Answer:
V₂ = V₁
Step-by-step explanation:
Let the height of the rectangular prism = h
Let s represent the side length of the base of the square prism, we have;
The volume of the prism, [tex]V_{prism}[/tex] = s²·h
The volume of the square pyramid, [tex]V_{pyramid}[/tex] = (1/3)·s²·h
∴ V₁ = The area not taken up by the square pyramid = [tex]V_{prism}[/tex] - [tex]V_{pyramid}[/tex]
∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h
Similarly, for the cylinder, we have;
Let h represent the height of the cylinder
Let r represent the radius of the base of the cone, we have;
Therefore;
The volume of the cylinder, [tex]V_{cylinder}[/tex] = π·r²·h
The volume of the cone, [tex]V_{cone}[/tex] = (1/3)·π·r²·h
∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h
V₂ = (2/3)·π·r²·h
[tex]V_{cone}[/tex] = [tex]V_{pyramid}[/tex]
Therefore;
(1/3)·π·r²·h = (1/3)·s²·h
∴ π·r² = s²
Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁
V₂ = V₁.
The velocity of a car over five hours is given by v(t) = 60 ln(t + 1), 0 < t < 5
in kilometers per hour. What is the total distance traveled from t = 0 to t = 5?
Round your answer to the nearest whole number and do not include units.
Answer:
345
Step-by-step explanation:
The velocity of a car over five hours is given by:
[tex]\displaystyle v(t)=60\ln(t+1),\, 0 \leq t \leq 5[/tex]
And we want to find the total distance traveled from t = 0 to t = 5.
Recall that distance is the integral of the absolute value of the velocity function. Since we want to find the total distance traveled from t = 0 to t = 5, our limits of integration are t = 0 and t = 5. Hence:
[tex]\displaystyle D=\int_0^5 |\underbrace{60\ln(t+1)}_{v(t)}|\, dt[/tex]
Since v(t) ≥ 0 for all t in the interval [1, 5], we can remove the absolute value. Use a calculator:
[tex]\displaystyle D=60\left(6\ln(6)-5)=345.0334...\approx 345[/tex]
The side of a rectangle legnth x+2 and width x-5. WHich equation describes the area A of the rectangle in terms of x?
Answer:
[tex] {x}^{2} - 3x - 10[/tex]
Step-by-step explanation:
Area= length× width
[tex](x + 2)(x - 5) \\ {x}^{2} + 2x - 5x - 10 \\ {x}^{2} - 3x - 10[/tex]
Prove: AAB
Step
Statement
Reason
Given
1
ABCD is a parallelogram
ABCD
Select a Reason!!
2
A
B
N
given circle o, what are the values of x and y?
Answer:
x = 38°
y = 90°
Step-by-step explanation:
x is an inscribed angle, so, 78/2=39
y is an inscribed angle of which connects two endpoints of the diameter, so y = 90°
Answered by GAUTHMATH
Does the point (1, 3) satisfy the equation y = 5x? yes no
Answer:
Nope
Step-by-step explanation:
we can graph y = 5x as y = 5 units up and one unit to the right
but for right now let me be specific on what i mean
Specifically:
y = 5x is a Slope-Intercept equation, the original Slope-Intercept equation would be y = mx + b but in this case, we don't have b so we're focusing now on y = 5x, but what are we suppose to do with 5x??? well 5x represents the slope of the line so to graph a slope, use rise over run = rise/run. so only 5 is being used so 5 = rise/run = 5/1.
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Answer: (1, 3) doesn't satisfy the equation
Answer:
No, it does not satisfy the equation
Step-by-step explanation:
Hi there!
We are given the equation y=5x and we want to know if the point (1,3) will satisfy the equation
If we substitute the values of a point into the equation, and the result is a true statement (ex. 2=2), then the point satisfies the equation
If we substitute the values of a point into the equation and the result is a false statement (ex. 0=7), then the point doesn't satisfy the equation
The reason for this is because when we plug the value of a point into an equation, we're seeing if the equation will pass through that given point.
So let's substitute 1 as x and 3 as y into y=5x
3=5(1)
multiply
3=5
The result is a false statement; therefore, the point doesn't satisfy y=5x
Hope this helps!
Find the measure of the third angle of a triangle if the measures of the other two angles are given.
118.6 and 42.3
The three inside angles of a triangle equal 180.
Subtract the two known angles from 180.
180 - 118.6 - 42.3 = 19.1
The third angle is 19.1
Someone tell me where everyone is going right please !!
Answer:
Step-by-step explanation:
( 2 , 3 ) , ( 6 , - 5) , ( - 1 , 3 ) - is a function
( 1 , 9 ) , ( -3 , - 2 ) , ( 1 , - 4 ) - is a function
( 7 , - 4 ) , ( 0 , 9 ) , ( 2 , - 2 ) - is a function
( 0 , 3 ) , ( 0 , 7 ) , ( 4 , 0 ) - is a function
( -6 , 5 ) , ( -5 , 6 ) , ( 8 , 2 ) - is a function
A baker's bread recipe calls for 3
cups of flour. She plans to make 2 loaves of
bread
If the baker's measuring scoop holds cup, how many scoops of
flour will she need in all?
A company is selling specialty ice cream. Their profit is modeled by the equation p(x) = x2 + 3, where x represents the number of cartons sold. Their cost to make the carton is represented by c(x) = -3x + 24, where x represents the number of cartons produced.
A. What does it mean to find the solution to this system?
B. What is the solution to the system? How did you find the solution?
C. What does the solution mean in context of the problem?
D. How do you solve this system when x does not stand for the same thing? What system are you referring to?
Answer:
The given function for the profit of the company is p(x) = x² + 3
The function for the cos of the company, c(x) = -3·x + 24
Where;
x = The number of cartons sold
A. To find the solution of the system means to find the number of cartons sold at which the profit and cost are equal
B. The solution of the system can be found by equating both functions as follows;
p(x) = c(x)
Therefore;
x² + 3 = -3·x + 24
∴ x² + 3 + 3·x - 24 = 0
x² + 3·x - 21 = 0
x = (-3 ± √(3² - 4×1×(-21)))/(2 × 1)
∴ x = (-3 ± √(93))/2
x = (-3 + √(93))/2 ≈ 3.32 or x = (-3 - √(93))/2 ≈ -6.32
Therefore, the possible solution is x = (-3 + √(93))/2 ≈ 3.32
C. The solution means that when the company sells about 3 cartons of specialty ice, the cost to make the carton and the profit from selling the cartons will be approximately equal
D. Part 1
To solve the system, we rewrite the functions using common variables, to obtain a consistent system of equations
Part 2 Inconsistent system of equations
When x does not stand for the same thing in both equations, we have an inconsistent system of equations and there are no solutions
Step-by-step explanation:
What is the solution for this equation:
Answer:
c) x=126
Step-by-step explanation:
tell me if I get it right
In a group of 36 pupils, 10 play the flute only. 15 play the piano only. 4 play neither instrument. A student is selected at random. What is the probability the student plays both instruments?
Answer:
9
Step-by-step explanation:
First you would need to subtract all the irrelevant students.
So, subtract 4 from 36, which is 34.
34 - (10 + 15) =
34 - 25 =
9
The answer is 9 pupils.
Find the value of y...
Answer:
y=0
Step-by-step explanation:
Rewrite Evaluate Powers:
3[tex]3^{2y-1}+3^{-1}+2*3^{y}*3^{-1}=1[/tex]
Calculate:
[tex](3^{y})^{2}*\frac{1}{3} +2*3^{y}*\frac{1}{3}=1[/tex]
Solve using substitution:
[tex](3^{y})^{2}*\frac{1}{3} +\frac{2}{3} *3^{y}=1[/tex] [tex]t=3^{y}[/tex]
Solve the equation for t:
[tex]t^{2}*\frac{1}{3}+\frac{2}{3}t=1[/tex]
t=-3
t=1
Substitute back to t=3^y
3^y=-3
3^y=1
y∉R
[tex]3^{y}=1[/tex]
y=0
solve the following problems
Suppose that x - y = 2 and 2x – 3y = 11. Then x + y =
Answer:
x + y = -12
Step-by-step explanation:
x - y = 2
2x – 3y = 11
-2x +2y = -4
2x – 3y = 11
-y = 7
y = -7
x = -5
x + y = -12
The two figures shown are congruent. Which statement is true?
A). One figure is a translation image of the other.
B). One figure is a rotation image of the other.
C). Neither figure is a translation or rotation image of the other
Answer:
C
Step-by-step explanation:
They are the same without rotation and translation
Graph the function F(x)=2^x-4
Answer:
The plotting are correct .
HOPE IT HELPED!!
As part of the math assignment, jane makes a graph pf her cookie function. Before handling it in, she compares it to the table. Do the table and the graph represent the same function
Answer:No
Step-by-step explanation:
Sandra needs a new bicycle tire. Her tire has a circumference of about 113,04 inches. What is the radius of her tire?
Answer:
113,04 square root is 10.632027088 divided by Pi
3.38427933228
so the radius of her tire is 3.38
Hope This Helps!!!
What is the quotient of
Answer:
x^5+8x^4+17x^3-14x^2-84x-72
Step-by-step explanation:
The angle A of a triangle ABC is 20% less than the sum of other two angles. If angle C is [tex]\frac{2}{3}[/tex] times angle B, then find the value of angle B.
car travels at an average speed of 40 km/h for 0.5 hours.
How far did the car travel in km?
Given :-
A car travels at an average speed of 40 km/h for 0.5 hours.To Find :-
The distance travelled.Solution :-
We know that ,
→ Distance = Speed × Time
So that ,
→ Distance = 40 km/hr × 0.5 hr
→ Distance = 40km/hr × 1/2 hr
→ Distance = 20km .
Hence the required answer is 20km .
Find the measure of the missing angle using the exterior angle sum theorm
Answer:
r = 30°
Step-by-step explanation:
According to the Exterior Angle Sum Theorem, the exterior angle, which is 90°, is equal to the 2 interior angles, which are 60° and r°. We know that the angle next to the exterior angle is 90°, and since all angle sums add up to 180°, r = 30°.
What’s the equation of the line that passes through the point (5,1) and has a slope of 1
Answer:
y = x + 4
Step-by-step explanation:
y = mx + b
y = 1x + b
5 = 1 + b
b = 4
y = x + 4
Find the area
Help me please
Answer:
72
Step-by-step explanation:
You add the base which is 8 and 18 then multiply by 11 which is 144. after that you divide by two and get your answer 72
What did I do wrong in notes, and why is the answer what it shows on screenshot
Answer:
Hope you find it helpful and usef
25. Kendra owns a toy store. She charges $8.00 for two puzzles and a piece of candy. She charges (1 poi
$4.50 for one puzzle and a piece of candy. How much does each puzzle cost?
O $3.50
O $4.50
O $1.00
$2.25
Given:
Kendra charges $8.00 for two puzzles and a piece of candy.
She charges $4.50 for one puzzle and a piece of candy.
To find:
The cost of each puzzle.
Solution:
Let x be the cost of a puzzle and y be the cost of piece of candy.
Kendra charges $8.00 for two puzzles and a piece of candy.
[tex]2x+y=8[/tex] ...(i)
She charges $4.50 for one puzzle and a piece of candy.
[tex]x+y=4.50[/tex] ...(ii)
Subtracting (ii) from (i), we get
[tex]2x+y-(x+y)=8-4.50[/tex]
[tex]2x+y-x-y=3.50[/tex]
[tex]x=3.50[/tex]
The cost of puzzle is $3.50. Therefore, the correct option is A.
Which statement describes the relationship between x and y?
As x increases, y decreases.
As x increases, y increases.
As x increases, y increases and then decreases.
As x increases, y decreases and then increases.
Answer:
as x increases, y increases
Step-by-step explanation:
Answer:
B. as x increases, y increases
Step-by-step explanation:
Michelle did a survey in four butterfly parks and wrote the following observations:
Answer:
A. 55%
Step-by-step explanation:
First we should make these into fractions
A. 33/60
B. 36/78
C. 40/89
D. 24/59
these are the fractions, The question wants us to pick the Park with the Greatest Percentage, Not The Greatest Amount, so Lets look at these fractions A. 33/60 Is 55% B. 36/78 is 46% . C. 40/89 is 44% D. 24/59 is about 40%
I also remember doing this on a quiz!!
A rectangle has an area of 18 cm2
The lengths of the sides are whole numbers.
How long could the sides of the rectangle be?
Give all the examples you can think of
Answer:
9 possible values of length and breadth.
Step-by-step explanation:
Given that the area of the rectangle is 18cm² . And the lengths of the sides are whole numbers. We need to tell the possible dimensions of the rectangle .
Let :-
[tex]\rm\implies Length = x [/tex]
[tex]\rm\implies Breadth = y [/tex]
We know that :-
[tex]\rm\implies Area = length \times breadth [/tex]
Put in the assumed variables[tex]\rm\implies Area = x y \\\\\rm\implies xy = 18cm^2 [/tex]
Now look out for the possible factors of 18 . That is , ( 1 × 18 ) , ( 2 × 9) , ( 3 × 6 ) , ( 6 × 3 ) , ( 9 × 2 ) , (18 × 1 ) . That is total 9 possible values .
what are the lengths of SV and QT? no links.
ok so we see that TR is 17 units, so RV is the same amount
3x+2 so 3x=15 so divide both sides by 3 we get x=5
now we know x=5 4x+1=21 and 9x-4=41
*drops microphone*
Answer:
TR = 12
=> 3x + 2 =17
=> x = 5
We have QT = QV (because QTV is an isosceles triangle)
=> QT = 4x+1=4x5+1=21 units
We have TS = SV (because TSV is an isosceles triangle)
=>SV = 9x-4= 9x5-4=41 units
