Answer:
[tex]\mathbf{ \dfrac{128}{3}}[/tex]
Step-by-step explanation:
Given that:
[tex]y^2 + z^2 = 16; \\ \\ where; \ x = 2y , x =0, z= 0[/tex]
[tex]Replace \ z = 0 \ \text{in the given equation ;} y^2+z^2=16[/tex]
[tex]Then;[/tex]
[tex]y^2 = 16 \\ \\ y = \sqrt{16} \\ \\ y = \pm 4[/tex]
[tex]\text{So; in 1st octant \ limits of y }= 0 \to 4 \ \text{and for x }= 0 \to 2y[/tex]
∴
[tex]\text{Volume of solid: (V) = }\int ^{4}_{y=0} \int ^{2y}_{x=0} \sqrt{16-y^2} \ dxdy \\ \\ = \int^4_{y=0} \sqrt{16 -y^2} \ (x)^{2y} _o \ dy \\ \\ = \int^4_{y=0}\sqrt{16 -y^2} (2y -0) \ dy \\ \\ V = \int^{4}_{y=0} \ 2y \sqrt{16 - y^2} \ dy[/tex]
[tex]Now, let:\\\\ 16 - y^2 = u \\ \\ -2ydy = du \\ \\ 2ydy = -du \\ \\ Hence, when \ y = 0; u = 16 \\ \\ and \\ \\ when \ y = 4 \ then \ u = 0[/tex]
∴
[tex]V = \int ^4 _{y=0} \ 2y \sqrt{16 -y^2 } \ dy \\ \\ = \int ^0_{16} - \sqrt{u}\ du \\ \\ = - \int^0_{16} \ u^{^{\dfrac{1}{2}}} \ du \\ \\ = \Bigg [\dfrac{u^{^{\dfrac{1}{2}+1}}}{\dfrac{1}{2}+1 } \Bigg]^0_{16} \\ \\ =\Bigg[ -\dfrac{u^{\dfrac{3}{2}}}{\dfrac{3}{2}}^0_{16} \Bigg] \\ \\[/tex]
[tex]= - \dfrac{2}{3}\Big( u^{\dfrac{3}{2}}\Big)^0_{16} \\ \\ = - \dfrac{2}{3} \Big(0^{^\dfrac{3}{2}}}- 16^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(0 - (4^2)^{^{\dfrac{3}{2}}}\Big ) \\ \\ = - \dfrac{2}{3} \Big(-(4)^{3}}\Big )[/tex]
[tex]= - \dfrac{2}{3} \Big(64\Big )[/tex]
∴
[tex]\mathbf{V = \dfrac{128}{3}}[/tex]
at a farm the ratio of the number of hens to the number of ducks is 3:5 there are 125 ducks at the farm how many hens are there on the farm
3 : 5
x : 125
125 ÷ 5 = 25
25 × 3 = 75
no. of hens = 75
Evaluate each function.
11) f(a) = 3a? + 3a; Find f(a – 2)
The table shows the height of a softball that Hallie threw in the air. Is the relationship shown linear? Why or why not?
Answer:
No
Step-by-step explanation:
Because .5 = 7.2
So 1 = 14.4
PLEASE HELP ITS URGENT DONT GUESS (also if you get it right ill mark you as brainliest)
Answer:
106.83ft
Step-by-step explanation:
29 + 29 + 19 = 77ft
Now we must calculate the semicircle, The diameter is 19ft
19ft x 3.14 = 59.66
since 59.66 would be a full circle, you divide it in half.
59.66/2=29.83
77+29.83=106.83ft
Find the surface area
Will give brainliest to first answer!!!!
what's nine times 4?
Answer:
9 x 4 = 36
9 multiply by 4 is 36.
Answer:
36
Step-by-step explanation:
If you do 9 * 9 * 9 * 9 you would get 36.
Hence, study your nines. (lol)
Hope this helps! ;)
Which statement is true?
A. (1,1) is the x- and y-intercept of the
function.
B. (0,1) is the x- and y-intercept of the function.
C. (0,0) is the x- and y-intercept of the function.
D. The function has no intercepts.
Answer:
C. (0,0) is the x- and y-intercept of the function.
Step-by-step explanation:
It is because the function is passing through the origin.
Mi-young is cooking kalguksu for a large family kalgusku is a korean soup with noodles. She makes two kinds of kalguksu,chicken and seafood.
Mi-young makes 24 cups of seafood kalguksu. This is 60% of the total kalguksu she makes
HELP I DONT PAY ATTENTION IN CLASS
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the ratio and percentages.
let's be the total kalguksu soup quantity be x
hence, 60% of x = 24 cups, so we get as
===> 60/100 * x = 24
=> 0.6*x = 24
hence, x ==> 24/0.6
=====> x = 40 cups
hence the answer is 40 cups are in total kalguksu soup.
A survey found that 68% of students do their homework before 10:00 P.M. Predict how many students out of 1,095 do their homework before 10:00 P.M.
Answer:
744.6 or if you round it 745
Step-by-step explanation:
Step 1: Divide 1095 by 100
In this case, the number that we are "comparing" to 100 is 1095, so we must first normalize the number by dividing it by 100. The operation we have to solve is this:
1095/100= 1095÷100= 10.95
Step 2: Multiply 10.95 by 68 to get the solution
Now that we have our normalized number, 10.95, we just have to multiply it by 68 to get our final answer. The forumla for this is obviously quite simple:
10.95×68= 744.6
ASAP HELP TYYY
A purse with a price of $58.45 has an 8% sales tax. What is the sales tax dollar amount?
please help really need it will give thanx points
Answer:
62x49
Step-by-step explanation:
take away 16 from both sides
hi please help......
Answer:
9/20
Step-by-step explanation:
45%=45/100
hope this helps
Determine if each ordered pair is a part of the solution set of the linear inequality. Select Yes or No.
Ordered Pair
Yes
No
(0,-5)
O
(7, – 4)
O
(-6, -7)
o
(-4,1)
O
(4,8)
O
Answer:
yes
Step-by-step explanation:
5x-2y=44 and x=-4y solve for x
Answer:
I believe x is 8
how many roots does y= x^5- 4x^2+ 3x
A.3
B.4
C.5
D.6
(x^2 is the power to)
Answer: 4
Step-by-step explanation:
We can write the equation as
[tex]x(x-1)^{2}(x^{2}+2x+3)=0\\\\x=0, 1, -1 \pm i\sqrt{2}[/tex]
Therefore, there are 4 distinct roots.
Please I need help (dont answer if you don't know ill report you)
9514 1404 393
Answer:
x = 25
Step-by-step explanation:
The marked angles are "vertical" angles, so are congruent.
150° = (4x +50)°
100 = 4x . . . . . . . . . . . divide by °, subtract 50
25 = x . . . . . . . . . . divide by 4
The angles of a triangle are (x - 5), (x + 15)°
and (2x + 10). Given that the sum of the
angles of a triangle is 180°, calculate the size
of each angle.
Answer:
35°, 55°, 90°
Step-by-step explanation:
Since all the angles of a triangle equal 180, add them all together and set them equal to 180.
(x-5)+(x+15)+(2x+10)=180
Now solve for each angle.
(40-5)
=35°
(40+15)
=55°
(2(40)+10)
=90°
Now check your work.
35°+55°+90°
=180°
Please help me please
Answer:
2
_
3
Step-by-step explanation:
i think at least hopefully
oscar earns extra money, m, working two weekends with his uncle. he is saving to buy a new scooter that costs $138. Fantasia says that Oscar needs to earn more than $7 each hour he works to have enough money to buy the scooter. Explain why she is incorrect.
Answer:
Step-by-step explanation:
30
One angle of an isosceles triangle measures 70°. Which other angles could be in that isosceles triangle?
Answer:
Step-by-step explanation:
The total of all 3 angles in every triangle equals 180 degrees. An isosceles triangle has two side lengths equal and two angle degrees equal.
So you either have two angles with each having 70 degrees and the third angle is 40 degrees,
70 + 70 + 40=180
OR
One angle of 70 degrees and two angles that are 55 degrees each.
70 + 55 +55 =180
Answer:
Step-by-step explanation:The total of all 3 angles in every triangle equals 180 degrees. An isosceles triangle has two side lengths equal and two angle degrees equal. So you either have two angles with each having 70 degrees and the third angle is 40 degrees, 70 + 70 + 40=180OROne angle of 70 degrees and two angles that are 55 degrees each. 70 + 55 +55 =180
A car dealer sets the sticker price of a car by taking 115% of the wholesale price. if a car sells wholesale at $17,000 what is the sticker price?
Answer:
Step-by-step explanation:
sticker price = $17,000 × 1.15 = $19,550
write the equation for the line that goes through point (12,5) with slope m= -2
Answer:
y=-2x+29
Step-by-step explanation:
y-y1=m(x-x1)
y-5=-2(x-12)
y=-2x+24+5
y=-2x+29
PLEASE HELP D:
What is the area of a triangle that has a height of 10 feet and a base length of 8 feet?
A - 10 feet^2
B - 20 feet^2
C - 40 feet^2
D - 80 feet^2
Answer:
C. 40 ft²Step-by-step explanation:
Triangle area formula:
A = bh/2, where b- base, h- heightWe have:
b = 8 ft, h = 10 ftThe area is:
A = 8*10/2 = 40 ft²Correct choice is C
In a triangle, its midsegment is (2x + 8) units long and its parallel side is (5x - 9) units long. How long is the midsegment?
Answer:
The midsegment is 58 units long.
Step-by-step explanation:
Midsegment Theorem:
It states that the length of the midsegment is half the length of the parallel side.
In this question:
Midsegment: 2x + 8
Parallel side: 5x - 9
Parallel side is double the midsegment. So, we use this to find x:
[tex]5x - 9 = 2(2x + 8)[/tex]
[tex]5x - 9 = 4x + 16[/tex]
[tex]x = 25[/tex]
Midsegment:
[tex]2x + 8 = 2(25) + 8 = 50 + 8 = 58[/tex]
The midsegment is 58 units long.
Please help I don’t understand this
PLS SOLVE THIS I WILL GIVE BRAINLIEST BECAUSE THIS IS DUE IN THIRTY MINUTES. I WILL GIVE BRAINLIEST IF YOU ANSWER ALL OF THE PROBLEM.
Thirty is what percent of 20?
Answer:
150 percent
Step-by-step explanation:
30/20. Multiply both sides by 5. 150/100. 30 is %150 of 20
Answer:
150
Step-by-step explanation: from goog .le
i will love you if u please answer this question PLSS
Answer:
On the dive boat deck
Step-by-step explanation:
This is above the water level and water level is considered to be 0
pls love me <3
5th grade math. Correct answer will be marked brainliest.
Answer:
(2,2)
Step-by-step explanation:
The horizontal line is always x, and the vertical line is always y. You can see that B is 2 to the right and 2 up, so the answer will be (2,2)
5y=585
what is y in da equation
Answer:
Step-by-step explanation:
5y = 585
Y = 585/5
Y = 117
Answer:
y = 117
Step-by-step explanation:
[tex]5y=585\\\\\frac{5y=585}{5}\\\\ \boxed{y=117}[/tex]
Hope this helps.