Answer:
She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume
Step-by-step explanation:
Length = L = 10 inches
Width = W = 6 inches
Suppose x is cut from the 4 corners to make a box.
Dimensions of the Box:
L= 10 - 2x
W = 6 - 2x
H = x
Volume of the Box:
V = (L)(W)(H)
V = (10-2x)(6-2x)(x)
V = 4x³ - 32x² + 60x
For Maximum value:
[tex]\frac{dV}{dx}=0[/tex]
[tex]\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0[/tex]
The values of x found are:
x= 4.12 , x = 1.21
If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.
We discard 4.12. Now x=1.21
So,
If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V
Help please this is due in a couple minutes!!!! Anyone know the answer??!!!?
Answer:
the second one
Step-by-step explanation:
correct me if it is wrong
evaluate.
(−1 2/3)^2=
Answer:
Step-by-step explanation:
(-5/3)(-5/3)= 25/9= 2 7/9
hat logarithmic function represents the data in the table?
x f(x)
25 2
125 3
625 4
Answer:
1
Step-by-step explanation:
Answer:
The answer is A!
Over the past ten years, the town's population doubled in size. The population is currently 12,000. What was the population ten years ago? Which of the following represents the given word problem if "P" represents the population ten years ago? 2(P + 10) = 12,000 2P = 12,000 P = 2(12,000)
Answer:
2p=12,000
Step-by-step explanation:
please answer asap! A couple plans to have 5 children. The gender of each child is equally likely. Design a simulation involving 125 trials that you can use to model the genders of the children. Write your answers as numbers.
Step-by-step explanation:
The gender of a child which is either a boy or a girl is determined by the XX-chromosomes, or XY-chromosomes.
Since the couple plan to have 5 children, the chance of a child being a boy is equal to the chance of it being a girl - the chances are 50/50.
What we do to achieve our aim is to run a simulation that would add an X or Y to an X for all 5 children.
Doing this 125 times, we obtain the number of trials we desire.
For each trial, we get for each child, C:
C1: X + (X or Y)
C2: X + (X or Y)
C3: X + (X or Y)
C4: X + (X or Y)
C5: X + (X or Y)
Since the chance of having an X is equal to the chance of having a Y, they equal probability, which is 0.5 for each.
How much water can a rectangular pool hold if it has a length of 30 feet, a width of 25 feet, and is 8 feet deep?
Answer:
44,886 gallons
Step-by-step explanation:
We need to find the volume
V = l*w*h
V = 30ft*25ft*8ft
V =6000 ft^3
We know that 1 ft^3 = 7.481 gallons
6000 ft^3 * 7.481 gallons/1 ft^3 = 44886 gallons
Answer:
44,883 gallons
Step-by-step explanation:
The amount of water the pool can hold can be found by calculating the volume of the pool.
We know that the pool is rectangular, and it is a three dimensional shape (3 dimensions: length, width and depth). Therefore, we can use the formula for finding the volume of a rectangular prism:
V=l*w*h
We know the length is 30 feet and the width is 25 feet. The height is also the depth, so the height is 8 feet.
l= 30 feet
w=25 feet
h= 8 feet
Substitute these values into the formula.
V= 30 feet * 25 feet * 8 feet
Multiply the numbers together.
V= (30 feet * 25 feet) * 8 feet
V= 750 feet^2 * 8 feet
V=6000 feet^3
Now, let's find how many gallons the pool can hold.
1 ft^3 is equal to 7.4805 gallons. Therefore, we can multiply 6000 ft^3 and 7.4805
6000 ft^3 * 7.4805 gallons/1 ft^3
6000* 7.4805 gallons
44,883 gallons
The pool can hold 44,883 gallons of water.
Can you please help
HELP ASAP PLEASE!!! Explain how you will benefit most from improving your math skills.
Answer:
Some of the most lucrative jobs are all about math. Most engineering fields are all about sharp math skills, whether it’s civil and mechanical or software engineering. Working in finance also obviously involves a lot of math, and what better way to make money than working in the field that’s all about money? You can also become a statistician or actuary; it’s not easy to find good statisticians, despite the need for them. If you want to earn good money, then you do need good math skills.Then again, you could use math in life anyway.
Step-by-step explanation:
The perimeter of the given triangle is
Answer:
~73.68
Step-by-step explanation:
In the right triangle with one angle = 45 deg
=> Isosceles right triangle
=> a = b = hypotenuse/sqrt(2) = (12sqrt(2))/sqrt(2) = 12
In other right triangle with 3 sides are a, c, and d, we have:
sin (30 deg) = a/d
=> d = a/sin(30 deg) = 12/(1/2) = 12 x 2 = 24
Othwise, cosine (30 deg) = c/d
=> c = d x cos(30 deg) = 24 x sqrt(3)/2 = 12sqrt(3)
=> The perimeter of the biggest triangle is calculated by:
P = 12sqrt(2) + b + c + d = 12sqrt(2) + 12 + 12sqrt(3) + 24 = ~73.68
Hope this helps!
i need help pls asap!!
Answer:
No, Electric Pole is 40 ft
Step-by-step explanation:
tan 66.8° = [tex]\frac{x}{15}[/tex]
x = 35
but that is from the top of Danny, so you need to add 5 (his height)
Electric Pole is 40 ft
please help thank youuu!
Answer: D. All interior angles and all sides are congruent.
Step-by-step explanation:
If it is a regular polygon, then all angles and sides have to be congruent.
The interior angles aren’t congruent to the exterior angles.
Not all angles have to be congruent, in regular or irregular.
Since this polygon has 25 sides, opposite pairs aren’t parallel because there are an odd number of sides. That means there are no opposite pairs.
Answer:
D
Step-by-step explanation:
Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 26, the length of A C is 10, and the length of B C is 24. Given right triangle ABC, what is the value of tan(A)? Five-thirteenths Twelve-thirteenths Twelve-fifths Thirteen-twelfths
Answer:
The right option is twelve-fifthsStep-by-step explanation:
Given a right angle triangle ABC as shown in the diagram. If ∠BCA = 90°, the hypotenuse AB = 26, AC = 10 and BC = 24.
Using the SOH, CAH, TOA trigonometry identity, SInce we are to find tanA, we will use TOA. According to TOA;
Tan (A) = opp/adj
Taken BC as opposite side since it is facing angle A directly and AC as the adjacent;
tan(A) = BC/AC
tan(A) = 24/10
tan(A) = 12/5
The right option is therefore twelve-fifths
Answer:
The correct answer is option C. 12/5
Step-by-step explanation:
Hope this helps!
Brainliest would be greatly appreciated :D
What is the leading coefficient of the polynomial f(x)f(x) defined below? f(x)=−3x^4−10x^3
Answer:
9x^8
Step-by-step explanation:
f(x) is a binomial. Multiplying a binomial by itself results in a trinomial. In this problem we need ONLY to specify what the leading coefficient (coefficient of this trinomial product) is.
Here this is obtained by squaring the coefficient −3x^4. We get"
(-3)^2*(x^4)^2 = 9x^8
For the function y = -2x + 4, the input is 3. What is the output?
Answer:
y = -2
Step-by-step explanation:
Plug in 3 for x
y = -2 (3) + 4
y = -6 + 4
y = -2
I hope this helps :))
find the value of each trigonometric ratio part 3
Answer:
hope this helps you
Given the points (-2,-4) and (-3,-5) what is the slope
Answer:
1/1
Step-by-step explanation:
What is 2 with an exponent of -2 equal to?
Answer:
1/4
Step-by-step explanation:
Answer:
[tex] \boxed{\frac{1}{4} } [/tex]
Step-by-step explanation:
[tex]{2}^{ - 2} = \frac{1}{ {2}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: = \frac{1}{4} [/tex]
[tex] Negative \: exponent \\ \\ = > {a}^{-x} = \frac{1}{{a}^{x}} [/tex]
a rectangular inflatable swimming pool is 2 [tex]\frac{4}{5}[/tex] yards long, 2 yards wide, and [tex]\frac{3}{5}[/tex] yard tall. What is the volume of the pool? Round to the nearest tenth
Answer:
3.4 yd^3
Step-by-step explanation:
The volume is
V = l*w*h
V = 2 4/5 * 2 * 3/5
Changing the mixed number to an improper fraction
2 4/5 = ( 5*2+4)/5 = 14/5
V = 14/5 * 2 * 3/5
= 84/25
Changing back to a mixed number
3*25 = 75 with 9 left over
3 9/25
3.36 yd^3
To the nearest tenth
3.4 yd^3
Answer: 3.4 yards cubed, after rounding.
Step-by-step explanation:
To find the volume of a rectangular prism, use the following formula:
[tex]V = wlh[/tex], where w is the width, l is the length, and h is the height
Substitute the values given to you into the formula:
[tex]V = 2 * \frac{3}{5} * 2\frac{4}{5}[/tex]
Simplify the mixed number by multiplying both the numerator and denominator of 2/1 by 5 to get 10/5 and add it to the fraction to get 14/5.
[tex]V = \frac{2}{1} * \frac{3}{5} * \frac{14}{5}[/tex]
Now, multiply the numerators and denominators of the fractions and simplify:
[tex]V = \frac{2 * 3 * 14}{5 * 5}\\\\V = \frac{84}{25}\\\\\\V = 3.36[/tex]
The volume is 3.36 yards cubed. Round to the nearest tenth to get 3.4 yards cubed.
What can be concluded about the sequence 19, 15, 11, 7, . . . represented on the graph? Check all that apply. The common difference of the sequence is the same as the slope of the graph. The slope of the graph is –4. The next term in the sequence is represented by point (4, 3). f(x) = –4x + 19 represents the sequence. An infinite number of points can be determined to follow this sequence.
Answer:
3, -1
Step-by-step explanation:
the answer is A,B,E
i took the test
Help me with this question please
Answer:
x < 6
Step-by-step explanation:
There is an open circle ( no equals) at 6 and the line goes to the left
This means that it is less than 6
x < 6
IThe first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
72, 24, 8, ...
Find the 8th term.
Answer: the eight term is 8/243
Step-by-step explanation:
Each term in this geometric sequence is equal to the previous term, divided by 3.
72,24, 8
a = 72, r = 1/3
a = first term, r is common ratio
tn = ar^n-1
t8 = 72÷ 3^8–1
t8 = 72÷ 3^7
= 72/ 3^7
= 8/243
Which shows the fractions in order from greatest to least?
A.5/10,1/4,3/4,5/7
B. 3/4,5/7,5/10, 1/4
C. 5/10,5/7,3/4,1/4
D.1/4, 3/4, 5/7,5/10
Answer:
Step-by-step explanation:
D
Can someone please explain what I did wrong here? Thank you!
Answer: The total number of ways is wrong. Since there is 12 members, each of them could be the president, vice president, etc.
Step-by-step explanation:
Answer ASAP, please!!!!!! Will mark brainliest!!!!! 25 points!!!!!
Explain how the Distributive Property can be used to expand the expression on the left side of the equation.
3(x + 4) = 36.
A. Add 3 to each term inside the parentheses.
B. Subtract 3 from each term inside the parentheses.
C. Multiply each term inside the parentheses by 3.
D. Divide both terms inside the parentheses by 3.
Answer:
C
Step-by-step explanation:
The 3 is directly outside the parentheses, meaning you need to distribute the 3 to the x and the 4 because they are inside the parentheses. There is no addition, subtraction, or division involved in this so C is correct.
Answer:
C
Step-by-step explanation:
i took the test
gbhujiklbvnhjkml dxfcgvhj
Answer:
C. 2 1/2
Step-by-step explanation:
Since there is a distance of 6 1/2 units, you have to add and subtract 6 1/2 from the number.
-4 - 6 1/2 = -10 1/2
-4 + 6 1/2 = 2 1/2
Looking at the answer choices, 2 1/2 can represent point Q.
Inscribed Angles - What is the value of x? WILL GIVE BRAINLIEST!
Answer:
18
Step-by-step explanation:
hope it helps!
At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x-axis?
-5
-2
Ο Ο Ο Ο
2
5
Answer:
At x = -2 the graph of this polynomial will touch the x-axis.
Step-by-step explanation:
Recall the behavior difference between power functions of even and odd power. Odd powers are associated with the crossing of the x-axis, while even powers are associated with "touching" of the x axis.
in this cases, since they give you the function in factor form, the actual roots (x-values where the function adopts value zero) of the function are evident :
[tex]f(x)=(x-5)^3\, (x+2)^2[/tex]
It has a root at x = 5 [notice that at such x-value the factor (x-5) becomes zero], and this root is of multiplicity "3" (given by the power associated with the binomial factor for this root)
and has another root at x = -2 [notice that at such x-value the factor (x+2) becomes zero], and this root is of multiplicity "2" (given by the power associated with the binomial factor for it)
It is just the second root analyzed the one that shows an even power (2) associated to its binomial factor, and therefore it is at x= -2 that the graph of this function will show as "touching" the x axis.
true or false ? why and why not ?
8a - (8a - 8) is equivalent to 8
Answer:
True
Step-by-step explanation:
Apply the distributive property
8a-(8a)- -8
Multiply 8 by -1
8a-8a- -8
Multiply -1 by -8
8a-8a+8
Simplify by adding terms
Subtract 8a from 8a
0+8
Add 0 and 8
8
Hope this helps :)
part 3. Find the value of the trig function indicated, use Pythagorean theorem to find the third side if you need it.
Answer: [tex]\bold{9)\ \sin \theta=\dfrac{1}{3}\qquad 10)\ \sin \theta = \dfrac{4}{5}\qquad 11)\ \cos \theta = \dfrac{\sqrt{11}}{6}\qquad 12)\ \tan \theta = \dfrac{17\sqrt2}{26}}[/tex]
Step-by-step explanation:
Pythagorean Theorem is: a² + b² = c² , where "c" is the hypotenuse
[tex]9)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{12}\quad \rightarrow \large\boxed{\dfrac{1}{3}}[/tex]
Note: 4² + (8√2)² = hypotenuse² → hypotenuse = 12
[tex]10)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{16}{20}\quad \rightarrow \large\boxed{\dfrac{4}{5}}[/tex]
Note: 12² + opposite² = 20² → opposite = 16
[tex]11)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{\sqrt{11}}{6}\quad =\large\boxed{\dfrac{\sqrt{11}}{6}}[/tex]
Note: adjacent² + 5² = 6² → adjacent = √11
[tex]12)\ \tan \theta=\dfrac{\text{side opposite of}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{17}{13\sqrt2}\quad =\large\boxed{\dfrac{17\sqrt2}{26}}[/tex]
Note: adjacent² + 7² = (13√2)² → adjacent = 17
What is the solution to the equation Negative (5 minus (a + 1)) = 9 minus (5 minus (2a minus 3))? a = –5 a = –3 a = 3 a = 5
Answer:
a = -5
Step-by-step explanation:
negative (5 minus (a + 1)) = 9 minus (5 minus (2a minus 3)) can be expressed mathematically as follows.
- (5 - (a + 1)) = 9 - (5 - (2a - 3))
using the principle of PEMDAS, all the parenthesis values are first solved
- (5 - a - 1) = 9 - (5 - 2a + 3)
-5 + a + 1 = 9 - 5 + 2a - 3
collect like terms
-5 + 1 - 9 + 5 + 3 = 2a - a
-5 = a Therefore,
a = -5
Answer:
-5
Step-by-step explanation:
