Answer:
The volume of the solid is 243[tex]\sqrt{2} \ \pi[/tex]
Step-by-step explanation:
From the information given:
BY applying sphere coordinates:
0 ≤ x² + y² + z² ≤ 81
0 ≤ ρ² ≤ 81
0 ≤ ρ ≤ 9
The intersection that takes place in the sphere and the cone is:
[tex]x^2 +y^2 ( \sqrt{x^2 +y^2 })^2 = 81[/tex]
[tex]2(x^2 + y^2) =81[/tex]
[tex]x^2 +y^2 = \dfrac{81}{2}[/tex]
Thus; the region bounded is: 0 ≤ θ ≤ 2π
This implies that:
[tex]z = \sqrt{x^2+y^2}[/tex]
ρcosФ = ρsinФ
tanФ = 1
Ф = π/4
Similarly; in the X-Y plane;
z = 0
ρcosФ = 0
cosФ = 0
Ф = π/2
So here; [tex]\dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}[/tex]
Thus, volume: [tex]V = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4} \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho ^2 \ sin \phi \ d\rho \ d \theta \ d \phi[/tex]
[tex]V = \int \limits^{\pi/2}_{\pi/4} \ sin \phi \ d \phi \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho ^2 d\rho[/tex]
[tex]V = \bigg [-cos \phi \bigg]^{\pi/2}_{\pi/4} \bigg [\theta \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3} \bigg ]^{9}_{0}[/tex]
[tex]V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ][/tex]
V = 243[tex]\sqrt{2} \ \pi[/tex]
Cooper wrote checks on his checking account for $20 and $35. He also deposited $63 in the account. Which number describes the change in the balance of his account? A.$12 B.$8 C.$15
Answer:
the change is b 8. 63-55=8 35+20=55
4x2 divided by 3 please help thanks you
Answer:
2 2/3 or 2.6... in decimal
Step-by-step explanation:
4*2 = 8
8/3 = 2 2/3
Hiiii I really need helppppp pls pls
Step-by-step explanation:
sas
side angle side
mark me as brainliest
Which scenario could be represented by this graph?
The scenario that could be represented by this graph is option: 3.
What is the rate of change of height?The rate of change of height represents the change in height with time.
Here, the given graph represents:
For some time the water level of the Humpy Dam doesn't change.
After a heavy rain spell, the water level rises, increasing at a constant rate.
After the rain subsides, it levels off again.
Here, the x-axis represents time and the y-axis represents the height of the water behind the dam.
The water height behind the dam was constant for a certain period. After rainfall, the height of the water increased at a constant rate. When the rain stopped, the water height behind the dam is constant at a newer height.
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I don’t understand this at all pls help I will mark brainliest
Answer:
D
Step-by-step explanation:
-2/3 is -.666
-3/5 is -.60
1/2 is .5
and 5/8 is a little more than half since 4/8 is half. so -2/3, -3/5, 1/2, 5/8, or D
Which sequences are geometric? Check all that apply.
–2, –4, –6, –8, –10, …
16, –8, 4, –2, 1
–15, –18, –21.6, –25.92, –31.104, …
4, 10.5, 17, 23.5, 30, …
625, 125, 25, 5, 1, …
B) 16, -8, 4, -2, 1
C) -15, -18, -21.6, -25.92, -31.104
E) 625, 125, 25, 5, 1
==================================================
Explanation:
Part (A)
Divide each term over its previous term. If each result is the same, then we have a geometric sequence.
(term2)/(term1) = (-4)/(-2) = 2
(term3)/(term2) = (-6)/(-4) = 1.5
We can stop here since we got a different result.
This sequence is not geometric.
--------------------------------------
Part (B)
Same idea as part (A)
(term2)/(term1) = (-8)/16 = -0.5
(term3)/(term2) = 4/(-8) = -0.5
(term4)/(term3) = (-2)/4 = -0.5
(term5)/(term4) = 1/(-2) = -0.5
We get the same result each time. The common ratio is r = -1/2 = -0.5. This sequence is geometric.
--------------------------------------
Part (C)
(term2)/(term1) = (-18)/(-15) = 1.2
(term3)/(term2) = (-21.6)/(-18) = 1.2
(term4)/(term3) = (-25.92)/(-21.6) = 1.2
(term5)/(term4) = (-31.104)/(-25.92) = 1.2
This sequence is geometric since each result is the same. The common ratio is r = 1.2
note: 6/5 = 1.2
--------------------------------------
Part (D)
(term2)/(term1) = (10.5)/4 = 2.625
(term3)/(term2) = (17)/(10.5) = 1.619
We don't get the same result, so we can stop here. This sequence is not geometric.
--------------------------------------
Part (E)
(term2)/(term1) = (125)/(625) = 0.2
(term3)/(term2) = (25)/(125) = 0.2
(term4)/(term3) = (5)/(25) = 0.2
(term5)/(term4) = (1)/(5) = 0.2
The common ratio is r = 0.2 or r = 1/5
This sequence is geometric.
Answer:
C) -15, -18, -21.6, -25.92, -31.104
E) 625, 125, 25, 5, 1
Step-by-step explanation:
The table shows the weekly profits of a fruit
vendor. What is the mean profit for these weeks?
Week
1
2
3
4
Profit -$125 -$86
$54
- $35
The mean profit is $
Answer:
-48
Step-by-step explanation:=-48
The mean profit of the fruits will be $75.
What is mean?Mean is defined as the ratio of the sum of the number of data sets to the total number of data. The mean is just like an average it is calculated by taking the ratio of the sum of all the numbers to the total count of the numbers.
Given that the weekly profit of the fruits is $125, $86, $54, and $35. The mean will be calculated as:-
Mean = ( 125 + 86 + 54 + 35 ) / 4
Mean = 300 / 4
Mean = $75
Therefore, the mean profit of the fruits will be $75.
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Morning can someone help me please and can you please let me know how you got the answer
Answer:
The customary system states that one pound is equivalent to sixteen ounces(oz).
Step-by-step explanation:
Since the package is one pound, it contains sixteen ounces(oz).
(HELP 50 POINTS)
In the figure above, point O is located at the centroid of triangle ABC. What is the combined lengths of segments DO and BO?
Select one:
A. 22
B. 25
C. 26
D. 29
Answer:
c
Step-by-step explanation:
An oil well produces 159 gallons of oil every day. A standard oil barrel holds 42
gallons of oil. About how many barrels of oil will the well produce in one day? Estimate.
Answer:
there are 2 full barrels and one that is almost full so intotal there are 3 barrels.
Step-by-step explanation:
A statement of an employee's biweekly earnings is given below.
Earnings
Deductions
Week Ended
Regular
FED. SOC. MED STATE
WITH. WITH. CARE. WITH.
NET PAY
8/18
$_____
$72.00 $35.05 $15.54 $14.40
$793.01
What is the employee's gross pay?
A.
$900.50
B.
$1000
C.
$930
D.
$975.10
Answer:
kjj ,mStep-by-step explanation:
(QUICK DUE IN 50 MINUTES)
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
I need help with this! 20 points pls dont take advantage.
the average adult drinks 1095 cups of coffee annually, About how many cups does the average adult drink per week? 1 year=52 weeks
15
91
21
3
Answer:
the answer is 21
Step-by-step explanation:
If they drink 1,095 cups per year, and there are 52 weeks in a year, you would divide 52 from 1,095(1,095/52) to get your answer which is 21.05769231. If you round it to the nearest whole number, than it is 21. I hope this helps have a great day.
equivalent fraction of 6/126
Answer:
1/21
Step-by-step explanation:
Answer:
1/21
Step-by-step explanation:
6/126 = 1/21 because 6 divided by 6 equals 1 and 126 divided by 6 equals 21.
About 1/5 of all adults in the United States have type O blood. If four randomly selected adults donate blood, find the probability of each of the following events.
a. All four are type O.
b. None of them is type O.
c. Two out of the four are type O .
Answer:
We know that:
1/5 = 0.2 of all adults in US have type O blood.
Then: 4/5 = 0.8 of all adults in US do not have type O blood.
a) All four are type O.
Let's think this, as four events with two possible outcomes, having type O blood, with a probability of 0.2, and not having type O blood with a probability of 0.8
Now if we want the four people to have type O blood, then we have the outcome with probability 0.2 four times, and as we know, the joint probability is equal to the product of the individual probabilities:
P =0.2^4 = 0.0016
b) None of them is type O.
Similar to the above case, but this time we work with four times the probability 0.8
P = 0.8^4 = 04096
c) Two of the four are type O.
Here we will have two times the probability 0.2, and two times the probability 0.8.
p = 0.2^2*0.8^2
But, if the people is ordered, the two persons with type O blood can be:
first and second
first and third
first and fourth.
second and third
second and fourth
third and fourth.
6 different combinations, then the actual probability for this case will be:
P = 6*p = 6*(0.2^2*0.8^2) = 0.1536
The probability of All four are type O, None of them is type O, and Two out of the four are type O is 0.0016, 0.4096, and 0.0256 respectively.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
About 1/5 of all adults in the United States have type O blood.
p = 0.2
q = 1 - p = 1 - 0.2 = 0.8
a. All four are type O. The probability will be
P = p⁴
P = 0.2⁴
P = 0.0016
b. None of them is type O. The probability will be
P = q⁴
P = 0.8⁴
P = 0.4096
c. Two out of the four are type O. The probability will be
P = p² × q²
P = 0.2² × 0.8²
P = 0.04 × 0.64
P = 0.0256
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What is the sum of the interior angles of a quadrilateral?
90°
180°
270°
360°
Answer:
360º
Step-by-step explanation:
too easy
Answer:
360
Step-by-step explanation:
I had it on a quiz also plz mark brainliest im trying to level up
7. Jenny is saving to buy a laptop worth $960. Her parents promise to match every $3 saved
by her with $5 of their own.
a. How much will Jenny contribute?
b. How much will Jenny's parents have to pay?
Solve five and three sixths minus two and one third.
(GIVING EXTRA POINTS ON THIS ONE! IM ALSO GIVING BRAINLIEST!) (Btw three and two ninths is incorrect :) )
A) Two and three eighteenths
B) two and two ninths
C) three and two ninths
D) three and three eighteenths
(Here is an image if needed) :
Answer:
3 3/18
Step-by-step explanation:
I did this on paper, but im typing on computer, sorry I cant send a photo
Answer:
D is the answer 3 3/18 i am sure it is correct
Which table represents a linear function?
Please help?
Answer:
I think its the fourth one sorry if I am wrong
Step-by-step explanation:
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer:
m= 1
Step-by-step explanation:
find to ordered pair on the graph and [tex]y^{1} - y^{2} \\ x^{1} - x^{2}[/tex]
When Solving Quadratics, What questions should I ask myself?
Answer:
Step-by-step explanation:
In as much as I might give a warning on not to doubt oneself, I also need to put out what one should take note of when solving quadratic problems.
Using the general formula, it's of utmost importance to not mix the variables together. Remember, making "a", "b" and "b", "a" will lead to an entirely different answer, which is most likely wrong anyway.
It's important to take note of the signs too. Remember, the formula say,
-b ± √(b² - 4ac) / 2a
The first b is negative, and that means a negative value will turn positive there. These are very trivial steps, but they can also make or mar our efforts in getting the correct answer
Find the slope-intercept equation of the line that passes through (0,-1) and has a slope of -2/3 .
Answer:
y= -2/3x-1
Step-by-step explanation:
Hope this helps!
Help me out please I beg you
Answer:
tesrdxtcfygvoubucewh cwcs wuehcbwch w
Step-by-step explanation:
w edch dwjbsxchwej chwxc
Drag and drop the constant of proportionality into the box to match the table.
If the table is not proportional, drag and drop "not proportional" into the box.
x 0 2 4 6
y 0 3 6 9
Answer: it is NOT proportional
Step-by-step explanation: it doesn’t stick to 1 number going up if that makes sense, it’s adding 1 each time it goes up but it has to stick to one number going up making this NOT proportional
Answer:
2/3
Step-by-step explanation:
x adds by 2's: 0 2 4 6...
y adds by 3's: 0 3 6 9...
help plz and it’s not 61.6 because that’s what someone has said
Answer: 250 total kids and 140 girls
Step-by-step explanation:
%56=girls that means %44= boys that means 110 is %44 of the number of kids is 110/44*100= 2.5*100=250kids 56%=girls that means %56 of 250 which is 140 girls
Solve for h: h + 4.18 = 19.74
I just need an answer
Answer:
Step-by-step explanation:
The similar things between the two is that they both to through the y-intercept and x-intercept, but one graph is positive and the other is negative and also have different slopes.
Find the slope of a line that passes through the given two points
(2,4) and (3,6).
Answer:
The slope is 2.
Step-by-step explanation:
hope that helps
y²-y¹/x²-x¹
6-4/3-2
2/1
=2
The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches. What is the length of the rectangle?
Answer:
l = w + 3cm
l = w + 3cmp = 2l + 2w = 58cm
l = w + 3cmp = 2l + 2w = 58cm
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cm
l = w + 3cmp = 2l + 2w = 58cm Solve by substitution:2l + 2w = 58 ⇒ 2(w + 3) + 2w = 58⇒ 2w + 6 + 2w = 4w + 6 = 58⇒ 4w = 52 ⇒ w = 13 Plug back in:l = (13cm) + 3cm = 16cmStep-by-step explanation:
I hope this helps you.
If the measure of the width is 21 inches. Then the measure of the length of the rectangle will be 66 inches.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
The length of a rectangle is 3 more than 3 times its width. The perimeter of the rectangle is 174 inches.
Then the length of the rectangle will be
We have
L = 3W + 3
Then the perimeter will be
P = 2(L + W)
174 = 2 (3W + 3 + W)
87 = 4W + 3
84 = 4W
W = 21 inches
Then the length will be
L = 3W + 3
L = 3 x 21 + 3
L = 63 + 3
L = 66 inches
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Find the solution to the equations.
3x - y = -4
x + y = 0
(0,0)
(-1, 1)
(1,-1)
Answer:
(-1,1)
Step-by-step explanation:
also use elimination steps by using simultaneous