The volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16 is 24.74 cubic units.
What is the volume of the solid?Find the volume of the solid that lies inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 16
From the sphere and cylinder, the cylindrical coordinate will be
[tex]z = \pm \sqrt{16 - r^2}[/tex]
And the radius of the cylinder is |r| < 1 and the 0 ≤ θ ≤ 2π.
Then the volume will be given as
[tex]\rm V = \int _0^{2\pi} \int _0^1 \int _{- \sqrt{16 - r^2}}^{\sqrt{16-r^2}} \left ( r \ dz \ dr \ d\theta \right ) \\\\\\V = 2\pi \int_0^1 \left ( 2r\sqrt{16-r^2} \right ) \ dr\\\\\\V = 4\pi \left [ -\dfrac{1}{3} (16 - r^2)^{3/2} \right ]\\\\\\V = \dfrac{4\pi}{3} \left ( 16^{3/2} - 15^{3/2} \right )\\\\\\V = 24.74[/tex]
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Please help me on this!
Answer:
C. the amount the tomato plant grows each week
Step-by-step explanation:
its height is already 23 and it grows by 2.4 each week (x)
Have a nice day! :)
Which of the following could be the length of the sides of the triangle. YES or NO
1. 13,10,11
2. 12,8,10
3. 2,2,4
4. 6,7,8
5. a,b,a+b
6. 21,9,38
7. 20,20,41
8. 4.5,8.5,12.5
9. 12.4,7.2, 20
10. 56,44,90
Answer:
it's I'd 20,20,41 number seven
help meee pleaseee ~ :)) <3
[tex]v = \frac{lwh}{3} [/tex]
[tex]v = \frac{9 \times 8 \times 9}{3} [/tex]
[tex]v = 216 \: {cm}^{3} [/tex]
Volume of the rectangular prism:[tex]v = lwh[/tex]
[tex]v = 8 \times 7 \times 9[/tex]
[tex]v = 504 \: {cm}^{3} [/tex]
Total volume:[tex]v = 216 + 504[/tex]
[tex]v = 720 \: {cm}^{3} [/tex]
volume of the rectangular pyramid is 216 cm^3.
volume of the rectangular prism is 504 cm^3.
Total volume is 720 cm^3.
if 5(3x-1)=55 what is the value of 2x-2
Hey ! there
Answer:
Value of 2x - 2 is 6 .Step-by-step explanation:
In this question we are provided with an equation that is 5 ( 3x - 1 ) = 55 and we are asked to find the value of 2x - 2 .
Firstly , we need to find the value of x . So we need to solve the equation .
SOLUTION : -
[tex] \quad \longmapsto \qquad \: 5(3x - 1) = 55[/tex]
Step 1 : Dividing with 5 on both sides :
[tex] \quad \longmapsto \qquad \: \dfrac{ \cancel{5}(3x - 1)}{ \cancel{5}} = \cancel{\dfrac{55}{5} }[/tex]
On cancelling , We get :
[tex] \quad \longmapsto \qquad \:3x - 1 = 11[/tex]
Step 2 : Adding 1 on both sides :
[tex] \quad \longmapsto \qquad \:3x - \cancel{1} + \cancel{1} = 11 + 1[/tex]
On simplifying , We get :
[tex] \quad \longmapsto \qquad \:3x = 12[/tex]
Step 3 : Dividing with 3 on both sides :
[tex] \quad \longmapsto \qquad \: \dfrac{ \cancel{3}x}{ \cancel{3}} = \cancel{ \dfrac{12}{3} }[/tex]
We get ,
[tex] \quad \longmapsto \qquad \: \underline{\boxed{\frak{x = 4}}}[/tex]
→ Therefore , value of x is 4 .
Verifying : -
Now we are verifying whether our answer is wrong or right . So ,
5 ( 3x - 1 ) = 555 { 3( 4 ) - 1 } = 555 ( 12 - 1 ) = 555 ( 11 ) = 55L.H.S = R.H.SHence , Verified .Therefore , our value of x is correct/valid .
We need to find the value of 2x - 2 .
[tex] \quad \longmapsto \qquad \:2x - 2[/tex]
So substituting value of x in it :
[tex]\quad \longmapsto \qquad \:2( \bold{4}) - 2[/tex]
Multiplying 2 with 4 :
[tex]\quad \longmapsto \qquad \:8 - 2[/tex]
Subtracting 2 from 8 :
[tex]\quad \longmapsto \qquad \: \blue{\underline{\boxed{\frak{6}}}} \quad \: \bigstar[/tex]
Henceforth, value of 2x - 2 is ❝ 6 ❞.#Keep Learningif 6y+3x+=15 what is the value of 5(3x+6)?
Answer: 15x+30
Step-by-step explanation:
The value of 5(3x+6) is 15x+30
What is the distributive propertyTo “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given that;
[tex]5(3x+6)[/tex]
/ \
[tex]15x+30[/tex]
Therefore, The value of 5(3x+6) is 15x+30
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Find the sum.
796
583
+ 889
Answer:
2258
Step-by-step explanation:
#45 will give brainliest
Answer:
(-2, 3)
Step-by-step explanation:
julia and her friends are making kites out of paper. For each kite, they need a piece of paper that is \dfrac{65}{100} \text{ meter} 100 65 meterstart fraction, 65, divided by, 100, end fraction, start text, space, m, e, t, e, r, end text wide. How many centimeters of paper will they need to make 444 kites?
Answer:
260 cm
Step-by-step explanation:
Each 1/00 of a meter is 1 cm, so 65/100 meters is 65 cm. If that is the length of paper required for 1 kite, then 4 times that length will be required for 4 kites.
__
The paper required for 4 kites is ...
(65 cm) × 4 = 260 cm
Question 2 of 10
What is the value of the fraction below?0/25
the answer is A.0 because 0 devided by a number iz zero
What is the slope of the line shown below?
Answer:
7/3
Step-by-step explanation:
-5-9/0-6
-13/-6= 2.167777
y2-y1/x2-x1
Answer:
C
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (6, 9) ← 2 points on the line
m = [tex]\frac{9-(-5)}{6-0}[/tex] = [tex]\frac{9+5}{6}[/tex] = [tex]\frac{14}{6}[/tex] = [tex]\frac{7}{3}[/tex]
This is an example of which method/property?
Answer:
distributive
Step-by-step explanation:
(x+y) (z) = xz+ yz is distributive
On Amber’s math test, she was asked whether the equation x=1/2y^2 represents a function. She made the following table and graph. Amber concluded that the equation represents a function. Which additional point could be added to the graph to show Amber that the equation does not represent a function?
A. (–2, 2)
B. (0, 0)
C. (8, –4)
D. (8, 8)
Answer:
C
Step-by-step explanation:
I took the test.
The additional point could be added to the graph to show Amber that the equation does not represent a function will be (8, -4). Then the correct option is C.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The equation is given below.
x = (1/2)y²
For the single value of x, the value of y is not single.
Thus, it is not a function.
The additional point could be added to the graph to show Amber that the equation does not represent a function will be (8, -4).
Then the correct option is C.
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Mallory wants to buy a new window air conditioning unit. The cost for the unit is $329.99. If she plans to run the unit three months out of the year for an annual operating cost of $108.78, which function models the cost per year over the lifetime of the unit, C(n), in terms of the number of years, n, that she owns the air conditioner?
The function (329.99 + 108.78n)/n will represent the cost per year over the lifetime of the unit in terms of the number of years.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Cost for the unit = $329.99
Annual operating cost = $108.78
C(n) represents the cost per year
n represents the number of years
The function can be modelled:
C(n) = (329.99 + 108.78n)/n
Thus, the function (329.99 + 108.78n)/n will represent the cost per year over the lifetime of the unit in terms of the number of years.
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Emma is great at the standing long jump. Her best jump is 10 feet 8 inches. How many inches is this?
Answer:
128 in.
Step-by-step explanation:
1 ft = 12 in
10 x 12 = 120
120 + 8 = 128
128 in.
3.75
divided by 25
round off to the nearest rand
Answer:
0.15 is the answer
Step-by-step explanation:
(6×1,000)+(1×100)+(2×10)+(9× 10 1 )+(4× 100 1 )=?
Answer:
11033
Step-by-step explanation:
ms. Diaz buys strawberries by the pound at a farmers market . she pays $21.25 for all her strawberries. one pound of strawberries cost $4.25
Answer:
5 strawberries
Step-by-step explanation:
$21.25÷$4.25=5
7. If the perimeter of the rectangle is 6x + 18, then what is the length of the rectangle? (level 4)
x + 5
length
Answer:
[tex]l = 2x + 4[/tex]
Step-by-step explanation:
[tex]p = 6x + 18 \\ w = x + 5 \\ p = 2(l + w) \\ 6x + 18 = 2(l + x + 5) \\ 6x + 18 = 2l + 2x + 10 \\ 2l = 4x + 8 \\ l = 2x + 4[/tex]
Find the distance between (5, 6) and (-9, -2)
Answer:
So we must determine the distance between our two given points and that can be found using the distance formula [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
Plugging the values into the equation and solve
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(-9-5)^2+(-2-6)^2}[/tex]
[tex]d=\sqrt{(-14)^2+(-8)^2}[/tex]
[tex]d=\sqrt{196+64}[/tex]
[tex]d=\sqrt{260}[/tex]
[tex]d=16.125\ units[/tex]
Therefore, our final answer is that the distance is 16.125 units
Hope this helps! Let me know if you have any questions
BRAINLIEST To whoever can give the correct answer with an in-depth explanation !
Step-by-step explanation:
1
area of the square :
6×6 = 36 cm²
area of the triangle :
6×4/2 = 6×2 = 12 cm²
height of triangle :
area of the triangle is
10×height/2 = 40
10×height = 80
height = 80/10 = 8 cm
width of the logo :
the central square has ashtray an area of 5×5 = 25 cm².
that leaves us 125 - 25 = 100 cm² for the 4 triangles.
I assume all 4 triangles are equal, so each has an area of 100/4 = 25 cm².
the area of such a triangle is
baseline × height / 2.
so, in our case
5 × height / 2 = 25
5 × height = 50
height = 10 cm
and so, the width of the logo is 2 times the height of these side triangles, and 1 time the side length of the central square :
2×10 + 5 = 25 cm
what is 635 divided by 8
Answer: 79.375
Step-by-step explanation:
Answer:
79.375
Step-by-step explanation:
hope i helped
I NEED HELP ASAP
The area of a square is 196 in2. What is the length of its side?
Choose one answer.
A. 12 inches
B. 16 inches
C. 13 inches
D. 14 inches
area of a square = s²
s² = 196
s = √196
therefore s = 14cm
hope it helps...!!!
Answer:
D. 14
Step-by-step explanation:
14 x 14
= 196
Hope it helps :))
PLEASE HELP
Eleanor and Max used two rectangular pieces of plywood, placed end-to-end, to make a long rectangular stage for the school play. One board was 4 feet long, and the other was 4 1/2 feet long. The two pieces of plywood had equal widths. The total area of the stage was 44 5/8 square feet. What was the width of the plywood?
Select the quotient that is less than 1?
A) 2.805 ÷ 2.58
B) 1.001 ÷ 1.01
C) 0.46 ÷ 0.406
Victoria wants to purchase a skateboard. She has $125 to spend. She
finds one that regularly sells for $140 and is on sale for 15% off. Sales
tax is 7%.
Victoria says that she has enough money to buy the skateboard. Is she
correct?
Answer:
we know that
Victoria has $125 to spend
[purchase price skateboard]=$139.99-0.15*$139.99-----> $139.99-$21
[purchase price skateboard]=$118.99
sales tax is 7%----------> 0.07*$118.99----------> $8.33
sales tax is $8.33
Victoria has to pay [$118.99]+[$8.33]=$127.32
$127.32 > $125
therefore
Victoria has not enough money to buy the skateboard
the answer is
Victoria has not enough money to buy the skateboard
Step-by-step explanation:
On average, indigo drinks 2/5 of a 10-ounce glass of water in 4/5 of an hour. how much water does she drink, in glasses per hour? enter your answer as a whole number, proper fraction, or mixed number in simplest form.
Indigo drinks 5 ounces glasses per hour.
What is fraction?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
As in [tex]\frac{4}{5}[/tex] hour she drinks =10*[tex]\frac{2}{5}[/tex]
= [tex]\frac{20}{5}[/tex]
=4 ounce
She is drinking 4 ounce in [tex]\frac{4}{5}[/tex] hours,
= [tex]\frac{4}{\frac{4}{5} }[/tex]
= [tex]4*\frac{5}{4}[/tex]
=5 ounce in an hour.
She drink 5 ounces glasses per hour.
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8.
Find the probability that two of the customers get the silver cars and one gets a white ca
Answer: 2:1
Step-by-step explanation:
the probability that they get they get the silver cars and someone else gets the white is 2:1
Solve 2 log x = log 36. x = 1.6 x = 6 x = 18 x = 72
Answer:
Answer is B. X=6, Positive and negitive terms cancel out
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
I took the test
A diagonal of a cube measures
150 cm. The diagonal of a face measures 10 cm.
3999
What is the length, in centimeters, of an edge of the cube? Round the answer to the nearest tenth.
centimeters
Save and Fit
S
Answer: 7cm
Step-by-step explanation:
Use pythagorean theorum:
Variables:
Let the edge = A
Face diagonal (F) = 10cm
Inner diagonal (I) = sqrt(150) cm
A^2 = I^2 - F^2
A^2 = [sqrt(150)]^2 - 10^2
A^2 = 150 - 100
A^2 = 50
A = sqrt(50)
A = 7.0710678 cm
A = 7cm (to the nearest tenth)
so, length of an edge = 7cm
Does anyone know this one I would love help
Answer:
c
Step-by-step explanation:
the graph shows a constant speed an no change in distance