Answer:
The radius of the silo is 5.788 feet.
Step-by-step explanation:
Since the silo has the shape of a cylinder, then;
Volume of the silo = Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
Where: r is the radius of the silo, and h is the height.
Given that: volume = 2106 cubic feet, and height = 20 feet.
Then,
2106 = [tex]\frac{22}{7}[/tex] x [tex]r^{2}[/tex] x 20
2106 = [tex]\frac{440}{7}[/tex][tex]r^{2}[/tex]
2106 x 7 = 440[tex]r^{2}[/tex]
14742 = 440[tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]\frac{14742}{440}[/tex]
[tex]r^{2}[/tex] = 33.5045
⇒ r = [tex]\sqrt{33.5045}[/tex]
= 5.78831
r = 5.788 feet
The radius of the silo is 5.788 feet.
can someone please help me
Answer:
X<2
Step-by-step explanation:
- signs will be cancelled after taking common.
then 6 is subtracted from 18 and we get 12.
then 12 is divided by 6 and we get 2.
the inequality sign will remain the same.
Answer:
Inequality Notation: x < 2See screenshot belowI hope this helps!
1. The main show tank has a radius of 70 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
2. The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 35 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
3. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
Using the information from #3, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answer:
1. Volume = 5128.67 ft³
The volume if sphere is given by:
V = (4/3)πr³
If the tank is cut into half vertically, then the volume of sphere becomes.
V = (4/3)πr³ / 2
If the tank is cut into half again horizontally, then the volume of the sphere becomes.
V = (4/3)πr³ / 4
Hence, as the main tank forms a quarter sphere, its Volume is given by:
V = (4/3)πr³ / 4
It is given in the question that the radius is 70 ft.
Substitute that in the given formula:
V = (4/3)π(70)³ / 4
V = 5128.67 ft³
2. Volume of tank = 461,814 ft³
Step-by-step explanation:
Congruent tanks implies that both tanks are of identifical shape, form & dimensions. Congruent means that the tanks have the same radius as well as height. Hence, the heights and radii of tanks #1 and #2 are equal and the same.
Let's list out the information given us:
radius(tank #1) = 35 ft ⇒ radius(tank #2) = 35 ft, height(tank #2) = 120 ft ⇒ height(tank #2) = 120 ft
Volume of cylinder = πr²h
The tanks have been cut into half, as such:
Volume of tank = ½πr²h
Volume of tank = Volume(tank #1) + Volume(tank #2)
Since the tanks are congruent (same dimensions), we have:
⇒ ½πr²h + ½πr²h ⇒ πr²h
Volume of tank = π * 35² * 120 = 147,000 π
Volume of tank = 461,814 ft³
3. 1047.2 ft³
Step-by-step explanation:
The following information is missing:
The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally)
The only dimension needed for the main show tank is its radius. Then the model radius will be 1/6 * 60 = 10 feet
The volume of a sphere is:
V = 4/3 * π * r³
For a quarter sphere it is:
V = 4/3 * π * r³ * 1/4
V = 1/3 * π * r³
For the smaller mock-up tank:
V = 1/3 * π * 10³
V = 1047.2 ft³
HELP PLSS
Solve the equation 17−(3x+5)=3x−6
Answer:
x = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
17 - (3x + 5) = 3x - 6
Step 2: Solve for x
Distribute negative: 17 - 3x - 5 = 3x - 6Add 3x on both sides: 17 - 5 = 6x - 6Combine like terms: 12 = 6x - 6Isolate x term: 18 = 6xIsolate x: 3 = xRewrite: x = 3Step 3: Check
Plug in x into the original equation to verify it's a solution.
Substitute in x: 17 - (3(3) + 5) = 3(3) - 6Multiply: 17 - (9 + 5) = 9 - 6Add: 17 - 14 = 9 - 6Subtract: 3 = 3Here we see that 3 does indeed equal 3.
∴ x = 3 is the solution to the equation.
Answer:
x = 3
Step-by-step explanation:
17 - 1(3x + 5) = 3x - 6
17 − 3 − 5 = 3x − 6
12 - 3x = 3x - 6 subtract five
-3x + 12 = 3x - 6 rearrange terms
-3x = 3x - 18 subtract twelve
-6x = 18 subtract negative three
divide by negative six
x = 3
By what percent would the area of the rectangle change if the width of the rectangle is increased by 50% and the length is increased by the same number of units?
Answer:
. i think it's wrong
7 divided by 276 is what? I am terrible at division
Answer:
39.4285714286
Step-by-step explanation:
Hope this helps and have a great day!!!
Help me pls it’s important
Answer:
The value of x = -10 if g(x)=0.
i.e.
When x = 0, g(-10)=0
Step-by-step explanation:
From the given graph, it is clear that the graph passes through the x-axis when x = -10.
In other words, the function becomes zero at x = -10.
Thus, the x-intercept x = -10 will determine that:
at x = -10 , g(-10) = 0
Thus, the value of x = -10 if g(x)=0.
i.e.
When x = 0, g(-10)=0
You began membership in a new health and fitness club which has access to a dietician and personal trainer. They help you develop a special eight-week diet and exercise program. The data in the following table represents your weight, w, as a function of time, t, over an eight-week period.
Time (weeks)
0
1
2
3
4
5
6
7
8
Weight (lb)
150
144
143
141
140
137
137
132
129
If you lost 13 pounds in the first five weeks, what is the average rate of change of weight with respect to time over the first five weeks of the program?
a.
+0.38 pounds per week
b.
-0.38 pounds per week
c.
+2.6 pounds per week
d.
-2.6 pounds per week
Answer:
d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Just took the test
Complete the flow proof
Answer:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. ∠VWZ = ∠YWZ [tex]{}[/tex] Definition of bisection of angle
4. [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex] [tex]{}[/tex] Reflexive property
5. ΔWVZ ≅ ΔWYZ [tex]{}[/tex] Angle-Angle-Side congruency postulate
6. [tex]\overline {VZ}[/tex] ≅ [tex]\overline {YZ}[/tex] [tex]{}[/tex] CPCTC postulate
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. Given that ∠VWY is bisected by [tex]\overline {WZ}[/tex], therefore ∠VWY is split into two equal angles, ∠VWZ and ∠YWZ, from which we have ∠VWZ = ∠YWZ [tex]{}[/tex] by the definition of bisection of angle ∠WXY by [tex]\overline{WZ}[/tex]
4. By reflexive property, a line is congruent to itself, therefore, [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex]
5. Given that two adjacent angles and a side adjacent to the two angles in ΔWVZ are congruent to the corresponding two adjacent angles and adjacent side in ΔWYZ, ΔWVZ is congruent to ΔWYZ by the Angle-Angle-Side (AAS) congruency postulate
6. Given that ΔWVZ ≅ ΔWYZ, and side [tex]\overline {VZ}[/tex] of ΔWVZ is the corresponding side to side [tex]\overline {YZ}[/tex] of ΔWYZ, therefore, [tex]\overline {VZ}[/tex] is congruent to [tex]\overline {YZ}[/tex] by the Congruent Parts of Congruent Triangle are Congruent (CPCTC) postulate.
What is the slope of the line through the points (3, 7) and (5, 15)?
Answer:
[tex]m=4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (3, 7)
Point (5, 15)
Step 2: Find slope m
Substitute [Slope Formula]: [tex]m=\frac{15-7}{5-3}[/tex]Evaluate Subtraction: [tex]m=\frac{8}{2}[/tex]Evaluate Division: [tex]m=4[/tex]Answer:
4
Step-by-step explanation:
cuz
What property is represented?
40 + 0 = 40
• identity
• inverse
• associative
• commutative
Identity property!
Because the identity property for addition tells us that zero added to any number is the number itself. Zero is called the "additive identity." In this case, 0 is being added to 40.
Ltd say we're given the quadratic equation x + 2x2 - 4 = -7x + 6
Enter your answers separated by a comma
Answer:
x=1 ,x= -5
Step-by-step explanation:
x+2x2-4=-7x+6
2x2+x+7x-4-6=0
2x2+8x-10=0
divide through out by 2 to reduce the equation
x2+4x-5=0
by using formula method
x=[-b+\-√b2-4ac]/2a. a=1, b=4 c=-5
x=[-4+\-√4^2-4*1*-5]/2*1
x=[-4+\-√16+20]/2
x=[-4+\-√36]/2
x=[-4+\-6]/2
x=(-4+6)/2 ,x=(-4-6)/2
x=2/2 , x=-10/2
x=1 , x=-5
The number of solutions to the equation are two and Real in nature. The solutions are x = 1 and x = - 5.
We have the following quadratic equation -
x + [tex]2x^{2}[/tex] - 4 = -7x + 6
We have to determine its solutions.
What is the Quadratic formula to find the roots of a quadratic equation ?The Quadratic formula is -
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
According to question, we have -
x + [tex]2x^{2}[/tex] - 4 = -7x + 6
Rearranging the equation -
[tex]2x^{2}[/tex] + x + 7x - 4 - 6 = 0
[tex]2x^{2}[/tex] + 8x - 10 = 0
Using the quadratic formula -
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
[tex]$x=\frac{-8\pm\sqrt{64-(-80)}}{4}$[/tex]
[tex]$x=\frac{-8\pm\sqrt{144}}{4}$[/tex]
[tex]$x=\frac{-8 +12}{4}[/tex] and [tex]$x= \frac{-8-12}{4}[/tex]
x = 1 and x = - 5
Hence, the number of solutions to the equation are two and Real in nature. The solutions are x = 1 and x = - 5.
To solve more questions on Quadratic Equations, visit the link below -
brainly.com/question/23458698
#SPJ6
Juan invested $100 in a savings account the earns 5% annually. The value, A, of the investment can be calculated using the equation A=p(1+r) with and exponent of t, where p is the investment in dollars, r is the interest rate, and t is the time of years. What amount will be in the savings account in two years?
Answer:
$110.25
Step-by-step explanation:
Step one:
given
principal= $100
rate= 5%
time = 2 years
Required
The final amount
Step two:
The compound interest formula is
[tex]A=p(1+r)^t[/tex]
substituting we have
[tex]A=100(1+0.05)^2\\\\A=100(1.05)^2\\\\A=100*1.1025\\\\A=110.25\\\\[/tex]
The final amount is $110.25
What is the area of a right triangle 6 centimeters
high with a base of 2 centimeters?
The area of the triangle enclosed by 3 sides of a triangle is 6 cm²
What is the area of a triangle?The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. To find a triangle's area, use the formula area = 1/2 * base * height.
Given here: The dimensions of a triangle as 6 cm and base 2 cm
We know the area of the triangle is equal to half of the base times height,
A=1/2×6×2
=6 cm²
Hence, The area of the triangle enclosed by 3 sides of a triangle is 6 cm²
Learn more about area of the triangle here:
https://brainly.com/question/29133099
#SPJ2
Element X decays radioactively with a half life of 13 minutes. If there are 830 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 20 grams?
Answer:
26.92 min
if I'm not wrong!
If x = 3 (y + 2) minus 1 what is the value of w in terms of x and y?
A.) w = StartFraction x minus 3 y Over 3 EndFraction
B.) w = StartFraction x minus 3 y + 1 Over 3 EndFraction
C.) w = x minus 3 y + 1
D.) w = StartFraction x + 1 Over 9 y EndFraction
Answer:
B!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation x = 3y + 3w - 1 can be written as in terms of x and y by making the subject w is w = (x - 3y + 1)/3 option (B) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is:
If x = 3 (y + w) -1 what is the value of w in terms of x and y?
A.) w = StartFraction x minus 3 y Over 3 EndFractionB.) w = StartFraction x minus 3 y + 1 Over 3 EndFractionC.) w = x minus 3 y + 1D.) w = StartFraction x + 1 Over 9 y EndFractionWe have an expression:
x = 3 (y + w) -1
To find the value of w in terms of x and y.
By using the distributive property:
x = 3y + 3w - 1
By arranging the equation:
3w = x - 3y + 1
Divide by 3 on both the side:
w = (x - 3y + 1)/3
Thus, the equation x = 3y + 3w - 1 can be written as in terms of x and y by making the subject w is w = (x - 3y + 1)/3 option (B) is correct.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ5
In the figure below, what is the value of x
Answer:
x = 49°
Step-by-step explanation:
Angles in a Triangle
The sum of the internal angles in any triangle adds up to 180°.
The figure shows a triangle that includes two angles with the same tick mark. This means they are congruent, i.e. they measure the same.
The larger triangle has three defined angles: 43°, 39°, and 2x. Since the sum of them is 180°:
43° + 39° + 2x = 180°
Operating:
82° + 2x = 180°
Subtracting 82°:
2x = 180° - 82° = 98°
x = 98°/2 = 49°
x = 49°
F R E E P O I N T S ! !
Answer:
thank you
Step-by-step explanation:
happy holidays have a good day
Answer:
thank you
Step-by-step explanation:
what is the answer of 18x 2 and 3
Cameron invests $1000. He has a choice of two schemes:
Scheme A offers $25 every year.
Scheme B offers 2% interest compounded annually.
Over what periods of investment (in whole years) is scheme A better than scheme B?
Answer: 2 year
Step-by-step explanation: After 3 years scheme B would be 80$ while Scheme A would be 75$
4. Is the relation shown in the table a function? Use the graph
to justify your answer.
2
4
8
y
3
2
0
y
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8
Answer:
67
Step-by-step explanais the bigges number taht u could find
Isabella wants to purchase a new refrigerator. When she applies for an installment loan at the appliance store, her loan application is turned down. What consumer law says that a lender must give her the reason, in writing, that she was denied the loan?
Answer:
fair credit billing act
Read the excerpt from Heart of a Samurai.
The water was so clear, he could see straight to the bottom. A snail was making a path like a shiny ribbon slowly unfurling on the sand.
What does the author use the most precise words to describe in the excerpt?
A. the water’s movement
B. the water
C. the snail
D. the snail’s path
Answer: D. the snail’s path
Step-by-step explanation: because The author uses the most precise words to describe the snail's path.
This excerpt has been taken from Heart of a Samurai, a historical novel written by Margi Preus in 2010. Precise words such as 'shiny', 'ribbon' and 'unfurling' have been used in the second sentence to describe the path of the snail, which is a small animal that has a wet body and moves very slowly. In other words, the author describes the way the path looks by establishing a comparison between the path and a shiny ribbon.
Hope this help
Answer:
the snails path
Step-by-step explanation:
If you have 3 sticks of length 2 cm, 3 cm and 5 cm. What kind of triangle these sticks would form? Justify your answer.
Answer:
Scalene triangle (As the definition says)
(this is a rhombus btw) for what value of x is the figure the given special parallelogram? HELP PLS, show work.
Answer:
x = 2 or 3
Step-by-step explanation:
Diagonal of a rhombus bisects the vertex angles. So,
[tex]x^{2} =5x-6[/tex]
[tex]=> x^{2} -5x + 6 = 0[/tex]
Lets factorise the eqn.
[tex]=> x^{2} - 2x - 3x + 6 = 0[/tex]
[tex]=> x (x - 2) -3(x-2)[/tex]
[tex]=> (x-2)(x-3) = 0[/tex]
Here x will have 2 values.
1) [tex]x-2=0[/tex]
[tex]=> x =2[/tex]
2) [tex]x - 3 = 0[/tex]
[tex]=> x = 3[/tex]
To go to school each day, Myra walks 20 yards due south to the bank then 48 yards east.
Answer: 68
Step-by-step explanation:
(-1/3+1/9) • 4^2 +5/8
A.) - 2/9
B.) 32/9
C.) -59/18
D.) 73/18
Answer:
B
Step-by-step explanation:
Find the perimeter of the figure
Answer:
142
Step-by-step explanation:
Ok explanation
we know the sides 9, 11, 38, and 13.
there are 2 missing sides we need to find
so the first one whic is the longer one is we know that the 38 is already 1 part of it but not the whole thing. We know the 9 is part of the 38 since it connects. So that gives us that side of 47.
Now for the shrter side, we know 1 part of it is 13 And the other part is 11. So we Add them up and get 24
Now the sides are 9, 11, 38, 13, 47, and 24
We add them up and get 142
Answer:
142 mi
Step-by-step explanation:
Top = 9 +38 = 47
Right Side = 13
Bottom Right = 38
11 + 9 = 20
Left Side = 24
47 + 13 +38 + 20 + 24 = 142
Explain what happens when you divide a fraction by itself.
Answer:
you will get 1
Step-by-step explanation:
because it can only go into its self one time
What type of number is v64?
Choose all answers that apply:
A)Whole number
B) Integer
c Rational d) irrational
The correct answers are A) Whole number, B) Integer, and C) Rational.
The number √64 is equal to 8. It satisfies the condition √64 = 8 because 8 multiplied by itself (8 x 8) equals 64.
Based on the options provided, the correct answers are:
A) Whole number: Yes, √64 is a whole number. Whole numbers are non-negative integers, and 8 is a non-negative integer.
B) Integer: Yes, √64 is an integer. Integers are numbers that can be positive, negative, or zero without any fractional or decimal parts. In this case, 8 is a positive integer.
C) Rational: Yes, √64 is a rational number. Rational numbers can be expressed as a fraction p/q, where p and q are integers, and q is not zero. The square root of 64 can be written as 8/1, which is a fraction where both the numerator and denominator are integers.
D) Irrational: No, √64 is not an irrational number. Irrational numbers cannot be expressed as fractions and have an infinite non-repeating decimal expansion. However, √64 is a terminating decimal, as it equals 8, which means it is not an irrational number.
Therefore, the correct answers are A) Whole number, B) Integer, and C) Rational.
Learn more about Numbers click;
https://brainly.com/question/1616373
#SPJ6
An ice sculpture is melting because of heat. Assuming its height changes by negative 2 over 25 m every hour, what will be the change in the height after 5 hours? negative 2 over 5 meter negative 2 over 125 meter 2 over 125 meter 2 over 5 meter
Answer:
[tex] \frac{ - 2}{25} \times 5[/tex]
first you multiply 2 by 5. Then you get 10 over 25. Then you simplify it. What is the common factor of both 10 and 25? Is it 2? No 2 is a factor of 10 but not 25. It's 5. After you get the common factor you divide both numbers by it. So 10/5 would be 2. 25 divide by 5 would be 5. And the negative sign remains
-2/25 x 5/1 = -10/25 = -2/5
hope this helps :}