The volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48 is 384.
In the given question, we have to find the volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48.
Cut by a plane at x = x(0) = constant, then z= 48-6x-8y while you are moving with y at x=x(0) constant
At this plane (x = x(0)), an element of area will be dA = z dy and an element of volume dV = dA dx
So , V = [tex]\int\int zdydx[/tex]
v = [tex]\int_{0}^{8}\int_{0}^{(48-6x)/8}(48-6x-8y)dy.dx[/tex]
v = [tex]\int_{0}^{8}[48y-6xy-4y^2]_{0}^{(48-6x)/8}dx[/tex]
v = [tex]\int_{0}^{8}[48\times((48-6x)/8)-6x\times((48-6x)/8)-4((48-6x)/8)^2-0]dx[/tex]
v = [tex]\int_{0}^{8}[9/4(x-8)^2]dx[/tex]
Let u = x-8
v = [tex]9/4\int_{0}^{8}(u)^2[/tex]
v = [tex]9/4\left[\frac{(u)^3}{3}\right]^{8}_{0}[/tex]
v = [tex]3/4[(x-8)^2]_{0}^{8}[/tex]
v = 3/4[(8-8)^3+(0-8)^3]
v = 3/4[0-(-512)]
v = 384
The volume of the given solid. bounded by the coordinate planes and the plane 6x + 8y + z = 48 is 384.
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Estimate a 20% tip on a dinner bill of $142.74 by first rounding the bill amount to the nearest ten dollars.
Estimated tip:
X
6
?
Answer:$171.29
Step-by-step explanation:
if the tip amount is around $28.55 and your putting 20% it would $171.29 but it would determine how many people they are.
Joan paid $47.98 for a jacket. If the tax rate is 8.25%, what was the cost of the jacket before tax?
Answer:
$44.021
Step-by-step explanation:
$47.98 - 8.25% = $44.021
1. Complete the table to find the sample space for rolling a
particular product on two number cubes
Step-by-step explanation:
is there supposed to be a pic attached?
The diameter of a circle is 5 cm. Find its circumference in terms of .
Answer:
If you are round the answer, you would get 15.7 cm. If not, you would get around 16 cm.
Step-by-step explanation:
The diameter is 5 and π is 3.14. You multiply those two together to get 15.7 cm. If the teacher asks to round, you will get 16 cm.
Observe as afirmativas
Answer:
?
Step-by-step explanation:
please help, and thank you.
Answer:
G: Ms Ruiz
Step-by-step explanation:
She had the lowest slope
Which equation below describes the angle measurements of a night isosceles
triangle?
А
90 + 2(45) = 180
B
180 = 90 + 40 + 50
c (180) = 60
D (90) + 90 = 180
2\sqrt((25)/(64))-(3)/(8)
Answer:
ookStep-by-step explanation:
oaxy8g7qd c7heuhwciwycowbobwxicx
donvc
Triangle ABC is similar to triangle FED, find the measure of x. A. X = 9 B. X = 11 C. X = 110 D. X = 231
Answer:
[tex]A+B+C=130[/tex]
[tex]F+E+D=273[/tex]
Step-by-step explanation:
From the question we are told that:
Dimension of ABC
A=9
B=11
C=110
Dimension of FED
D=231
Generally the equation for the similar triangles is mathematically given by
[tex]\frac{A}{F}=\frac{B}{E}=\frac{C}{D}[/tex]
Therefore solving for F
[tex]\frac{9}{F}=\frac{110}{231}[/tex]
[tex]F=\frac{9*231}{110}[/tex]
[tex]F=18.9[/tex]
Therefore solving for E
[tex]\frac{11}{E}=\frac{110}{231}[/tex]
[tex]E=\frac{11*231}{110}[/tex]
[tex]E=23.1[/tex]
Measure of [tex]\triangle ABC[/tex]
[tex]A+B+C=130[/tex]
Measure of [tex]\triangle FED[/tex]
[tex]F+E+D=273[/tex]
Holly Chris and tony each collect action figures.Chris has twice as many action figures has 3 fewer action figures than Tony.
Answer:
i have the same question brainly peeps help out
Step-by-step explanation:
1. Point D (9,-8)
is
reflected to D' (9.8).
X axis or y axis
Answer:
X-Axis
Step-by-step explanation:
The Y changed from negative to positive meaning that it reflected across the X-Axis
(っ◔◡◔)っ ♥ Hope It Helps ♥
Answer:
x axis
Step-by-step explanation:
Since the x value stayed the same and the y value changed, we can tell that the point was reflected over the x axis.
Another way to think of it:
If you draw a graph and put both points on the graph, try to fold the paper on one of the axis's. Whichever fold causes the two points to touch, is the axis that point D was reflected on.
any body can help me like pls
Answer:
Option D
Answer is D- 1/5Please mark as brainliest for future answers :)Sketch the graph of the following equations: y=x+5, y=-(x+5), and y = |x+5|
The graph of functions y=x+5, y=-(x+5), and y = |x+5| are shown in figure.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Equations are,
y = x + 5
y = - (x + 5)
y = |x + 5|
Since, All equations shows equation of line.
Hence, We can draw all the equations as shown in figure.
y = x + 5
Slope = 1
y - intercept = 5
y = - x - 5
Slope = - 1
y - intercept = - 5
Thus, The graph of functions y=x+5, y=-(x+5), and y = |x+5| are shown in figure.
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6. The height distributions of two different classes at Dover Elementary School are shown below. Both groups have the same interquartile range (IQR). Dover Elementary School Class Heights Third grade Fourth grade + 46 + 47 + 48 + 49 + 50 + 51 + 52 + 53 54 '55 which class has the greater median height?
Answer:
G.fourth grade
Step-by-step explanation:
The media is the line inside the box that’s the middle
In third grade the median is 50 but in fourth grade the median is 52 so therefore your answer is fourth grade
And the reason I know this is because I’m in 7th and have the exact same question
WHY DO U HATE ME?? ALSO HELP IN PIC!!!!!!!!!!!!
Answer:
Don't know u is correct. Also I'm not a h0* how rude >:(
Answer:
None of the above because I love you
Step-by-step explanation:
I don't hate you and if some people do they must have there reasons which I don't know, but some people just hate for no reason and if they can hate for no reason some people can love for no reason.
You may be a complete stranger to me but I love you
Evaluate y=x/7+15 when y=21
Answer:
x = 42
Step-by-step explanation:
y = x/7 + 15 ; y = 21
21 = x/7 + 15
21 - 15 = x/7
6 = x/7
x = 6 × 7
x = 42
Thus, The answer is 42
-TheUnknownScientist
Answer:
x = 42
Step-by-step explanation:
I hope its helps.........
what is the measure of AT in 0 below?
Answer:
97 degrees
Step-by-step explanation:
Answer:
97
Step-by-step explanation:
What is the independent and dependent variable in this statement, types of pizza or number of votes
Answer: type of pizza is dependant and the number of votes is independent
Step-by-step explanation:
the type of pizza they get depends on how many votes there are
Priscilla received 240 votes in the election for student council president. That was 60% of the students who voted in the election. How many students voted in the election? *
Answer:
400 students voted in the election
Step-by-step explanation:
Given:
Total number of votes received by Priscilla = 240
This was 60% of the students who voted in the election.
To find: Total number of students who voted in the election
Solution:
Total number of votes received by Priscilla = 60% of Total number of students who voted in the election
240 = 60% of Total number of students who voted in the election
240 = [tex]\frac{60}{100}[/tex] × Total number of students who voted in the election
So,
Total number of students who voted in the election [tex]=\frac{240(100)}{60}=400[/tex]
Can some one help? PLEASE!!!!!!!!
please help I am in fourth I don't know how to do this :(
Answer:
D
Step-by-step explanation:
I think so because you are divideng by 10*10 so it is 100 and you have to move to the right 2 places. I think thats it
In a science experiment, Shelly has to weigh a compound in grams. The balance in her school measures in milligrams (mg). Shelly finds that the weight of the compound is 8,450 mg. What is the value in grams (g) that Shelly should enter?
Answer:
8.45 grams
Step-by-step explanation:
In a science experiment, Shelly has to weigh a compound in grams. The balance in her school measures in milligrams (mg). Shelly finds that the weight of the compound is 8,450 mg. What is the value in grams (g) that Shelly should enter?
1 mg = 0.001 g
8450 mg = x
Cross Multiply
= 8450 × 0.001 g
= 8.45 g
Therefore, Shelly should enter 8.45 grams
In the expression 4x3 + 12, which is a coefficient, which is the variable, and which is a constant?
Answer:
4 and 3 are coefficanta and 12 will be a constant.
if 4 and 3 are being shared by the variable they would be coefficants
if x is not a variable then all the numbers are constants
Step-by-step explanation:
Solve each triangle for the missing values shown. Show all work necessary. Use exact values
3)
[tex] Cos 60°= \frac{1}{2} = \frac{Adjacent} {Hypotenuse} = \frac{y} {10} \\\\ 2y=10 \\\\ y=5 [/tex]
Now, use Pythagoras theorem to find x
[tex] x^2+y^2=10^2 \\\\ \to x^2+5^2=10^2 \\\\ \to x^2+25=100 \\\\ \to x^2 = 100-25 \\\\ \to x^2= 75 \\\\ \to x= \sqrt{75} \\\\ \bf 5 \sqrt{3} [/tex]
Similarly,
4)
[tex] Sin 45°= \frac{1}{\sqrt{2}} = \frac{Opposite} {Hypotenuse} =\frac{2 \sqrt{2}} {a} \\\\ a= 2 \sqrt{2} \times \sqrt{2} \\\\ a=4 [/tex]
Now, use Pythagoras theorem to find b
[tex] b^2+(2 \sqrt{2}) ^2=a^2 \\\\ \to b^2+8=4^2 \\\\ \to b^2=16-8 \\\\ \to b^2 = 8\\\\ \to b= \sqrt{8} \\\\ \bf b=2 \sqrt{2} [/tex]
You can solve all of them in a similar way.
: )
PLEASE HELP AND FAST i will give brainly if rightThe circle graph shows the results of a survey about favorite hobbies. A total of 1,000 people were surveyed.
Answer:
180
Step-by-step explanation:
It wants me to find m∠2 from this
Answer:
Alternate interior angles have the same measure. As we know that 'angle 1 ' and 50° are alternate interior angles hence they must be equal. Also we now that sum of all the angles of a triangle is equal to 180°. Hence, m∠2=15°
Step-by-step explanation:
Answer:
90°
Step-by-step explanation:
This is a kite.
The angle measures of the diagonals (the lines in the middle) are always going to be 90° if they looks like this without any other measures. This goes for all other quadrilaterals as well.
m∠2=90°
Hope I helped.
I don’t know if this is correct !!!!!!! Please answer correctly !!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!
Answer:
that is correct!!! and good job
HELPPPPPPP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
Answer:
answer is 9
Step-by-step explanation:
1st method: Proportion
15/100 = n/60
cross-multiply to get:
100n = 900
n = 900/100
n = 9
2nd method: Convert % to Decimal and Multiply
.15 × 60 = 9
What is the following product
Answer:
1.) y3
Step-by-step explanation:
X^2(x+5)
Help me PLS
Answer: x^3+5x^2
Step-by-step explanation: