Answer:
6.51 cm
Step-by-step explanation:
Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.
Since V = V',
4πr³/3 = πR²h
dividing through by π, we have
4r³/3 = R²h
multiplying both sides by 3/4, we have
r³ = 3R²h/4
taking cube-root of both sides, we have
r = ∛(3R²h/4)
Substituting the values of the variables into the equation, we have
r = ∛(3(7 cm)² × 7.5 cm/4)
r = ∛(3 × 49 cm² × 7.5 cm/4)
r = ∛(1102.5cm³/4)
r = ∛(275.625 cm³)
r = 6.508 cm
r ≅ 6.51 cm to 2 decimal places
The vertices of a triangle are (-1,3) (6,3) and (-1,-4)
Find the area of the triangle
Please show all workings
Answer:
24.5 unit²
Step-by-step explanation:
Area of ∆
= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |
= ½ | -7 - 42 |
= ½ | - 49 |
= ½ (49)
= 24.5 unit²
Method 2:
Let the vertices are A, B and C. Using distance formula:
AB = √(-1-6)² + (3-3)² = 7
BC = √(-6-1)² + (-4-3)² = 7√2
AC = √(-1-(-1))² + (4-(-3))² = 7
Semi-perimeter = (7+7+7√2)/2
= (14+7√2)/2
Using herons formula:
Area = √s(s - a)(s - b)(s - c)
here,
s = semi-perimeter = (14 + 7√2)/2
s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2
s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2
s - c = (14+7√2)/2 - 7 = (7 + √2)/2
Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²
Answer:
24.5
Step-by-step explanation:
To find the area with the coordinates provided:
(-1,3), (6,3), (-1,-4)
First we count the units that are inside the triangle which is area.
[tex]\frac{49}{2}[/tex]
So we know that there are [tex]\frac{49}{2}[/tex] units and then we divide 49 by 2 which gets you 24.5.
49 ÷ 2 = 24.5
The answer is 24.5 units.
Can anyone help me please ?
how many times can 10 go into 111? lol i need help
Answer:
11.1 times
Step-by-step explanation:
Answer:
11 times
Step-by-step explanation:
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110
Can someone Please help Ill mark brainliest.
Can you help me fast and show work plsssss I need it now
3. An ELA test is worth 100 points. There are a total of 26 questions. They are spelling word questions that are worth 2 points each and vocabulary word questions worth 5 points each. How many of each type of question are there? *
Answer:
There are 10 two point questions and 16 five point questions.
Step-by-step explanation:
x = the number of 2 points questionsy = the number of 5 points questionsx + y = 262x + 5y = 100x = 10 two points questionsy = 16 five points questionsFIND THE 2 MISSING Y VALUES (brainliest)
Answer:
first blank 8, 2nd blank 12
Step-by-step explanation:
plug X into the equation to find y
y = -4(-2) = 8
y = -4(3) = -12
pls help asap!! will give brainliest
Answer:
i believe the answer is A 90
Step-by-step explanation:
what is the logarithmic form for
[tex]2 { }^{x - 4} = 32[/tex]
Answer:
[tex]2^x-4=32\quad :\quad x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=5.16992\dots \right)\\\\2^x-4=32 \\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\2^x-4+4=32+4\\\mathrm{Simplify}\\2^x=36\\\\apply exponential rule\\x\ln \left(2\right)=\ln \left(36\right)\\x\ln \left(2\right)=\ln \left(36\right)\\x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}[/tex]
hope it helps:)
What is an equivalent expression for 2s+(-4s) and what are way for me to remember how to do equations like these
Multiple choice. Use the Law of Sines to find the missing angle of the triangle. Find m angle C to the nearest tenth if c = 111 a = 42, and m angle A=22 .
A. 81.9
B. 98.1
Answer:
Both A and B are possible.
Step-by-step explanation:
It's both!
This is a might tricky. First you have to find the altitude. You have to determine if this is a real triangle.
Sin(22) = opposite / hypotenuse. The hypotenuse = 111. The angle is 22
opposite = hypotenuse * sin(22)
opposite = 111 * sin(22)
opposite = 41.58 and this is the altitude.
What have you learned?
Since 42 is larger than 41.58 you have 2 solutions to the triangle. One of the angles is acute, and the other one is obtuse. They are supplementary angles.
Sin(C) / c = Sin(A) / a
Sin(C) = c * Sin(22) / 42
Sin(C) = 111*sin(22)/ 42
Sin(C) = .99003
Sin(C) = 81.9
So that's your first answer. The second answer comes from Finding the supplement to this angle
supplement + 81.9 = 180
supplement = 180 - 81.9
supplement = 98.1
Let's start form the product `x^{2}+11x+30,` and get back to the binomials we started with. Show your steps.
Answer:
Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].
Step-by-step explanation:
The polynomial [tex]x^{2}+11\cdot x + 30[/tex] is a polynomial of the form [tex]x^{2} - (r_{1}+r_{2})\cdot x + r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})[/tex], where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the polynomial. Then, we find the following system of equations:
[tex]-r_{1}-r_{2} = 11[/tex] (1)
[tex]r_{1}\cdot r_{2} = 30[/tex] (2)
After some algebraic handling, the solution of this system is [tex]r_{1} = -5[/tex] and [tex]r_{2} = -6[/tex].
Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].
Solve the simultaneous equation
Log(x-1)+2 log y=2 log 3
Log x + log y = log 6
Answer:
x = 2, y = 3
Step-by-step explanation:
Log x + log y = log 6 Log xy = Log 6 xy = 6
y = 6/x
Log(x-1)+2 Log y=2 Log 3
Log(x-1) = 2 Log 3 - 2 Log y = Log 3² - Log y² = Log 9 - Log y² = Log (9 / y²)
x - 1 = 9/y²
x - 1 = 9 / (6/x)² = 9 /(36/x²) = x²/4
4x - 4 = x²
x² -4x + 4 = 0
(x-2)² = 0
x = 2
y = 6/x = 3
How long will it take to accumulate $1200
in an account, if you begin with $1000 and
the account pays 6% compounded
monthly?
Answer:
it will take 4 months
Step-by-step explanation:
Solve for x = [?]
2x+ 20
3x + 15
2x + 20
Answer:
x=29
Step-by-step explanation:
3x+15+2x+20=180
3x+2x+15+20=180
5x+35=180
5x=180-35
5x=145
x=145/5
x=29
Uriel's hiking stick is 3 2/3 feet long, and Nat's is 3 3/8 feet long. Whose walking stick is longer and by how much?
Answer:
Uriel's stick is LONGER by 7/24 feet
Step-by-step explanation:
Uriel's hiking stick is 3 2/3 feet long, and Nat's is 3 3/8 feet long. Whose walking stick is longer and by how much?
The above question is solved as
Uriel's stick - Nat's stick
= 3 2/3 feet - 3 3/8 feet
= 7/24 feet
Hence, Uriel's stick is LONGER by 7/24 feet
help pls i don't know how to solve this
Answer:
x = - 8 and (- 8, 0 )
Step-by-step explanation:
Given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the equation of the axis of symmetry which is also the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 16x + 64 ← is in standard form, with
a = 1 and b = 16, then
x = - [tex]\frac{16}{2}[/tex] = - 8
Equation of axis of symmetry is x = - 8
Substitute x = - 8 into the quadratic and evaluate for y
y = (- 8)² + 16(- 8) + 64 = 64 - 128 + 64 = 0
vertex = (- 8, 0 )
Factor completely x2 - 4x - 12
A. Prime
B. (x - 2)(x - 6)
C. (x + 2)(x - 5)
D. (x - 2)(x + 6)
can you explain how to do it?
Answer:
(x-6)(x+2) D
Step-by-step explanation:
first you need to see which two numbers add up to -4 and multiply to -12 which is -6 and 2
HELP!!! Which is a solution to the equation?
(x −2)(x + 5) = 18
x = −10
x = −7
x = −4
x = −2
Mark this and return
Answer:x=-7
Step-by-step explanation:
Step-by-step explanation:
I'm not sure it's probably x=-2
Tell which number is greater. 50%, 13/25 HELP MEEEE
Answer:
13/25
Step-by-step explanation:
if you put it in decimal the fraction is greater
Answer:
13/25 is larger then 50%
Step-by-step explanation:
13/25=52%
50%=12.5/25
A river guide buys protein bars and bottles of water for participants on a rafting trip. Including taxes, the river guide pays $ 2.50 for each protein bar and $ 1.25 for each bottle of water, spending a total of exactly $ 22.50 . Which combinations of protein bars and bottles of water are possible for the given amounts? Select ALL that apply.
Answer:
Step-by-step explanation:
2.50 for water
1.25 for protein bar interesting that is exactly half of the water
22.50 exactly was spent
I couldn't come up a slick equation, so I just applied some logic and used brute forced (trail and error) to solve the problem.
2.5Water + 1.25Protein = 22.5
8W + 2P = 22.5
6W + 6P = 22.5
4W + 10P = 22.5
2W + 14P = 22.5
There are the possible combinations of both protein bars AND water, since he bought both. He could have also bought 10 water or 18 protein bars, but that is not part of the combination.
Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level. What expression shows how much farther Adam can see to the horizon? In simplest terms, Adam can see a√b feet farther than Pam.
Answer:
B
A=2
B=6
Step-by-step explanation:
The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.
Calculation of the expression:Since
Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level.
So here the expression be like The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.
Learn more about an expression here: https://brainly.com/question/4700495
A basketball backboard set that sold for $79 is discounted 15% what is this sale price
Answer: $67.15
Step-by-step explanation:
Stephanie and Jill share a reward of $65 in a ratio of 1:4. How much does Stephanie
get?
Answer:
Step-by-step explanation:
Each part is equal to 65/(1+4)=$13
Since Stephanie only got 1 part, she got $13.
write the equation of the circle given a center of (1,3) and a point on the circle at (-2,7)
Answer:
Ecuación estándar de un círculo
(x−2)2+(y−2)2=25
Forma general de la ecuación de un círculo
x2−4x+y2−4y−17=0
Ecuaciones paramétricas de un círculo
x=5cosθ+2y=5sinθ+2
Step-by-step explanation:
Ecuación Estándar de un Círculo
La ecuación estándar de un círculo con el centro en (x_0, y_0) y radio r es
(x^2-x_0) + (y^2-y_0)=r^2
Ecuaciones Paramétricas de un Círculo
Las ecuaciones paramétricas de un círculo con el centro en (x_0, y_0) y radio r son
x=r cos \theta + x_0\\y=r sin \theta + y_0
Ecuación General de un Círculo
La ecuación general de un círculo con el centro en (x_0, y_0) y radio r es
x^2+ax+y^2+by+c=0,
donde
a=-2x_0\\b=-2y_0\\c=x^2_0+y^2_0-r^2
What is m∠G to the nearest tenth?
Answer: The answer is 133.4 degrees.
Sorry if it’s wrong, and hopes this is helps.
The measure of the angle ∠G to the nearest tenth will be 31.6°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The length of the perpendicular is 28.2 units and the length of the base is 45.8 units, Then the measure of the angle ∠G is calculated as,
tan G = Perpendicular / Base
Substitute the value, then the angle is given as,
tan G = 28.2 / 45.8
tan G = 0.6157
G = 31.6°
The measure of the angle ∠G to the nearest tenth will be 31.6°.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ2
PLEASE HELP ASAP I WILL GIVE BRAINLILIST
Let () = −3(2)^ and () = − 14.
Complete the table to determine the solutions of () = −3(2)^ = () = − 14.
The solution of () = −3(2)
= () = − 14 is = ______
Step-by-step explanation:
-3. 2
-2. 1
-7. 6
i did my best.
help pls i need help
Answer:
The second and third one
Step-by-step explanation:
According to the statement, numbers between 4 and 5 is 4.1 - 4.9
But it is doubled so it is 8.2 - 9.8
These numbers are greater than 8 and less than 9
These numbers are also greater than 9 and less than 10
Which figure shows a reflection of pre-image ABC over the y-axis?
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Two. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (negative one, one), B-prime (negative three, four), and C-prime (negative three, one).
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Three. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (negative one, negative one), B-prime (negative three, negative four), and C-prime (negative three, negative one).
Two right triangles graphed on a grid. Right triangle A B C, with right angle C, is in Quadrant One. Right triangle A-prime, B-prime, C-prime, with right angle C-prime, is in Quadrant Four. The coordinates of triangle A B C are A (one, one), B (three, four), and C (three, one). The coordinates of triangle A-prime, B-prime, C-prime are A-prime (one, negative one), B-prime (three, negative four), and C-prime (three, negative one).
The figure that shows a reflection of pre-image ABC over the y-axis is the third figure.
How to depict the figure?From the complete information, the triangle ABC is reflected over the y axis.
The vertices of the triangle are A(1, 1), B(3, 4) and C(3, 1). The vertices of the images are A(1, 1) = A'(-1, 1). B(3, 4) = B(-3, 4) ans C(3, 1) = C'(-3, 1).
In conclusion, the figure that shows a reflection of pre-image ABC over the y-axis is the third figure.
Learn more about reflection on:
https://brainly.com/question/3643476
ABCD is a kite. Solve for x.