Answer:
Step-by-step explanation:
center(-7,0)
radius= radical 119
A rectangular sheet of cardboard 3 feet by 5 feet will be made into an open box by cutting equal-sized squares from each corner and folding up the four edges. A diagram of the unfolded box is provided in figure, the shaded region represents the area
that was cut from the corners of the box. What is the largest volume of such a box?
Answer:
4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x
Step-by-step explanation:
length = 5 - 2x
width = 3 - 2x
heighth = x
x(5 - 2x)(3 - 2x)
x(15 -16x + 4[tex]x^{2}[/tex])
4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x
The largest volume of such a box is 4.345[tex]ft^{3}[/tex].
Given that,
A rectangular sheet of cardboard 3 feet by 5 feet will be made into an open box by cutting equal-sized squares from each corner and folding up the four edges.
The shaded region represents the area that was cut from the corners of the box.
We have to determine,
The largest volume of such a box.
According to the question,
The height will be x
The width will be (3 − 2 x)
And the length will be ( 5− 2 x)
.
The formula for volume will be,
[tex]Volume = Length \times Height \times Width\\\\[/tex]
Substitute the values in the formula,
[tex]Volume = x(3-2x).(5-2x)\\\\Volume = (3x-6x^{2}).(5-2x)\\\\Volume = 3x(5-2x) - 6x^{2}(5-2x)\\\\Volume = 15x - 6x^{2} - 30x^{2} + 12x^{3}\\\\Volume = 12x^{3} -36x^{2} + 15x[/tex]
Then,
To Find the derivative of the equation,
[tex]V = 12x^{3} -36x^{2} + 15x\\\\Differentiate\ with\ respect\ to\ x\ both\ sides,\\\\\dfrac{dv}{dx} = \dfrac{d(12x^{3} -36x^{2} + 15x)}{dx}\\\\V' = 36x^{2} - 72x+15[/tex]
The critical numbers by seeing where V ' = 0,
[tex]= 36x^{2} -72x +15\\\\= 3 ( 12x^{2} - 24x +5 )\\[/tex]
By using the quadratic formula or your calculator to solve for
x = 0.23, and 1.6
x = 1.6 is not in the domain since that would make one of our side lengths less than zero. x = 0.23
Plug x back into the equations to get the dimensions,
[tex]3-2x = 3- 2 \times -0.23 = 3+0.46 = 3.46\\5-2x = 5 - 2 \times -0.23 = 5+0.46 = 5.46[/tex]
Therefore, the dimension are 0.23 ft x 3.46 ft x 5.46 ft.
Hence, The largest volume of such a box is 4.345[tex]ft^{3}[/tex].
To know more about Dimension click the link given below.
https://brainly.com/question/23288467
Choose all the expressions that are equivalent to 4x-20.
x (4 - 20)
2 (2x - 10)
4(x - 20)
4(x - 5)
Answer:
4(x-5)= 4x-20
so the equivalent equation is 4(x-5)
Answer:
I don't actually know sorry
Step-by-step explanation:
I don't know
Which choice is equivalent to the quotient below shown here when x>0?
Answer:
B
Step-by-step explanation:
step 1 - rationalize the denominator to get:
[tex]\sqrt{35x^5}[/tex] ÷ [tex]\sqrt{7x^3}[/tex] = ([tex]\sqrt{245}[/tex] ·x^5/2·x^3/2) ÷ 7x³
= ([tex]\sqrt{5}[/tex][tex]\sqrt{7}[/tex][tex]\sqrt{7}[/tex]·x^4) ÷ 7x³
= 7[tex]\sqrt{5}[/tex]·x^4 ÷ 7x³
= [tex]\sqrt{5}[/tex]x
Please help me with my math ASAP!
Hello !
Answer:
[tex]\large\boxed{\sf Option\ 3 : 66cm}[/tex]
Step-by-step explanation:
The circumference of a circle is given by [tex]\sf C=2\times\pi\times r[/tex], where r is the radius.
Given :
d = 21 cmr = d/2 = 10.5 cmπ =3.14Let's replace r with its value in the previous formula :
[tex]\sf C=2\times 3.14\times 10.5[/tex]
[tex]\sf C=65.94[/tex]
[tex]\boxed{\sf C\approx 66cm}[/tex]
Have a nice day
En un parque de forma circular de 700 m de radio hay situada una fuente,
tambien de forma circular, de 5 m de radio. Calcula el área de la zona de
paseo.
área del parque
A=Pi . R^2
A=Pi (700m^2)
A=3.1416 x 490000m^2
A= 1539380.4 m ^2
área de la fuente
a= Pi. r^2
a=Pi (5cm^2)
a=3.1416 x 25cm^2
a= 78.54 cm^2
Luego lo que hacemos que al area grande le restamos la pequeña.
pero antes que nada convertiremos los metros a centimetros.
A= 1539380.4 m^2
1539380.4 m^2 (100cm/1m)
eliminaras los metros y te quedara asi
1539380.4 ( 100 cm/ 1)
153,938,040 cm^2
luego restamos A-a
153,938,040 cm^2 - 78.54cm^2
R/ el area de la zona de paseo es de 153937961.5 cm^2 !!
13 and 14, 10 points no links please
Answer:
13 is c
14 is b
Step-by-step explanation:
If a line contains the point (0, 1) and has a slope of 2, then which of the following points also lies on the line? (1,3) (3,1) (2,2) (2,3)
Answer:
(1,3)
Step-by-step explanation:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis, or when x is equal to 0).
We're given that this line contains the point (0,1). This tells us that the y-intercept (b) of the line is 1. We're also given that this line has a slope (m) of 2. Plug these values into [tex]y=mx+b[/tex]:
[tex]y=2x+1[/tex]
Now, plug in all of the possible points to see which are solutions.
1) (1,3)
[tex]3=2(1)+1\\3=2+1\\3=3[/tex]
Because the left side of the equation is equal to the right, (1,3) also lies on this line.
2) (3,1)
[tex]1=2(3)+1\\1=6+1\\1=7[/tex]
Because the left side is not equal to the right, (3,1) does not lie on the line.
3) (2,2)
[tex]2=2(2)+1\\2=4+1\\2=5[/tex]
Because the left side is not equal to the right, (2,2) does not lie on the line.
4) (2,3)
[tex]3=2(2)+1\\3=4+1\\3=5[/tex]
Because the left side is not equal to the right, (2,3) does not lie on the line.
I hope this helps!
what type of lines are x-3y=-3 and 6x+2y=-12
Answer:
Perpendicular
Step-by-step explanation:
Nhat properties can be used to identify a substance as solid, liquid, or gas? Check all that apply.
mass
compressibility
particle motion
weight
color
shape
HELP PLEASE
A shoe store donated a percent of every sale to hospitals. The total sales were $8900 so the store donated $356. What percent of $8900 was donated
Answer:
4%
Step-by-step explanation:
Given data
The total sales= $8900
Donated amount=$356
Hence the percent donated is
=Donated amount/Total Sales *100
= 356/8900*100
=0.04*100
=4%
Hence the donated percent is 4%
Find the average of the list of Fahrenheit temperatures.
- 17°, 2°, -90,30, 12°, -5°, and 7°F
Answer:
-8.71428571
Step-by-step explanation:
Calculator gl
Solve the following quadratic equation for all values of x in simplest form.
(x – 4)^2 – 47 = 32
Answer:
x=4-√79, x=4+√79
Step-by-step explanation:
please both the question please
Answer:
Boys: 2/17
Girls: 4/17
Step-by-step explanation:
2 + 15 = 17 (to get the total number of boys in Sapphire's class)
4 + 13 = 17 (to get the total number of girls in the class)
The proportion is how many who are left handed over the total number of girls/boys. ^^
So, left-handed for boys = 2, which makes the proportion 2/17
And there are 4 left-handed girls, so the proportion is 4/17
Find the radius when d=18
Answer:
9
Step-by-step explanation:
radius is half of the diameter
“The class buys 3 bags of apples. Each bag has 24 apples. The total cost of the 3 bags of apples is $12.24. The class sells the apples for $0.75 each. How much money will the class gain per apple”
© A new car cost $14875. Three years later, the insurance company valued it at $10700. Calculate the percentage
reduction in value over the three years.
Answer: either I don't understand the question or its 72% and I'm fairly certain its 72%
2. The mean weight of the students on the
Trail Middle School wrestling team is 150
pounds with a mean absolute deviation of
10 pounds. The mean weight of the
students on the Burlington Middle School
wrestling team is 130 pounds with a mean
absolute deviation of 10 pounds. By how
many pounds is the mean weight of the
students on Trail's team greater than the
mean weight of the students on
Burlington's team?
Answer:
The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School wrestling team
Step-by-step explanation:
Since the value of absolute deviation in case of Trail Middle School wrestling team and Burlington Middle School wrestling team is same. Hence, there will be no impact of it while determining the difference in mean deviation of both the team.
Thus, the difference in mean deviation is [tex]150-130 = 20[/tex]
The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School wrestling team
1. list the pairs of alternate exterior angles
2. list the pairs of corresponding angles
3. if m<a is 112°, find the measure of the remaining angles
Answer:
1. m<a and m<h, m<e and m<d
2.m<a and m<c, m<b and m<d, m<e and m<g, m<f and m<h
3. m<a= 112
m<c=112
m<f=112
m<h=112
m<b=68
m<d=68
m<e=68
m<g=68
Calculate the Mean Absolute Deviation of these data. Round answers to the nearest tenth (one decimal place).
12, 17, 20, 8, 13
Answer:
18/5
Step-by-step explanation:
12+17+20+8+13 =70
70/5 = 14 which is the mean
the distances from the mean are
2 3 6 6 1
add them which is 18 then divide by 5 to find the mean
18/5
Anne has worn a black shirt on 6 of the last 20 days. Considering this
data, how many times would you expect Anne to wear a black shirt in the
next 10 days?
Answer:
3
Step-by-step explanation:
Considering she wore a black shirt 6 times in 20 days will give you the statistic of 3/10. If the question is about the next 10 days then she will wear 3 black shirts. (It's also 1/2 of the original question.)
Find an equivalent ratio in simplest terms:
56 : 22
I need help with this one. Please. thanks!
Answer:
x=6
Step-by-step explanation:
30=6+4x
you have to combine the number that are the same, like 2 and 4 or 3x and 4x
30-6=4x (you should always remember when you move a number if it was - it will turn +)
30-6=4x
24=4x
x=24/4
x=6
Find the surface area of each pyramid round to the nearest tenth if necessary
Answer:
457.9
Step-by-step explanation:
The temperature in an oven changes from 350 degrees to 362% What is the percent increase in temperature, to the nearest tenth of a percent?
Answer:
3.43%
Step-by-step explanation:
362-350=12
12:350*100 =
(12*100):350 =
1200:350 = 3.43
What is the slope of the line that passes through the points (-8, -6)(−8,−6) and (-18, 6) ?(−18,6)? Write your answer in simplest form.
if y=3x - 6 and x=7, then y = ??
Answer:
y=15
Step-by-step explanation:
y=21 - 6
y = 15
hope this helped!
8. Jackie converted the following decimals to fractions. Which decimal did she
convert incorrectly?*
0.005
0.3
0.625
0.8
Please hurry and answer
Answer:
B
Step-by-step explanation:
Answer:
it's 0.625
Step-by-step explanation:
Find the value of angle A and angle B pls help (:
Answer:
m<A=97
m<B=97
Step-by-step explanation:
m<A=m<B
Congruent angles and they are vertical angles. The other two are also the same because the angles given have the same degrees.
m<A is supplementary to 83 degrees
Supplementary angles are two angles that sum up to 180 degrees.
180-83=97
97 degrees is the answer for each missing angles.
HELP ME!!! PLEASE I HAVE A G- MY PARENTS WILL KILL ME (LITERALLY PLEASE HELP)
Answer:
you should get math w ay it's good
what is the measure of EACH exterior angles t
of the polygon shown?
Answer:
45 degrees
Step-by-step explanation:
The following shape is an octagon, having 8 sides and knowing that any regular polygon has an exterior angle value of 360 degrees, you can say 360/8 to find the measure of each exterior angle, leading to equal 45 degrees.
Hope it helped! (: