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]
Which statement about the ordered pair (-6,8) is true?
Answer:
a
Step-by-step explanation:
solve for y in one equation
2x + y = -4
y = -4 - 2x
plug y into the other equation
5x + 3y = -6
5x + 3(-4 - 2x) = -6
5x -12 -6x = -6
-x - 12 = -6
-x = 6
x = -6
plug x into the equation to find y
y = -4 - 2x
y = -4 - 2(-6)
y = 8
ordered pair: (-6,8)
The height of one cylinder is 8 cm, and the radius of its base is 5 cm. The height of a second cylinder is 24 cm, and the radius of its base is 5 cm. How many times the volume of the first cylinder is the volume of the second cylinder?
Answer:
Step-by-step explanation:
volume₁ = π5²·8 = 200π cm³
volume₂ = π5²·24 = 600π cm³
volume₂ = 3×volume₁
Answer:
It is 3, hopefully you got a good score! :D
Step-by-step explanation:
pleeeaassee First person get brainliest!!!!
Answer:
D. 32 inches 65-33=32 so its 32 inches
Step-by-step explanation:
calculate the volume of a liquid with a density of 5.45g/km and a mass of 65g
Answer:
11.93 ml
rounded to two significant figures: 12ml
Step-by-step explanation:
65/5.45=11.93 ml
Please mark me as brainliest
The table below shows Greg's scores at a state golf tournament. What is Greg's
average score for the five rounds?
A. -4
B. -3
C. -2
D. -1
Answer: d
Step-by-step explanation:
You add all of his scores up and divide them by how many numbers there are which 3+1+ -3+ -2+ -4 equals -5 and you divide them by the five numbers which gives you one
Help me help me pls!
Answer:
13.6 units (to 3 significant figures)
Step-by-step explanation:
C ( -4,6) and D (-4,-5)
the formula for distance is : √(x2 - x1)² + (y2-y1)²
in this case x1= -4 , x2= -4 and y1 =6 , y2 = -5
so substitute the values and you will get the answers
Use the figure to find the measures of the numbered angles.
Answer:
1 = 81 degrees
2 = 99 degrees
3 = 81 degrees
4 = 99 degrees
5 = 81 degrees
6 = 99 degrees
7 = 81 degrees
Answer:
Step-by-step explanation:
1 = 81 degrees
2 = 99 degrees
3 = 81 degrees
4 = 99 degrees
5 = 81 degrees
6 = 99 degrees
7 = 81 degrees
If Sally walks 2 meter it takes her 1 second. If she walks 4 meters it takes her 2 seconds and 6 meters takes her 3 seconds. Is this a linear situation? Make a table and plot the points in the table to determine whether the following relationship is linear If it is, write an equation that represents the data.
Answer:
y=2x
Step-by-step explanation:
2 1
4 2
6 3
Of the pets in the pet show, 10/12 are cats. 6/10 of the cats are calico cats. What fraction of the cats are calico cats?
Answer:
6/10, simplified 3/5
Step-by-step explanation:
kinda tricky, but the fraction is stated right out.
Answer:
3/5
Step-by-step explanation:
Can someone help me ?
Answer:
The second one doesn't match.
Find the value of the ratio x ÷ y if the equation is 5x²-13xy+8y²
Answer:
x÷y=8/5 or 1÷1
Step-by-step explanation:
Please mark as brainliest
The circle graph shows how a family budgets its annual income. if the total annual income is $130,000, ehat amount is budgeted for clothing?
$?
Answer:
Step-by-step explanation:
17% = 0.17
$130 000 × 0.17 = $22 100
Four times w is 16.
Answer:
w = 4
Step-by-step explanation:
4w=16
w = 16/4
w = 4
Step-by-step explanation:
The question is unclear. If the original question is telling you to make the word expression into an algebraic expression, the answer would be 4w = 16. On the other hand, if it was asking you to solve the given equation, the answer would be w = 4.
The captain of a ship at sea sights a lighthouse which is 120 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 16 ^\circ. How far is the ship from the base of the lighthouse? feet
Answer:
As viewed on the deck, the lighthouse is 50-6 = 44 m above. First we need to compute the two distances from the captain and the lighthouse. For point1:
d1 = 44 / tan(60) = 25.403 m
For point2:
d2 = 44 / tan(30) = 76.210 m
The distance traveled by the ship in five minutes is 50.807 m or 0.050807 km. Five minutes is equivalent to 1/12 hours.
The speed is then equal to 0.050807/(1/12) kph = 0.61 kph.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Step-by-step explanation:
Mathilde has 20 pints of green paint. She uses 2/5 of it to paint a landscape and 3/10 of it while painting a clover. She decides that, for her next painting, she will need 14 pints of green paint. How much more paint will she need to buy?
Answer:
She would need one more pint.
Step-by-step explanation:
find the value of the expression below for x = 10
x'2 - 2(x+5)
A:10
B:70
C:85
D:90
Which statement about the area of a right triangle is true?
F :The area formula for a right triangle is the base times the height because a rectangle can be
divided into two right triangles.
G: The area formula for a right triangle is the base times the height because a right triangle
can be divided into two rectangles.
H: The area formula for a right triangle is one-half of the base times the height because a
rectangle can be divided into two right triangles.
J: The area formula for a right triangle is one-half of the base times the height because a right
triangle can be divided into two rectangles.
Answer:
H
Step-by-step explanation:
This is because a rectangle can be divided into two triangles.
Which statement best describes g(x) = 3 x + 6 - 8 and the parent function f(x) = 3x ?
The domains of g(x) and f(x) are the same, but their ranges are not the same.
The ranges of g(x) and f(x) are the same, but their domains are not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
Answer:
The answer is C: the ranges of g(x) and f(x) are the same, and their domains are also the same.
Step-by-step explanation:
Just took the test on edge!! :)
Option C The ranges of g(x) and f(x) are the same, and their domains are also the same is correct.
What is domain?
List of values of x an equation can satisfy is called Domain.
What is range?
List of values y the function can generate is called range
For example, f(x)=x
it can satisfy real domain i.e. x∈R
and range is R
g(x) = 3 x + 6 - 8 and f(x) = 3x
Domain for both the function is R
Both the function can satisfy all the real numbers, so its range is also R.
Therefore,Option C The ranges of g(x) and f(x) are the same, and their domains are also the same is correct.
Learn more about domain and range,
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In the sketch below, two parallel lines are cut by a transversal.
Answer:
m<1 = 150°
Step-by-step explanation:
Given:
m<1 = (4x + 50)°
m<2 = (7x - 25)°
Required:
m<1
Solution:
To find m<1, we need to create an equation that will enable us determine the value of x.
Thus,
4x + 50 = 7x - 25 => corresponding angles are congruent to each other
4x + 50 - 7x = 7x - 25 - 7x (subtraction property of equality)
-3x + 50 = - 25
-3x + 50 - 50 = -25 - 50 (substraction property of equality)
-3x = -75
-3x/-3 = -75/-3 (division property of equality)
x = 25
✅m<1 = (4x + 50)°
Plug in the value of x
m<1 = 4*25 + 50 = 100 + 50
m<1 = 150°
The graph of a line and and exponential intersect twice, once, or not at all. Describe the possible number of intersections of each of the following pairs of graph. Your solution to each part should include all of the possibilities and a quickly sketched example of each one. (Part 1)(SHOW WORK)
a. A line and a parabola
b. Two different parabolas
a) A line can intersect a parabola at 2 points, 1 point, or no points respectively. The only possible way at which it intersects at 1 point, would be if it were tangent to the parabola. [Check first attachment]
b) Two different parabolas can intersect at 2 points, 1 point or no points respectively. [Check second attachment]
It is possible for 2 parabolas to intersect at 4 and even 3 points. But one of the parabolas would be on it's side. You can consider those cases.
does anyone know how to solve this? I have to find lengths FJ, DM, and EM
Answer:
FJ= 24
DM= 16
EM= 18
Step-by-step explanation:
The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from.
So in the case of FJ, the median intersects the side at point J and extends from vertex F. This means that FM is twice as long as MJ. It tells us that MJ is 8, so MF would be 16. Now because FJ is just FM+MJ, FJ is 24.
It also tells us that DK is 24, which means that DM+MK = 24. If DM is twice as long as MK, that would make MK equal to 8 and DM equal to 16
Similarily, EM would be twice as long as ML. It says that ML=9 so that would make EM=18
HELPPP I MAKE BRAINLIESTT
A seamstress charges a $5 fee per garment, plus $15 for each hour of work that the garment requires. The graph below shows the cost of having a single garment fixed by the seamstress, according to the number of hours of work that are needed.
Which linear function models the data?
A. c(t) = 5t
B. c(t) = 15t
C. c(t) = 5 + 15t
D. c(t) = 15 + 5t
Answer:
C. c(t) = 5 + 15t
Step-by-step explanation:
Well because the initial fee is $5, the answer must have the value of 5 without a variable next to it because this is the y-intercept.
(Only the slope will have the t next to it.)
Because $15 is charged EACH HOUR this would be the slope because there is a constant increase
Therefore c(t) = 5 + 15t
Answer:
C. c(t) = 5 + 15t
Step-by-step explanation:
She charges $15 per hour, so each hour (represented by "t") she earns 15 dollars. She also charges a $5 fee per germent. So she would get $5 plus 15 times however many hours she worked. So your answer would be c(t) = 5 + 15t.
True or false?is the point(16,4) included in this function: Y=2x or Y=x2 or y= x+12 or y=x-12
Answer:
True
Step-by-step explanation:
It is true because the graph of [tex]y=x-12[/tex] passes through the point [tex](16,4)[/tex]
x = 16
y = 4
Substitute
4 = 16 - 12
4 = 4
Therefore, the answer is true.
Guys!!! Please help!! Geesh I need help
Answer:
42
Step-by-step explanation:
9 - 4 = 5
8 - 5 = 3
9 + 2 + 3 + 7 + 8 + 3 + 4 + 6 = 42
Answer:
Its 42 ;l
Step-by-step explanation:
6x+12 in its simplest form?
Answer:
It is already in simplest form.
Step-by-step explanation:
Answer:
Already in simplest form
Step-by-step explanation:
I mean you could do 6(x+2) but its already in its simplest form.
plz help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a 12/20 = 0.6
b 21/35 = 0.6
c 28.8/48 = 0.6
plz, help me with this plz!!!
Answer:
You need common denominators
Step-by-step explanation:
Because you need to have the same number on the bottom in order to correctly add/ subtract the fractions.
Use the Distributive Property to
REWRITE 5(p - 8)
What is the perimeter and area of the composite figure?
Step-by-step explanation:
▪AB = AC - EF
= 13 cm - 7 cm
= 6 cm
▪BD = CF - DE
= 16 - 8 cm
= 8 cm
BC = EF
perimeter = CF + EF + DE + AD + AB + BC
= 16 + 7 + 8 + 10 + 6 + 7
= 54 cm
Area of triangles = 1/2 × AB × BD
= 1/2 × 6 × 8
= 48/2
= 24 cm²
Area of rectangle = CF × EF
= 16 × 7
= 112 cm²
the total area = 24 + 112
= 136 cm²
#CMIIW
Which graph represents the solution set for the inequality: y > x-1
Answer:
F
Step-by-step explanation: