocity of 44 Feet per second is 3.3 seconds
Calculation of the elasped time:Since
An automobile's velocity, starting from a complete stop, is v(t) =140t/5t - 6 where v is measured in feet per second.
So, the time should be
[tex]44 = 140t \div 5t - 6[/tex]
44(5t - 6) = 140t
220t - 264 = 140t
-264 = 140t - 220t
-264 = - 80t
3.3 = t
Hence, The elapsed time would the automobile reach a velocity of 44 Feet per second is 3.3 seconds
learn more about time here: https://brainly.com/question/24308516
using the formula 1 =PxRxT what is the interest on a $500 tv at 2% rate for 2 years
Answer:
$20.
Step-by-step explanation:
2% = 0.02.
Interest = 500*0.02*2
= $20.
You and two of your friends go to eat pizza
together. There are two deals:
1. 10% off of 1 pizza )
2. 30% off of 3 pizzas
Do you want to each pay separately and get
10% off of your bill, or do you want to split the
bill 3 ways and get 30% off of 3 pizzas?
Write a response that convinces your teacher
Answer:
The second deal offers a lower cost for the three friends.
Step-by-step explanation:
Let consider that each pizza has a price [tex]c_{o}[/tex]. Now, we proceed to check the total cost for each case, the better choice is whose total cost after discounts is the lowest.
Case 1 - 10 % off of 1 pizza (Split costs and buy 3 pizzas separately)
[tex]C = 0.9\cdot C_{o} + 0.9\cdot C_{o} + 0.9\cdot C_{o}[/tex]
[tex]C = 2.7\cdot C_{o}[/tex]
The cost for each person is:
[tex]c = \frac{C}{3}[/tex]
[tex]c = 0.9\cdot C_{o}[/tex]
Case 2 - 30 % off of 3 pizzas (Split costs and buy 3 pizzas in a row)
[tex]C = 0.7\cdot (3\cdot C_{o})[/tex]
[tex]C_{o} = 2.1\cdot C_{o}[/tex]
The cost for each person is:
[tex]c = \frac{C}{3}[/tex]
[tex]c = 0.7\cdot C_{o}[/tex]
The second deal offers a lower cost for the three friends.
Which inequality has the solution shown?
pleas help due to night
Answer:
w = 28.4 yds
Step-by-step explanation:
P = 12.7 + 4 + 2w
73.5 = 16.7 + 2w
56.8 = 2w
w = 56.8/2
w = 28.4
Answer:
w = 28.4 yards. Sorry need the points.