Find where the two curves intersect:
y = 6x - 2x ²
y = x ²
6x - 2x ² = x ² → 3x ² - 6x = 3x (x - 2) = 0 → x = 0 and x = 2
Now, for a shell of radius x units away from the axis of revolution, the height of the shell would be the vertical distance between the upper curve and the lower curve. For 0 ≤ x ≤ 2, we have 6x - x ² ≥ x ², so the height of any given shell is (6x - x ²) - x ² = 6x - 2x ².
Then volume of the solid is
[tex]\displaystyle 2\pi \int_0^2 x(6x-2x^2)\,\mathrm dx = 2\pi \left(2x^3-\frac{x^4}2\right)\bigg|_0^2 = \boxed{16\pi}[/tex]
David’s watch broke. He decides to get it fixed instead of replacing it. The total cost to repair the watch can be represented by 0.07(45h) + 45h, where h represents the number of hours it takes to repair the watch. What part of the expression represents the amount of tax David has to pay? Explain.
MAX POINTS PLEASE HELp
part a. What are the values of x and y? If your answer is not a whole number, write it as a decimal and round to one decimal place if necessary.
part b:
Here is a triangular prism.
What is the volume of the prism, in cubic centimeters?
cubic centimeters
What is the surface area of the prism, in square centimeters?
cubic centimeters
Answer:
X=35 Y=73
Step-by-step explanation:
use the opposite angle theorem for x. X would equal 35.
we know that x is 35. So 2y+35=180
180-35=2y
y=72.5 or 73
srry I can’t help with question 2. I don’t know how
What is sec 0 when cot 0 = -4/2?
Answer:
[tex]sec 0=\frac{\sqrt{66} }{8}[/tex]
Step-by-step explanation:
[tex]Cot0=-4\sqrt{2}[/tex]
[tex]sec0=\frac{\sqrt{33} }{4\sqrt{2} }[/tex]
[tex]=\frac{\sqrt{33} }{4\sqrt{4} } *\frac{4\sqrt{2} }{4\sqrt{2} }[/tex]
[tex]=\frac{4\sqrt{66} }{32}[/tex]
[tex]=\frac{\sqrt{66} }{8}[/tex]
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hope it helps...
have a great day!!
How would you write the equation with a slope of 2/3 and a y-intercept of -3 in slope- intercept form
y=2/3x-2
Explanation:
The equation of a line can be written as y=mx+c
m=slope and c = y-intercept
The point at the x−intercept has coordinates (-3,0)
In y=mx+c
0=2/3(3)+c
0=2+c
-2=c
The equation is y=2/3x-2
Answer:
[tex] y = \frac{2}{3} x - 3[/tex]
Step-by-step explanation:
Slope (m) = 2/3
y-intercept (b) = - 3
Equation of line in slope intercept form is given as:
[tex] y = mx + b[/tex]
Plug the values of m and b in the above equation, we find:
[tex]y = \frac{2}{3} x + ( - 3) \\ \\ y = \frac{2}{3} x - 3[/tex]
IF A FUNCTION f(x) is defined AS 5x^2-3x+3, what is the expression for
Answer: C. 10x-3
Step-by-step explanation: I got this question correct on Edmentum.
The value of the expression will be 10x – 3. Then the correct option is C.
What is the limit?The value that approaches the output for the given input value. Limits are a very important tool in calculus.
The function is defined as,
f(x) = 5x² – 3x + 2
Then the value of the expression will be
[tex]\rightarrow \displaystyle \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}[/tex]
Substitute the value of the function, then the value of the expression will be
[tex]\rightarrow \displaystyle \lim_{h \to 0} \dfrac{5(x+h)^2 - 3(x + h) + 3- 5x^2 + 3x - 3}{h}\\\\\\\rightarrow \displaystyle \lim_{h \to 0} \dfrac{5x^2 + 5h^2 + 10xh - 3x - 3h + 3- 5x^2 + 3x - 3}{h}\\\\\\\rightarrow \displaystyle \lim_{h \to 0} \dfrac{ 5h^2 + 10xh - 3h }{h}\\[/tex]
Simplify the equation further, then we have
[tex]\rightarrow \displaystyle \lim_{h \to 0} 5h + 10x - 3 \\[/tex]
Substitute the value of the h = 0, then the value of the expression will be
⇒ 5(0) + 10x – 3
⇒ 10x – 3
Then the correct option is C.
More about the limit link is given below.
https://brainly.com/question/8533149
#SPJ2
Can someone help me with this question plz show work.
Answer:
d
Step-by-step explanation:
V=whl=3·4·6=72
D. 6*4*6≠72
Answer:
D 6x6x4
Step-by-step explanation:
the dimensions are 3x6x4 so 6x6x4 is not the volume of this rectangular prism
1. You are rolling a pair of dice. What's the probability of getting different numbers on both dice?
Answer:
5/6Step-by-step explanation:
Total outcomes:
6*6 = 36Outcomes with same numbers on both dice:
6Outcomes with different numbers on both dice:
36 - 6 = 30Probability of different numbers on both dice:
30/36 = 5/6(MATH) (6) ((PHOTO))
label is m
Multiply the length by the height:
6.5 x 2 = 13
The width is the volume divided by 13
Width = 52/13 = 4 m
Abigail ordered a 32 oz steak that cost $60.
(cost to weight)
Find the value of x. help please if you understand
In order to solve for the variable in the equation 2 (x + 3) + 5 x = 3 (2 x minus 1), Jaleesa begins by applying the distributive property, then combines like terms. Which equation is the result of these steps?
7 x + 6 = 6 x minus 3
2 x + 6 + 5 x = 6 x minus 3
2 x + 3 + 5 x = 6 x minus 1
7 x + 3 = 6 x minus 1
Answer: 7 x + 6 = 6 x minus 3
Step-by-step explanation:
2 (x + 3) + 5 x = 3 (2 x minus 1)Now you distribute.2(x) + 2(3) = 2x+6And 3(2x) minus 3(1) = 6x minus 32x+6+5x = 6x minus 3Then combine like terms2x +5x=7x and there are no other like terms on either side of the equation.7x+6= 6x minus 3Answer:7x+6=6x-3
Step-by-step explanation:
What is factor for 7x^2-21-280
How many faces does a triangular pyramid have?
A. 3
B. 6
C. 4
D. 5
[tex]\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}[/tex]
C. 4.
thanks hope it helpsProduct of ²/₇ with the reciprocal of ⁽⁻³⁾/₈ is
Answer:
Step-by-step explanation:
Reciprocal of (-3)/8 = -8/3
[tex]\frac{2}{7}*\frac{-8}{3}=\frac{2*(-8)}{7*3}=\frac{-16}{21}[/tex]
y = x2 – 3x + 2
use the discriminant to determine the number of solutions
Answer:
2 real solutions
Step-by-step explanation:
The formula for determining the discriminant is b² - 4ac.
So, let's identify our variables.
a = 1
b = 3
c = 2
Now, we can plug in our values.
3² - 4(1)(2)
9 - 8
1
1 is the discriminant of this function, and since 1 is positive, this indicates that there are two distinct real number solutions.
Plz help this is due today i would have done it myself but i totally forgot about these so PLZ HELP AND NO LINKS AND NO GROSS PICTURES OR I REPORT.
Answer:
Answer B will be the best answer for your question.
Step-by-step explanation:
Polygons usually have straight sides, but this one does not.
What is the theoretical probability that the spinner below will land on 6 if someone spins it 48 times?
Answer:
1/4 or 12*
Step-by-step explanation:
There are 8 possibilities. 2 of them are 6.
2/8=1/4
1/4 of 48 is 12
*The theoretical probability doesn’t change no matter how many times you spin the spinner. It will always be 1/4. (Or 0.25, or 25%). That could be what they’re asking. If you spun it 48 times, it would probably land on a six 12 times. That could also be what they’re asking for. 12:48 = 1:4.
Choose the sentence that is out of sequence.
Mary Jo began reading The Alphabet Book.
Mother put Jimmy to bed.
Jimmy helped read.
Jimmy fell asleep.
Answer:
C.
Step-by-step explanation:
Which expressions are equivalent to 3 1/4 - (- 5/8)?
Answer:
3.875
Step-by-step explanation:
A farmer wants to know the effect of using various amounts of fertilizer in relation to the yield of his crops. Be subdivided a portion of his land into 10 separate but essentially equal plots. He divided the land so that all of the plots had equal exposure to sun, rain, and other environmental conditions. He randomly selected 2 of the 10 plots and spread 2 pounds of fertilizer over each of them. Then he randomly selected 2 of the remaining plots and spread 3 pounds of fertilizer over each of them. He continued with the last sets of plots in the same manner, spreading 4, then 5, then 6 pounds of fertilizer over each of them. Below is a computer output for linear regression of amount of fertilizer versus yield for the 10 plots of land.
Predictor Coef SE Coef T P
Constant 10.100 0.7973 12.67 0.000
Fertiz 1.150 0.1879 6.12 0.000
Required:
What is the equation of the least squares regression line from this sample?
Answer:
The equation of line is
[tex]\text{yield}=1.15\times \text{fertilizer}+10.1[/tex]
Step-by-step explanation:
The general equation of line is given as
[tex]y=mx+b[/tex]
where
y is the dependent variable which is yield in this case.
x is the independent variable which is fertilizer in this case
m is the coefficient of the fertilizer whose value is 1.150 from the given values.
b is the constant whole value is 10.100 from the given values.
Thus the equation becomes.
[tex]\text{yield}=1.15\times \text{fertilizer}+10.1[/tex]
work out the value of (6-2.5)( 8+4)
Answer:
42
Step-by-step explanation:
Uh, I'm guessing what is being asked here is to solve, so, time to distribute.
(6 - 2.5)(8 + 4)
48 + 24 - 20 - 10
42
Plz need helppp Quick !!!!!!!
Step-by-step explanation:
A. 1 cup of blue rate for 3/5 cup of red paint
B. 1 cup of flour for 2.5 muffins
C. r = d/t = 420 miles/7 hours = 60 miles per hour.
D. 48/3 = $16 for every hour
E. $15/6 = $2.5 for every hot dog
multiplying and simplify radicals!
if u get it right I’ll give brainliest (show work pls!!!)
Answer: 8
Explanation: To multiply two square roots together, simply multiply the numbers inside the square roots together to get [tex]\sqrt{64}[/tex] which is 8.
Notice that when you multiply a square root times itself, the radical disappears, and you're left with the number inside the original square root.
GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)
Answer:
.764
Step-by-step explanation:
do it on a calculator (TI84)
Answer:
45.6°
Step-by-step explanation:
take the inverse cosine of 7/10: [tex]cos^{-1}(\frac{7}{10})[/tex]
plug it into a graphing calc and you get ≈ 45.573°, they want 1 decimal place so it would be ≈ 45.6°
A middle school has 220 students in each grade 6,7,8.The librarian wants to know which books are the most popular among the students in her school.
Answer:
?
Step-by-step explanation:
the choices, the question?
Type your answer and describe how
you found the answer
ROSS is a museum tour
guide at the Art Museum.
He charges $35 per person
for a 1 hour tour. He
typically has 54 people on
tours during the week. His
expenses for the week are
approximately
$108.63.
What is the amount of
profit that Ross will make?
Answer:
Ross's profit it 1,781.37
Step-by-step explanation:
$35 per person and 54 people= 35x54=1890
Profit= the amount of money he makes after his expenses.
1890-108.63=1781.37
what is the value of the expression below? (64^3)^1/6
Answer:
(64^3)^(1/6)
=(64)^(3×1/6)
=(64)^(1/2)
=(8^2)^(1/2)
=(8)^(2×1/2)
=8^1
=8
8 is the correct answer of your question...
Answer:
8
Step-by-step explanation:
Remember the phrase "power to a power means to multiply the exponents"
That is, if you have a number (call it x) raised to a power (call it b), and that whole expression is raised to a power (call it c), it's the same as that number x raised to the power of the product of those two powers.
[tex](x^a)^b = x^a^b[/tex]
Here's an example showing to give some intuition behind this (and a way to derive the above formula if you forget it):
[tex]x^3 = x*x*x\\(x^3)^2 = (x*x*x)^2 = x*x*x*x*x*x = x^6[/tex]
Or more simply,
[tex](x^3)^2 = x^(^3^*^2^) = x^6[/tex]
So in this case:
[tex](64^3)^\frac{1}{6} = 64^(^3^*^\frac{1}{6}^) = 64^\frac{1}{2} = 8[/tex] (remember a number raised the to the power of 1/2 is the square root of the number; in this case, the square root of 64 is 8)
what is the following product?
square root of 30 times the square root of 10
Step-by-step explanation:
That 'd be the square root of 300, which is equivalent to 10sqrt(3).
If the given figure is rotated 180° around the origin, what are the new coordinates of point Z?
please I really need help with this.
Answer:
New coordinates of the point Z are (-6, 9)
Step-by-step explanation:
If a point (x, y) is rotated 180° about the origin, coordinates of the image point is given by the rule,
(x, y) → (-x, -y)
Coordinates of the vertex Z → (6, -9)
Following the same rule,
Z(6, -9) → Z'(-6, 9)
Therefore, coordinates of the new (image) point will be (-6, 9).
1. Force is a push or a
upon an object
A heat
C. pull
B. motion
D. transfer
2 Which is needed to make an object move?
A density
C. porous
B. force
D. non-porous
Answer:
1. C
2.B
Step-by-step explanation:
Force is a push or a pull.. can be a twist too
to make an object move you have to apply force by pushing of pulling the object.
