The value of x that gives the box the greatest volume is approximately 2.08
How to determine the value that gives the greatest volume?The equation of the volume of the box is given as:
V(x) = x(12 - 2x)(13 - 2x)
Expand
V(x) = (12x - 2x^2)(13 - 2x)
V(x) = 156x - 24x^2 - 26x^2 + 4x^3
V(x) = 156x - 50x^2 + 4x^3
Differentiate the function
V'(x) = 156 - 100x + 12x^2
Set to 0
156 - 100x + 12x^2 = 0
Rewrite as:
12x^2 - 100x + 156 =0
Divide through by 4
3x^2 - 25x + 39 =0
Using a graphing calculator, the values of x are:
x = 2.08 and x = 6.26
Substitute these values of x in V(x)
V(2.08) = 2.08 * (12 - 2 * 2.08)(13 - 2 * 2.08) = 144.16
V(6.26) = 6.26 * (12 - 2 * 6.26)(13 - 2 * 6.26) = -1.56
The volume cannot be negative.
So, we have:
V(2.08) = 144.16
Hence, the value of x that gives the box the greatest volume is approximately 2.08
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help pleas for 12 points
Answer:
126 ft²
Step-by-step explanation:
surface area of rectangular prism: 2(LW + HW + WL)
Here Given:
Length: 9 ftWidth: 3 ftHeight:3 ftSurface Area:
2(LW + HW + WL)2(9*3 +3*3 + 9*3)2(27 +9 + 27)2(63)126height= 3 ft
width= 3 ft
length= 9 ft
to find:the surface area of the given prism.
solution:[tex]s.a = 2(hw + wl + hl )[/tex]
[tex]s.a = 2(3 \times 9 + 3 \times 9 + 3 \times 3)[/tex]
[tex]s.a = 126 \: {ft}^{2} [/tex]
therefore, the surface area of the given prism is 126 square feets.
Which of the following statements could be translated to the equation n - 5 = -2?
- A number less than five equals negative two.
- The difference between a number and five is negative two.
- If five is subtracted from a number, the result is two.
- Five less a number is equal to two.
Answer:
B.Step-by-step explanation:
We know that:
n - 5 = -2We also know:
A number that replaces the n value is less than 5.Here are the answers verified:
A. False. I don't know if it makes sense.B. Correct. The difference also means subtraction.C. False. I don't know if it makes sense.D. False. I don't know if it makes sense.The correct option is B.
A 15-foot ladder rest against a wall, The base of the ladder is 8 feet from the wall.
How far is the top of the ladder from the ground, Enter your answer as a decimal to the nearest tenth.
Can someone help I’ve been stuck on this question for almost a hour (please help).
Answer:
12.7
Step-by-step explanation:
Its a pythagerous question question
so if the ladder is 8 feet from the wall the base is 8
and the ladder is 15 foot and is the hypotemuse
so 15^2-8^2=161^2
The root of 161 = 12.69 rounded to 2 dp
so 12.7
The distance far the top of the ladder from the ground is 12.7 feet
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
We are given that;
Length= 15foot
Base= 8feet
Now,
In this case, the ladder is the hypotenuse, and the base and the height are the legs. So, we can write:
15^2 = 8^2 + h^2
where h is the height of the ladder from the ground. Solving for h, we get:
h^2 = 15^2 - 8^2
h^2 = 225 - 64
h^2 = 161
h = sqrt(161)
h = 12.688
Therefore, by Pythagoras theorem the answer will be 12.7 feet.
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Justus has a flexible container that holds 200 milliliters of alr at a temperature of 300 kelvins and a pressure of 100 kilopascals. Justus wants to
decrease the volume of the alr inside the container to 100 milliliters.
He can do this either by changing the temperature to
kelvins or by changing the pressure to
kilopascals.
Answer:
See below ~
Step-by-step explanation:
Based on the Ideal Gas Equation,
V ∝ TV ∝ 1/PUsing T :
V₁/T₁ = V₂/T₂200/300 = 100/T₂T₂ = 100/200 x 300T₂ = 0.5 x 300T₂ = 150 KUsing P :
P₁V₁ = P₂V₂100 x 200 = P₂ x 100P₂ = 200 kPaHe can do this either by changing the temperature to 150 kelvins or by changing the pressure to 200 kilopascals.
(giving brainliest and 40 points) a package of trail mix weighs \frac {7}{8} pound. raisins make up \frac {1}{10} of the trail mix. how much of the trail mix, in pounds, is raisins? move numbers to the boxes to show the answer. if there is no whole number, enter () in the first box. \frac {\square }{\square } 0 1 7 8 10 18 39 40 70 80
Answer:
7/80 lb
Step-by-step explanation:
We are given that 1/10 of the 7/8 pound package is raisins.
__
The weight of raisins is ...
(1/10)(7/8 lb) = 7/80 lb
.To help him start a business, Cameron took out a $10,000 loan from a bank. The loan has an annual interest rate of 5%. What expectation should Cameron have?
Answer:
[tex]A = 10,000(1.05t)[/tex] where t is in years
Step-by-step explanation:
I'm going to assume that the expectation that Cameron has is the amount of money after t years.
We can use the simple interest formula [tex]A = P(1+rt)[/tex] where A is the final amount, P is the principal, r is the rate, and t is time.
We can plug in 10,000 for P and 0.05 for r, giving us
[tex]A = 10,000(1.05t)[/tex]
A banker has a salary of £65000.
a) She is paid a bonus of £40000. What percentage of her salary is that?
b) She is given a pay rise of 16%. What is her new salary?
Answer:
I can only answer b but I hope it helps
B = £75,400
Explanation:
10% is £6500
6 % is £3900
=£10,400
+the original pay
=£75,400
That is her new salary
9. Use the compound-interest formula to find the account balance A, where P is principal, r is interest rate, n is number of compounding periods per year, t is time, in years, and A is account balance.
Answer:
$18019.37
Step-by-step explanation:
[tex]A = 12,385(1 + \frac{0.075}{365})^{365(5)}\\[/tex]
≈ $18019.37
I need help please !!!!!!!
Answer:
4 and 3/4 is the 5th shortest piece
a third of 4 and 3/4 is 1 and 7/12
the answer is: 1 7/12 in.
Step-by-step explanation:
4 and 3/4 is 19/4
19/4 divided 3 is 19/4 *1/3 = 19/12 = 1 7/12
Graph the linear equation y=2/3x-5
Answer:
As the given equation is a linear equation, to graph it, we simply need to calculate two points on the line, plot these points, then draw a straight line through them.
Given equation:
[tex]y=\dfrac{2}{3}x-5[/tex]
Calculating two points on the line:
[tex]\textsf{when }\: x=0 \implies \dfrac{2}{3}(0)-5=-5 \implies (0,-5)[/tex]
[tex]\textsf{when }\: x=6 \implies \dfrac{2}{3}(6)-5=-1 \implies (6,-1)[/tex]
Plot these points and draw a straight line through them (attached).
Andy has 36 CDs. He buys a case
that holds 4 CDs in each section.
How many sections can he fill?
Answer:
9 sections
Step-by-step explanation:
We can find the number of section by dividing the total number of CDs by the number of CDs that each case holds.
[tex]\sf \text{Number of CDs =$\dfrac{36}{4}$}[/tex]
= 9
Write an equation for the translation of y=6/x that has the asymptotes x = 4 and y = 5
Answer:
[tex]\displaystyle y=\frac{30x}{6(x-4)}[/tex]
Step-by-step explanation:
Keep in mind that a rational function with a vertical asymptote at [tex]x=4[/tex] means the denominator must be 0 when [tex]x=4[/tex] is plugged in.
This means we have [tex]\displaystyle y=\frac{6}{x-4}[/tex] so far.
To account for the horizontal asymptote at [tex]y=5[/tex], we need to adjust the numerator and denominator so that they are the same degree and that the leading coefficients have a ratio of 5. We can do this by multiplying the numerator by 5x and the denominator by 6.
This leaves us with [tex]\displaystyle y=\frac{30x}{6(x-4)}[/tex] as the translated equation since the end behavior of the function is [tex]\displaystyle y=\frac{30x}{6x}=5[/tex]. See attached graph.
Can someone help me with this geometry problem
Answer:
Step-by-step explanation:
Find the area of the shaded region.
Round your answer to the nearest tenth. 120 degrees 6cm
If the area of a semicircle and an isosceles triangle is 56.55 cm² and 18 cm². Then the area of the shaded region will be 38.55 cm².
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Then the area of the shaded region will be given by the difference between the area of the semicircle and the area of the isosceles triangle.
The area of the shaded region will be
Shaded area = area of semicircle - area of isosceles triangle
Then the area of the semicircle will be
Semicircle area = π 6² / 2
Semicircle area = π36/2
Semicircle area = 56.55 square cm.
The area of the isosceles triangle will be
Isosceles triangle area = 2 × (1/2) × 6 × 6 sin30°
Isosceles triangle area = 6 × 6 × 0.5
Isosceles triangle area = 18 square cm
Then the area of the shaded region will be
Shaded area = 56.55 - 18
Shaded area = 38.55 square cm
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(Screenshot included Need answer fast) easy question for experts. Select the graph that matches the equation y = 2 4/7x − 3
Answer: B
Step-by-step explanation:
This equation is in y = mx + b form, also known as slope-intercept form.
First, we will look at the y-intercept. Our y-intercept is -3, so the line will hit the y-axis at -3. This rules options A and C as incorrect.
Next, we will look to the slope. The slope is positive, 2 4/7, so the line will be going "up the stairs" from the bottom left to the top right. This rules out option D as incorrect, leaving us with our answer: B.
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Finding a probability a movie complex is showing three action films and three comedy films. you randomly select two
different films to watch. find the probability that you select a comedy to watchsecond given that you randomly selected a
comedy to watch first
The probability that you select a comedy to watch second given that you randomly selected a comedy to watch first will be,[tex]\rm \frac{1}{5}[/tex].
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.
Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
No of action films = 3
No of comedy films=3
The probability that you select a comedy to watch second given that you randomly selected a comedy to watch first is found as;
[tex]\rm P = \frac{C_3'}{C_6'} \times \frac{C_2'}{C_5'} \\\\\ P=\frac{3}{6} \times \frac{2}{5} \\\\ P=\frac{1}{5}[/tex]
Hence, the probability that you select a comedy to watch second given that you randomly selected a comedy to watch first will be,[tex]\rm \frac{1}{5}[/tex].
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The two tables give the number of pints of blue and yellow that are used to make different amounts of two shades of green dye.
Green #1 is made by mixing blue and yellow in a ratio of 2 : 3.
Green #2 is made by mixing blue and yellow in a ratio of 1 : 2.
Use the drop-down menus to complete each sentence below.
In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2 and green #1 is bluer shade of green than Green # 2.
What is ratio of two numbers?
The ratio of two number is the fraction part, which represent that how a number is more or less compare to the other.
There are two tables which give the number of pints of blue and yellow that are used to make different amounts of two shades of green dye. The table is given below;
Green #1 is made by mixing blue and yellow in a ratio of 2 : 3.Green #2 is made by mixing blue and yellow in a ratio of 1 : 2.The first one has 2 parts of blue at 3 parts of yellow. In the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2.
In grade two the blue part is half of the yellow part. This means that green #1 is bluer shade of green than Green # 2.
Hence, in the two highlighted rows show that for the same amount of yellow, Green #1 uses more blue than Green #2 and green #1 is bluer shade of green than Green # 2.
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Verify and show work
csc x - cos x • cot x = sin x
Answer: The answer is (d) ⇒ cscx = √3
Step-by-step explanation:
∵ sinx + (cotx)(cosx) = √3
∵ sinx + (cosx/sinx)(cosx) = √3
∴ sinx + cos²x/sinx = √3
∵ cos²x = 1 - sin²x
∴ sinx + (1 - sin²x)/sinx = √3 ⇒ make L.C.M
∴ (sin²x + 1 - sin²x)/sinx = √3
∴ 1/sinx = √3
∵ 1/sinx = cscx
∴ cscx = √3
11. Using the triangle below, set up and solve
an equation in order to find the value of x.
Answer:
x = 27.4
Step-by-step explanation:
[tex]\sf \angle Q+ \angle R+ \angle S=180^{o} [/tex]
[tex]\sf 34.6 + 118 + x = 180[/tex]
Add 34.6 and 118 = 152.6
[tex]\sf 152.6+x=180[/tex]
Subtract 152.6 from both sides.
[tex]\sf x=180 - 152.6[/tex]
Subtract 152.6 from 180 = 27.4.
Therefore, the missing angle "x" is 27.4.
please help !!!!!!!!!
Answer:
a) 1
b) 0
c) hundreths
d) .8
Step-by-step explanation:
The order, for this problem, is:
hundreds, tens, ones,
then after the decimal
tenths, hundredths, thousandths, ten thousandths, etc.
as for step d, imagine .08 as 8/100, and 8/10. Would you rather have 8 slices of pizza out of 100 slices, or 8 out of 10 slices of the whole?
I hope I helped!
Find the value of x in the parallelogram below.
Answer:
x = 25
y = 6
Step-by-step explanation:
In a parallelogram, opposite angles are equal.
2x and 50 are opposite angles,
2x = 50
Divide 2 on both sides,
x = 50 / 2
x = 25
In a parallelogram opposite sides are equal.
y + 5 and 11 are opposite sides,
y + 5 = 11
y = 11 - 5
y = 6
Answer:
x=25
y=6
Step-by-step explanation:
from the diagram,
2x= 50(opposite angles of a parallelogram)
2x= 50
dividing bothsides by 2
2x/2=50/2
x= 25
then,
y+5=11(opposite sides of a parallelogram)
y= 11-5
y= 6
What happens to warm air when it cools?
A) It sinks back down to Earth.
B) It is absorbed into clouds.
C) It remains in Earth’s upper atmosphere.
D) It breaks apart and disappears.
Answer:
b
Step-by-step explanation:
hj
Answer:Its B,dude
Step-by-step explanation:
(4x−7)^2 +16=40x−70 into a equivalent equation.
The equivalent equation of the algebraic Equation (4x - 7)² + 16 = 40x - 70 is; p² + 16 - 10p = 0
How to simplify Algebraic Equations?
We want to simplify the algebraic Equation;
(4x - 7)² + 16 = 40x - 70
Factorize right hand side to get;
(4x - 7)² + 16 = 10(4x - 7)
If p = 4x - 7, then we have;
p² + 16 = 10p
Using subtraction property of equality gives;
p² + 16 - 10p = 10p - 10p
p² + 16 - 10p = 0
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Which equation best represents the data? y = –1.026x2 1016.402x – 162075 y = –1.036x2 1024.771x – 163710 y = 298.214x – 66317.667 y = 196.2x – 18710
Based on the items produced, and the profit yielded from those items, the best model to represent the data is y = -1.026x² + 1,016.402x - 162,075.
Which model shows the profit and items produced best?You can find this out by testing the models using the items produced (independent or "x" value) to see if the model produces a close enough y value.
Assuming x is 100:
= -1.026x² + 1,016.402x - 162,075
= (-1.026 x 100²) + (1,016.402 x 100) - 162,075
= -$70,694.80
Assuming x is 400:
= -1.026x² + 1,016.402x - 162,075.
= (-1.026 x 400²) + (1,016.402 x 400) - 162,075.
= $80,325.80
These figures are very close to the actual y values given which makes this the best model.
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Answer: A. y = –1.026x2 + 1016.402x – 162075
Step-by-step explanation:
add the term that makes the given expression into a perfect square. write the result as the square of a bracketed expression b square +10b
Answer:
+ 25
Step-by-step explanation:
b² + 10b
using the method of completing the square
add ( half the coefficient of the b- term)²
b² + 2(5)b + 25
= (b + 5)² ← a perfect square
WILL MARK BRAINLIEST! WILL GIVE 57 POINTSSSS! NO FUNNY ANSWERS I WILL REPORT YOU UNTIL YOU GET BANNED.
Complete the function table. then write a rule for the function.
Pls Help Quickly! :)
Answer:
-5
-3
-2
Rule: Subtract 2 from the input value
Step-by-step explanation:
Examine the pattern of the input and the corresponding output for the two given ordered pairs:
Input -2 → Output -4
Output - Input = -4 - (-2) = -2
Input 1 → Output -1
Output - Input = -1 - 1 = -2
Therefore to get the output value (y-value), we subtract 2 from the input value (x-value).
[tex]\begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} -3 & -5 \\\cline{1-2} -2 & -4 \\\cline{1-2} -1 & -3 \\\cline{1-2} 0 & -2\\\cline{1-2} 1 & -1 \\\cline{1-2}\end{array}[/tex]
As the rule for the function is the subtract 2 from the input value to get the output value, we can write this as:
Output = Input - 2
or as an equation: [tex]y=x-2[/tex]
Alexei wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
2x^2 + 8x − 19.25 = 0
3x^2 + 5x − 19.25 = 0
4x^2 + 16x − 4.25 = 0
4x^2 + 16x + 15 = 0
The quadratic equation 4x² +16x - 4.25 = 0 can be used to determine the thickness of the frame option third is correct.
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have:
The mirror and frame must have an area of 19.25 square feet. The mirror is 3 feet wide and 5 feet long.
Let's suppose the thickness of the frame is x:
Then, the area of the rectangle:
(2x+3)(2x+5) = 19.25
4x² + 10x + 6x + 15 = 19.25
4x² +16x - 4.25 = 0
Thus, the quadratic equation 4x² +16x - 4.25 = 0 can be used to determine the thickness of the frame option third is correct.
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Please help!! Last question!
Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
There is no flaw in the steps. Hence, the correct option is A.
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graph the line y = -2x - 2
Answer:
-2x-2
For a line equation for the form of y = mx +b, the slope is m
m= -2
The function has no undefined points nor domain
constraints. There fore, the domain is
domain: -∞<x<∞
The range of polynomial with odd degrees is all the real numbers
range: -∞<f(x)<∞
Step-by-step explanation:
graph is inserted
Calculate the volume of the cone with the hemisphere scooped out of the base. Note: 20 cm is the slant height
Answer:
3418.02 cm²
Step-by-step explanation:
Volume :
Volume (cone) - Volume (hemisphere)
1/3πr²h - 2/3πr³
1/3 x π × 64 x (√20² - 8²) - 2/3 x π x (4)³
64π/3 (√336 - 2 x 2/3)
64π (18.33 - 1.33)
64π × 17
201.06 x 17
3418.02 cm²
