if the box is to be made out of wood that costs $4 per square foot, which of your designs would be less expensive to produce? Explain.
The second box is less expensive to make since it has a smaller surface area and hence requires less wood to construct the sides.
What is a cuboid?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
Here some data is not given, so we are assuming the volume of the box is 24 cubic feet.
If the volume is 24 cubic feet, the box's three dimensions must multiply to equal 24.
We can make two designs:
2 × 2 × 6 and 2 × 3 × 4.
Now, finding the surface area for each design.
First box
SA = 2wl + 2wh + 2hl
SA = 2×2×2 + 2×2×6 + 2×2×6
SA = 56 square feet
Second box
SA = 2×2×3 + 2×2×4 + 2×3×4
SA = 52 square feet
At $4 per square foot
For 56 ft², the price is $224
For 52 ft², the price is $208
Thus, the second box is less expensive to make since it has a smaller surface area and hence requires less wood to construct the sides.
Learn more about the cuboid here:
brainly.com/question/9740924
#SPJ1
Simplify: 5 3/4 divide5 5/9
by substituting a numerical value for a in the expression.
Answer: 8
Step-by-step explanation: divion
Which values are solutions to the inequality below? Check all that apply.
x^2 > 16
A. 4
B. -6
C. -1
D. 5
Answer:
B. -6 and D. 5
Step-by-step explanation:
x^2 - 16 > 0
y = (x - 4)(x + 4) > 0
The critical point are x = -4 and x = 4
When x < -4, y > 0
When x > 4, y > 0
When -4 < x < 4, y < 0
When x = -4 and x = 4 , y = 0.
So the values that apply are
B. -6 and D. 5
Pre-calc/Trig
Suppose that θ=arcsin(4/6). What is cos(2θ)? (round to 4 decimals)
Answer:
0.7453
Step-by-step explanation:
[tex]arcsin( \frac{4}{6} ) = 0.7297 \\ cos(0.7297) = 0.7453[/tex]
Please show your work and I'll mark brainliest if you do! Thank you :)
Answer:
what r u supposed to do with that perimeter or area pls state question well
The pattern 2, 5, 17, ________, ________ follows the rule multiply by 4, then subtract 3. What are the next two terms?
Group of answer choices
68, 260
68, 257
Answer:
None of the answer choices.
Step-by-step explanation:
The pattern to this problem is multiply by 4, and subtract 3. However when doing 17 * 4, you get 68. Look how both of the answer chouces start with 68, and we haven't even subtracted 3 yet. This shows that the answer choices are wrong.
Correct Answer: 65, 257
The answer: ———————> 68, 257
Which triangle is possible?
3 ft, 4ft, and 5ft 4yd, 5ft, and 10yd
3 ft, 3 ft, and 7 ft.
4 in, 4 in, and 8 in
Answer:
(a) 3 ft, 4 ft, 5 ft
Step-by-step explanation:
The triangle inequality requires the sum of the two short sides exceed the long side.
__
a) 3 ft + 4 ft = 7 ft > 5 ft . . . . . triangle is possible
b) 4 yd + 1 2/3 yd = 5 2/3 yd < 10 yd . . . . not a possible triangle
c) 3 ft + 3 ft = 6 ft < 7 ft . . . . not a possible triangle
d) 4 in + 4 in = 8 in . . . . not a possible triangle (not greater than 8 in)
__
The first set of side lengths can form a triangle: 3 ft, 4 ft, 5 ft.
If 1ml of water fills 1 cubic centimeter of space, how many ml of water are needed to fill each tank?
Answer:
Tank Volume/1 cubic centimeter.
Step-by-step explanation:
We dont know how big the tank is.
If a =3 and ab =6 then a²-b² =
Answer:
5
Step-by-step explanation:
a = 3
ab = 6
so b must be 2
3 squared is 9 and 2 squared is 4
so 9 - 4 is equal to 5
Answer:
Step-by-step explanation:
If a =3 and ab =6 then a²-b² =
a = 3
ab = 6
find b
b = 6:3 = 2
-------------------
3² - 2² =
9 - 4 =
5
NO LINKS!! Please help me with these graphs. Part 1
Problem 9
The instructions aren't stated anywhere, but I'm assuming your teacher wants you to find the equation of each parabola.
The vertex here is (h,k) = (-6,-4) which you have correctly determined.
This means
[tex]y = a(x-h)^2 + k\\\\y = a(x-(-6))^2 +(-4)\\\\y = a(x+6)^2 - 4\\\\[/tex]
Next we plug in one of the other points on the parabola. We cannot pick the vertex again. Let's pick the point (-4,0) which is one of the x intercepts. We'll do this to solve for 'a'
[tex]y = a(x+6)^2 - 4\\\\0 = a(-4+6)^2 - 4\\\\0 = a(2)^2 - 4\\\\0 = a(4) - 4\\\\0 = 4a-4\\\\4a-4 = 0\\\\4a = 4\\\\a = 4/4\\\\a = 1\\\\[/tex]
This means
[tex]y = a(x+6)^2 - 4\\\\y = 1(x+6)^2 - 4\\\\y = (x+6)^2 - 4\\\\[/tex]
represents the equation of the parabola in vertex form.
Answer: [tex]y = (x+6)^2 - 4\\\\[/tex]========================================================
Problem 10
The vertex is (h,k) = (-2,-6)
So,
[tex]y = a(x-h)^2 + k\\\\y = a(x-(-2))^2 + (-6)\\\\y = a(x+2)^2 - 6\\\\[/tex]
Now plug in another point on the parabola like (-1,-8) and solve for 'a'
[tex]y = a(x+2)^2 - 6\\\\-8 = a(-1+2)^2 - 6\\\\-8 = a(1)^2 - 6\\\\-8 = a(1) - 6\\\\a-6 = -8\\\\a = -8+6\\\\a = -2\\\\[/tex]
Answer: [tex]y = -2(x+2)^2 - 6\\\\[/tex]For each equation, you could optionally expand things out to get it into y = ax^2+bx+c form, but I think it's fine to leave it as vertex form.
Answer:
[tex]\textsf{9)} \quad y=(x+6)^2-4[/tex]
[tex]\textsf{10)} \quad y=-2(x+2)^2-6[/tex]
Step-by-step explanation:
Vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex
Question 9From inspection of the graph, the vertex is (-6, -4)
[tex]\implies y=a(x+6)^2-4[/tex]
To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.
Using point (-4, 0):
[tex]\implies a(-4+6)^2-4=0[/tex]
[tex]\implies a(2)^2-4=0[/tex]
[tex]\implies 4a=4[/tex]
[tex]\implies a=1[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]y=(x+6)^2-4[/tex]
Question 10From inspection of the graph, the vertex is (-2, -6)
[tex]\implies y=a(x+2)^2-6[/tex]
To find [tex]a[/tex], substitute the coordinates of a point on the curve into the equation.
Using point (-1, -8):
[tex]\implies a(-1+2)^2-6=-8[/tex]
[tex]\implies a(1)^2-6=-8[/tex]
[tex]\implies a-6=-8[/tex]
[tex]\implies a=-2[/tex]
Therefore, the equation of the parabola in vertex form is:
[tex]\implies y=-2(x+2)^2-6[/tex]
How many pieces 15/16 inch long can be cut from a strip of sheet metal 13 1/8 inches long?
Answer:
14 pieces
Step-by-step explanation:
Simplify 13 1/8 into fraction with denominator 16
13 1/8105/8210/16Number of pieces
(210/16)/(15/16)14 piecesI WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
HELPPPPPPP SO CONFUSED
Answer:
x = 80
Step-by-step explanation:
The diagram shows that arc AB is 80 degrees, and the measure of an arc defined as being equal to the central angle(the minor angle of the arc). Because the arc AB is 80, the central angle x is 80 degrees as well. Although if point O wasn't at the center of the circle, x might not be 80.
Please Answer The Following Maths Question: "Could you change $2 for me for the parking meter?" inquired the young woman.
"Sure," I replied, knowing I had more than $2 change in my pocket.
In actual fact however, although I did have more than $2 in change, I could not give the woman $2.
What is the largest amount of change I could have in my pocket without being able to give $2 exactly?
Answer:
$5
Step-by-step explanation:
Conditions
More than $2Not exactly $2In the currency bills are printed as : $1, $5, $10, $20, $50, $100
Hence, the largest amount he could give the woman is $5
Ted says that the triangle below cannot be classified because all sides are different lengths. Is Ted correct? Explain why or why not.
Answer:
Ted is wrong
The triangle is a right triangle because of the right 90° angle formed at the bottom.
PLEAZE HELP WILL MARK BRAINLIEST!
Answer:
B: π/6
Step-by-step explanation:
A: 0
B: π / 6
C: π / 4
D: π / 3
E: π / 2
F: π
G: 3π / 2
Here is a complete unit circle...
Which pair of angles are coterminal?
Answer:
5 pi / 9 & 23 pi / 9
Step-by-step explanation:
adding or subtracting multiples of 2pi are coterminal
2pi = 18pi/9
5 pi / 9 + 18pi/9 = 23 pi/9
please answer this question
Answer:
[tex]\dfrac{dy}{dx}=\cot x+\dfrac{1}{x}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Product\:Rule}\\\\$\dfrac{d}{dx}[f(x)g(x)]=f(x)g'(x)+f'(x)g(x)$\\\\\\\underline{Chain\:Rule}\\\\$\dfrac{dy}{dx}=\dfrac{dy}{du} \times \dfrac{du}{dx}$\\\end{minipage}}[/tex]
[tex]\textsf{Given}:y=\log (x \sin x)[/tex]
[tex]\textsf{Let }u=x \sin x \implies y=\log(u)[/tex]
Using the product rule, differentiate y with respect to [tex]u[/tex]:
[tex]\textsf{If }y=\log(u) \implies \dfrac{dy}{du}=\dfrac{1}{u}\implies \dfrac{dy}{du}=\dfrac{1}{x \sin x}[/tex]
----------------------------------------------------------------------------------------
Differentiate [tex]u=x \sin x[/tex] with respect to x using the product rule:
[tex]\implies \textsf{Let }f(x)=x \implies f'(x)=1[/tex]
[tex]\implies \textsf{Let }g(x)=\sin x \implies g'(x)=\cos x[/tex]
[tex]\implies \dfrac{du}{dx}=x \cos x + \sin x[/tex]
----------------------------------------------------------------------------------------
Use the chain rule to differentiate y with respect to x:
[tex]\implies \dfrac{dy}{dx}=\dfrac{dy}{du} \times \dfrac{du}{dx}[/tex]
[tex]\implies \dfrac{dy}{dx}=\dfrac{1}{x \sin x} \times (x \cos x + \sin x)[/tex]
[tex]\implies \dfrac{dy}{dx}=\dfrac{x \cos x + \sin x}{x \sin x}[/tex]
[tex]\implies \dfrac{dy}{dx}=\dfrac{x \cos x}{x \sin x}+\dfrac{\sin x}{x \sin x}[/tex]
[tex]\implies \dfrac{dy}{dx}=\cot x+\dfrac{1}{x}[/tex]
Answer:
[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle \large{y=\log (x\sin x)}[/tex]
Recall the (common) logarithmic differentiation & chain rules:
[tex]\displaystyle \large{\dfrac{d}{dx}[\log (u)] = \dfrac{u'}{u\ln 10}}[/tex]
Let [tex]\displaystyle \large{u=x\sin x}[/tex] then:
[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{(x\sin x)'}{x\sin x \ln 10}}[/tex]
Recall product rules:
[tex]\displaystyle \large{[f(x)g(x)]' = f'(x)g(x)+f(x)g'(x)}[/tex]
Hence:
[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{(x)'\sin x + x(\sin x)'}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{\sin x + x\cos x}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{\sin x}{x \sin x \ln 10} + \dfrac{x \cos x}{x\sin x \ln 10}}\\\\\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}[/tex]
From above, recall that:
[tex]\displaystyle \large{\dfrac{d}{dx}(\sin x) = \cos x}\\\\\displaystyle \large{\dfrac{A\pm B}{C} = \dfrac{A}{C} \pm \dfrac{B}{C}}\\\\\displaystyle \large{\dfrac{\cos x}{\sin x} =\cot x}[/tex]
Hence, the answer is:
[tex]\displaystyle \large{\dfrac{d}{dx}[\log(x\sin x)] = \dfrac{1}{x\ln 10} + \dfrac{\cot x}{\ln 10}}[/tex]
Find the area of the circle
r = 6 ft
If the radius of the circle is 6 feet. Then the area of the circle will be 113.097 square feet.
What is a circle?It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.
The radius of the circle is 6 feet.
Then the area of the circle will be
Area = πr²
where r is the radius of the circle. Then we have
Area = π × 6²
Area = 36π
Area = 113.097 square feet
More about the circle link is given below.
https://brainly.com/question/11833983
#SPJ1
Marni has 24 ounces of walnuts. she needs 14 ounces for one recipe and 1/2 pounds for another. how many total ounces does she need to make her recipes?
The total ounces she needs to make her recipes is 22 ounces
Calculating quantityFrom the question, we are to determine how many total ounces Marni needs to make her recipe
From the given information,
Marni has 24 ounces of walnuts
Also,
She needs 14 ounces for one recipe
and
1/2 pounds for another
First, we will convert 1/2 pounds to ounces
NOTE: 1 pound = 16 ounces
∴ 1/2 pound = 8 ounces
Then, we can rewrite that
She needs 14 ounces for one recipe
and
8 ounces for another
The total ounces she needs to make her recipes = 14 ounces + 8 ounces
The total ounces she needs to make her recipes = 22 ounces
Hence, the total ounces she needs to make her recipes is 22 ounces
Learn more on Calculating quantity here: https://brainly.com/question/238643
#SPJ1
PLEASE HELP ME WITH THIS! IM BEHIND
Answer:40
Step-by-step explanation: i may be wrong but i subtracted 136 from 95 and i got 40 im sorry if it is wrong
PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL PLS PLS HELP HELP ME ITS EASY ITS FREE PONTS LOL
Answer:
37
Step-by-step explanation:
90 - 53 = 37
Answer:
x = 37°
Step-by-step explanation:
Given angle AOB = 53°, angle AOC = 90°
To find x°
From above figure, angle AOC = angle AOB + angle BOC
Now angle AOB = 53°, angle AOC = 90°
90° = 53° + angle BOC
=> angle BOC = x° = 90 - 53
=> x° = 37°
HOPE THIS HELPS AND HAVE A NICE DAY <3
2 + 10n + 9 + 6n
Explain please
Answer:
11 + 16n
Step-by-step explanation:
Collect the like terms
2 + 9 = 11
10n + 6n = 16n
11 + 16n is the final answer, and cannot be simplified further
Answer:
16n + 11
Step-by-step explanation:
Simpifying
Combine like terms (n and number terms)
2 + 10n + 9 + 6n10n + 6n + 2 + 916n + 11Triangle ABC is dilated by a scale factor of 1.5 to create triangle A'B'C'. Which of
the following it not a true statement?
A. The image is larger than the pre-image.
B. The orientation of triangle ABC is preserved.
C. Segment AB is congruent to segment A'B'.
D. The angle measures in triangle ABC are equal to the angle measures in triangle
A'B'C'.
Answer:
C. Segment AB is congruent to segment A'B'.
Step-by-step explanation:
Since ABC is being dilated by 1.5, it means that A'B'C will be bigger than ABC.
So, since A'B'C will be bigger than ABC, it sides will also be bigger than the sides in ABC.
And since the sides/segments are bigger than the original, they are not congruent (congruent means equal).
Calculate the volume of the right rectangular prism shown.
Edulastic Question
since we have the area of the front side, to get its volume we can simple get the product of the area and the length, let's firstly change the mixed fractions to improper fractions.
[tex]\stackrel{mixed}{23\frac{2}{3}}\implies \cfrac{23\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{71}{3}} ~\hfill \stackrel{mixed}{4\frac{7}{8}}\implies \cfrac{4\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{39}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{3}\cdot \cfrac{39}{8}\implies \cfrac{71}{8}\cdot \cfrac{39}{3}\implies \cfrac{71}{8}\cdot 13\implies \cfrac{923}{8}\implies 115\frac{3}{8}~in^3[/tex]
A town population is 50,000 in 2018. The population has been growing at a rate of 3.7% each year. What is the estimated population of 2025?
Answer:
The formula for exponential growth is: Total = Starting value(1 + rate)^time
2018 to 2025 is 7 years:
Step-by-step explanation:
Total = 50,000(1+0.037)^7
Total = 50,000(1.037)^7
Total = 64,479 -(Answer)
A scale model of a skateboarding ramp is a right triangular prism as shown in the
figure.
In the actual ramp, the triangular base has a height of 15 in.
What is the VOLUME of the actual ramp?
Please explain in detail:)
The volume of the actual ramp including the underside is 16 cubic ft.
The height of the actual ramp = 15 feet
The height of the model = 6 cm
What is the volume of a right triangular prism?A right triangular prism is a 3-dimensional triangle with two congruent triangular faces and 3 rectangular faces that connect the triangular.
The volume of a right triangular prism = ( height× Base Area)
Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm
Actual base = 16 cm × 0.2 ft/cm = 3.2 ft
The volume of a right triangular prism = ( height× Base Area)
= [tex]5 \times 3.2\\ 16.0[/tex]
Hence, the volume of the actual ramp including the underside is 16 cubic ft.
Learn more about the volume here:
brainly.com/question/25292087
#SPJ1
find the surface area of this prism
3cm
7cm
5cm
Answer:
105cm
Step-by-step explanation:
please click crown below my answer.
A bottle of vanilla extract costs $1.28 & contains 48 teaspoons of extract. What is the cost per teaspoon?
Answer:
about 3 cents
Step-by-step explanation:
1.28 divided by 48 = 0.02667
whihc orunds to 0.03
I need help, Asap!’
Answer:
so on the bottom you will see an x and on the left side you will see an y, for 1,4 the 1 will be on the x and the 4, just go up to the four for 2,8 on the x you will go on two on the bottom, for y you will go up to the 8, for 4,16 the x is four and you will go up to 16, for 5,20 the x will be 5 and then go up to 20. I really hope that this helped
Step-by-step explanation: