Answers
Answer: 52
Step-by-step explanation:
11×4=44+8=52
Answer:
I'm pretty sure its 4.727
Related Questions
Which shows the use of the associative and commutative properties to make simplifying 3.2 + 20 – 3+ 4.8 + 19 easier?
Answers
Answer:
B
Step-by-step explanation:
(3.2+4.8)+[20+19+(-4)]
8. +. 47. -4
=43
When you graph a system of equations what are the three possible outcomes?
Answers
Answer:
i think its a beaner
Step-by-step explanation:
Which equation could generate the curve in a graph below?
Answers
can anyone please help. this is my last question!!!!
Answers
9514 1404 393
Answer:
x = 3.6
Step-by-step explanation:
The angle bisector divides the triangle proportionally.
The base segment to the right of the bisector is 6-x, so we can write the proportion ...
x/6 = (6-x)/4
Multiplying by 12, we get ...
2x = 3(6 -x)
5x = 18 . . . . . add 3x
x = 18/5 . . . . divide by 5
x = 3.6
_____
Alternate solution
Since the base of the triangle is given as a left-part and a sum-of-both-parts, we can write the proportion the same way:
left-part / sum-of-both-parts = x/6 = 6/(6+4)
Then the solution is x = 6(6/10) = 36/10 = 3.6.
Doing it this way avoids having x on both sides of the equation, so makes solving the equation be "one step."
The portion of the parabola y²=4ax above the x-axis, where is form 0 to h is revolved about the x-axis. Show that the surface area generated is
A=8/3π√a[(h+a)³/²-a³/2]
Use the result to find the value of h if the parabola y²=36x when revolved about the x-axis is to have surface area 1000.
Answers
Answer:
See below for Part A.
Part B)
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
Step-by-step explanation:
Part A)
The parabola given by the equation:
[tex]y^2=4ax[/tex]
From 0 to h is revolved about the x-axis.
We can take the principal square root of both sides to acquire our function:
[tex]y=f(x)=\sqrt{4ax}[/tex]
Please refer to the attachment below for the sketch.
The area of a surface of revolution is given by:
[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]
Where r(x) is the distance between f and the axis of revolution.
From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:
[tex]r(x)=y(x)=\sqrt{4ax}[/tex]
Now, we will need to find f’(x). We know that:
[tex]f(x)=\sqrt{4ax}[/tex]
Then by the chain rule, f’(x) is:
[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]
For our limits of integration, we are going from 0 to h.
Hence, our integral becomes:
[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]
Combine roots;
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]
Integrate. We can consider using u-substitution. We will let:
[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]
We also need to change our limits of integration. So:
[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]
Hence, our new integral is:
[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]
Simplify and integrate:
[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
FTC:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]
Simplify each term. For the first term, we have:
[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]
We can factor out the 4a:
[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
For the second term, we have:
[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =(2a)^3[/tex]
Hence:
[tex]\displaystyle =8a^3[/tex]
Thus, our equation becomes:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]
We can factor out an 8a^(3/2). Hence:
[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Hence, we have verified the surface area generated by the function.
Part B)
We have:
[tex]y^2=36x[/tex]
We can rewrite this as:
[tex]y^2=4(9)x[/tex]
Hence, a=9.
The surface area is 1000. So, S=1000.
Therefore, with our equation:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
We can write:
[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]
Solve for h. Simplify:
[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]
Divide both sides by 8π:
[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]
Isolate term:
[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]
Raise both sides to 2/3:
[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]
Hence, the value of h is:
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
You seem to have left out that 0 ≤ x ≤ h.
From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is
[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]
We have
y(x) = 2√(ax) → y'(x) = 2 • a/(2√(ax)) = √(a/x)
so the integral is
[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]
[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]
[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]
[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]
Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :
[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]
[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]
[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]
[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]
[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]
Peter and Judy together earn $5060 per month. Their mortgage payment is $1265
pr month. What percentage of their household income goes toward paying the
mortgage?
Answers
Answer:
25 percent
Step-by-step explanation:
Please help! I need help on this ! I will give brainliest!
Find the equation of a line that is parallel to the line x = 12 and contains the point (-6,4).
The equation of the parallel line is . (Type an equation.)
Answers
Answer:
x = -6 and x = 12 are parallel
Step-by-step explanation:
they are both vertical lines, one crosses the x-axis at -6, the other at 12
Consider the line y=5x-3.
Find the equation of the line that is parallel to this line and passes through the point (2, -5).
Find the equation of the line that is perpendicular to this line and passes through the point (2, -5).
Answers
Answer:
y=5x-15, y=-1/5x-23/5
Step-by-step explanation:
Parallel lines have the same slope, so we know the line that is parallel to y=5x-3 must have slope 5.
We now have y=5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=5x+b
-5=5(2)+b
-5=10+b
b=-15
So the equation of the parallel line is y=5x-15.
Perpendicular lines must have slopes that multiply to -1, so we know the line perpendicular to y=5x-3 must have slope -1/5.
We now have y=-1/5x+b. We are given the point (2, -5) so substitute the x and y coordinates into the equation.
y=-1/5x+b
-5=-1/5(2)+b
-5=-2/5+b
b=-23/5
So the equation of the perpendicular line is y=-1/5x-23/5.
Jada has read 3/5 of a book. She read 75 pages so far. How many pages are in the whole book
Answers
Step-by-step explanation:
3/5 of the book = 75 pages
5/5 of the book = 75 * (5/3) = 125 pages
Hence there are 125 pages in the whole book.
Answer:
Concept: Data Analysis
Jada has read 60% of the book So 60% of the book is 75 pages We want to find the whole count of pages An easy way to do this is to see that for every 20% you have 15 pages You need 40% So its 30 pages So 75+30= 105 pagesPLSSSSSS I NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Simplify the Expression:
[tex]\sqrt{9a^{2} }[/tex], if a<0
Answers
[tex]\sqrt{9a^{2}}=\sqrt{9}\sqrt{a^{2}}=3|a|[/tex]
As [tex]a < 0[/tex], [tex]|a|=-a[/tex], so [tex]3|a|=\boxed{-3a}[/tex]
Investors buy a studio apartment for $140,000. Of this amount, they have a down payment of
$42,000. Their down payment is what percent of the purchase price? What percent of the purchase
price would a $49,000 down payment be?
Their down payment is % of the purchase price.
Answers
Answer:
their down payment is 30%
Step-by-step explanation:
Answer:
Step-by-step explanation:
if the price of the apartment is 140,000 dollars
lets find out how much is 1%
140,000/100=1400
42,000/1400=30
42,000 is 30% of the apt price
49,000/1400=35
49,000 is 35% of the apt price
hellllllllllllllllp points if you answeer correctly
Answers
Answer:
the answer will be [-3/4,1/2]
Step-by-step explanation:
A certain radioactive isotope has a half-life of 50 years. A scientist determines that there are 200 grams of the radioactive material present today. How
Much of the isotope was present 200 years ago?
Answers
im guessing 800 50X4 = 200 and 200X4 = 800
i never learned this but i hope its correct.
The graphs below have the same shape. What is the equation of the red
graph?
Answers
one way to tell this is correct is the y-intercept is at positive 4
Answer:
C. F(x) = x^2 + 4
Step-by-step explanation:
Took the test
f(x) = x2. What is g(x)?
Answers
1/4 * 2^2 = 1/4 * 4 = 1
Point (2, 1)
You run 6 miles in one hour and 24 miles in four hours.
a. 6 miles
per hour
c. 4 hours
b. 4 miles per hour
d. 6 miles
Answers
Answer:b
Step-by-step explanation:
backpacks originally cost $24 but if 40% back to school sale is going on determine the sale price of the backpack.
I need help right now
Really Important!!!!!!!
Answers
Answer: The price is now 14.40
Step-by-step explanation: The difference is 9.60
A 4 inch by 6 inch picture is placed in a gram that creates a uniform border of x inches around the picture
Answers
Answer:
1.5 inches.
Step-by-step explanation:
A picture measuring 4 inches by 6 inches is placed inside a frame which has equal width around the entire picture.
The area of the frame and the picture is 63 square inches.
The mean running time of a certain variety of nickel-cadmium rechargeable flashlight battery is known to be normally distributed with a mean of 8.5. A change in production method for this battery has been proposed, and a simple random sample of 64 batteries produced by the new method has mean running time of 8.72 hours. Assume the population is normally distributed with a standard deviation of 0.55 hour as known and remains unchanged, test a claim that the new production method improving the battery mean running time using 0.05 significance level.
Answers
Answer:
answer is a
Step-by-step explanation:
Drag the missing word into place
My parents put
panels on our roof to harvest the
sun's energy
solar
geothermal
chemical
Answers
Answer:
Solar
Step-by-step explanation:
It would be Solar because the energy from the sun is called solar energy. Also, solar panels pick up the sun's energy, and harvests it.
Solve for n.
below
.....................
Answers
-n = -12
Divide by -1
Solution: n = 12
Answer:
n = 12
I hope this helps!
What equation is parallel to
y= - 1\4x + 5 and passes through (2,-3)
QUICK
Answers
Given:
The equation of parallel line is [tex]y=-\dfrac{1}{4}x+5[/tex].
Required line passes through (2,-3).
To find:
The equation of line.
Solution:
We have,
[tex]y=-\dfrac{1}{4}x+5[/tex]
On comparing this equation with [tex]y=mx+b[/tex], where m is slope, we get
[tex]m=-\dfrac{1}{4}[/tex]
Slope of two parallel lines are always same. So, slope of required line is [tex]m=-\dfrac{1}{4}[/tex].
The required line passes through the point (2,-3) having slope [tex]m=-\dfrac{1}{4}[/tex], so the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-3)=-\dfrac{1}{4}(x-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)-\dfrac{1}{4}(-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)+\dfrac{1}{2}[/tex]
Subtracting 3 from both sides, we get
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1}{2}-3[/tex]
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1-6}{2}[/tex]
[tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex]
Therefore, the equation of required line is [tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex].
Suppose you deposit $2,500 in a savings account that pays you 5% interest per year.
a. How many years will it take for you to double your money?
b. How many years will it take for your account to reach $8,000?
Answers
Answer:A=4 Years B=6 years
Step-by-step explanation:
!!! time sensitive please answer !!!
consider the sequence below. 3, 1, 1/3, 1/9
select the explicit function which defines the sequence
A. f(n) = 1/3 • 2^(n-1)
B. f(n) = 2 • (1/3)^(n-1)
C. f(n) = 3 • (1/3)^(n-1)
D. f(n) = 1/3 • 3^(n-1)
Answers
Which represents the equation of the roll line?
Answers
Answer:
A) y=3x-4
Step-by-step explanation:
Mrs. Matthews wrote three math expressions on the board.
She asked her students which expression would result in a product greater than 7.
Enter the number of the expression that Mrs. Matthews's students should have chosen.
Expression
will result in a product greater than 7.
Answers
Answer:
expression 3
because expression 1 = 1
and expression 2 = 7
A ps4 uses uses 8.8 watts when on stand by mode. If electricty in your area costs 0.10$ kwh, how much would this cost?
Answers
Answer0.88:
Step-by-step explanation: because for every watt 10 cents or .10 is being used so since there is 8.8 watts it would be a total of 0.88 in your area
Help me find the radius please
Answers
Answer:
The radius is 2.46686837338 or simplified: 2.5.
Step-by-step explanation:
A = 60 so it would be √60/3.14 =2.46686837338
I hope this helps and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
6a-2z
Please help me
Answers
Answer:
2(3a-z)
cannot be further simplified
Step-by-step explanation:
What do you divide by 90 to get 30?
Answers
Answer:
3
Step-by-step explanation:
3 times 30 = 90 then divide 90 and 30 you get 3