Answers
Answer:
B.) Reflection over y=-3
Step-by-step explanation:
Related Questions
Solve for y given the lines are parallel
Answers
Answer:
I believe the y is parallel :)))))))))
Answer:
35 degrees
Step-by-step explanation:
70 divided by 2 is 35.
And both sides are equal to each other bc the lines are parallel.
If you have five red balls and five blue balls in a jar what’s the probability of the first ball being red?
Answers
Answer:
red balls = 5
blue balls = 5
total balls = 5 blue+5 red
= 10
[tex]p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls} [/tex]
[tex]p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2} [/tex]
Answer:
Step-by-step explanation:
Total number of red balls = 5
Total number of blue balls = 5
Total number of balls in jar = 5 + 5
= 10
Probability of the first ball being red = total number of the red ball/total number of balls in the jar
= [tex]\frac{5}{10}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, the probability of the first ball being red = [tex]\frac{1}{2}[/tex], 50% or 0.5 (in any way you are instructed to write it in)
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]
PlEASE HELP ILL GIVE OUT BRAINLEIST
Answers
HELP PLS!!
Provide the length of x
Answers
Answer:
10
Step-by-step explanation:
the mid-segment, 5, is parallel to the base of the triangle and the side that the mid-segment is parallel to is always double the length of the mid-segment, so the base of the base is 10. this triangle is an equilateral triangle so the side, x, is also 10.
Bryson can travel 28 1/4 miles in 1/2 hour. What is his average speed in miles per hour?
Answers
Answer:
56 if rounding but 56.50 if not
Step-by-step explanation:
rate
The population of Garden City in 1995 was 2,400. In 200, the population was 4,000. Write a linear equation in slope-intercept form that represents this data.
Answers
Answer:
[tex]y = 320x +2080[/tex]
Step-by-step explanation:
Given
Population in 1995 = 2400
Population in 2000 = 4000
Required
Determine the linear equation
Let the years be represented with x.
In 1995, x = 1 i.e. the first year
In 2000, x = 6
Let y represents the population
When x = 1; y = 2400
When x = 6; y = 4000
First, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4000 - 2400}{6 - 1}[/tex]
[tex]m = \frac{1600}{5}[/tex]
[tex]m = 320[/tex]
Next, we calculate the line equation as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 2400 = 320(x - 1)[/tex]
[tex]y - 2400 = 320x - 320[/tex]
[tex]y = 320x - 320 + 2400[/tex]
[tex]y = 320x +2080[/tex]
Use special right triangle ratios to find the length of the hypotenuse. Right Triangle Trig.
Answers
Answer:
11 sqrt(2)
Step-by-step explanation:
We know that in a 45 45 90 triangle, the lengths of the sides are x, x ,x sqrt(2)
the length of x is 11
so the lengths of the sides are 11, 11, 11 sqrt(2)
The hypotenuse is 11 sqrt(2)
Please help
A town has a population of 14000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 41500?
Answers
Answer:
65.9
Step-by-step explanation:
10 more than a number w is -2.6
Answers
Answer:
10 + w = -2.6
Step-by-step explanation:
What’s the answer to this radical function
Answers
Step-by-step explanation:
We have,
[tex]f(x) = - 2 \sqrt[3]{x + 7} [/tex]
Taking limit,
[tex] \lim _{x \rarr \infty } f(x) \\ = \lim _{x \rarr \infty } - 2 \sqrt[3]{x + 7} [/tex]
If x approaches to positive infinity,
this implies f(x) approaches to negative infinity
if anyone knows the answer please help
Answers
Answer: B
Step-by-step explanation:
1/9(3)^x
(3)^(5) = 243
243(1/9) = 27
Hope this helps :)
please help me and my sister! Were a bit stuck!
Answers
Ok...
what exactly do you need help with?
Answer:
help with what lol
Step-by-step explanation:
When a gas is kept at a constant temperature and pressure on it changes, its volume changes according to the following formula, known as Boyle’s law
where P1 and V1 are the pressure (in atm) and the volume (in litres) at the beginning, and P2 and V2 are the pressure and the volume at the end. Find the final pressure P2 if V1 = 1.5 litres, P1 = 4.5 atm and V2 = 3.5 litres. Round to the nearest tenth of a atm.
Answers
Answer: Approximately 1.9 atm
============================================
Work Shown:
[tex]P_1*V_1 = P_2*V_2 \ \text{ ... Boyle's Law}\\\\4.5*1.5 = P_2*3.5\\\\6.75 = P_2*3.5\\\\P_2*3.5 = 6.75\\\\P_2 = \frac{6.75}{3.5}\\\\P_2 \approx 1.92857142857142\\\\P_2 \approx 1.9\\\\[/tex]
If the volume is 3.5 liters, then the pressure is approximately 1.9 atm.
Note the increase in volume leads to the reduction of pressure, and vice versa. The two variables have an inverse relationship.
-----------
As a check,
[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.9*3.5\\\\6.75 \approx 6.65\\\\[/tex]
We don't get the exact thing on both sides, but the two sides are close enough. We have rounding error due to P2 being not exact.
A more accurate check could be
[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.92857*3.5\\\\6.75 \approx 6.749995\\\\[/tex]
which has the two sides much closer to one another. This helps us verify the answer.
How do you work this problem? 10x2 +25x
Answers
Answer:
x=-5/2,0
Step-by-step explanation:
It is solved by first factorizing it
10x²+25x=5x(2x+5)=0
Finding the zeros
5x=0x=0/5=0
2x+5=0
x=-5/2
Therefore x is -5/2 or 0
Is this a function???
Answers
Answer:
pfft no lol
Step-by-step explanation:
yeah no
have a good day! :)
plz give me brainliest
Answer:
yes
Step-by-step explanation:
i think,because it goes past the center it all
Find the quotient for 3/2 divided by 3/5
Answers
Answer:
2.5
Step-by-step explanation:
Answer:
5/2
Step-by-step explanation:
To divide fractions, you flip the second fractions and change it to multiplication.
(3/2) / (3/5) =
(3/2) x (5/3)
To multiply them, you just multiply their numerators together to get the new numerator and multiply the denominators together to get the new denominator.
(3/2) x (5/3) =
(3 x 5) / (2 x 3) =
15/6
This can be reduced to:
5/2
How would I write f(x) = -4(x-2)+ 7 in standard form
Answers
Answer:
The standard form of the given equation is f(x) = 0x²-4x+15=0
Step-by-step explanation:
The standard form is ax²+bx+c=0
Given f(x) = -4(x-2)+ 7
we can write the standard form
= 0x² -4(x-2)+7 =0
⇒ 0x² -4x +8 +7 =0
⇒ 0x² -4x + 15 =0
now comparing the standard form ax²+bx+c=0
a = 0 , b= -4 and c =15
1. Assume that men’s weights are normally distributed with a mean given by = 172lb and a standard deviation given by =29lb. Using the Central Limit Theorem to solve the following exercises(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.
Answers
Answer:
1) 0.99348
2) 0.55668
Step-by-step explanation:
Assume that men’s weights are normally distributed with a mean given by = 172lb and a standard deviation given by =29lb. Using the Central Limit Theorem to solve the following exercises
When given a random number of samples, we use the z score formula:
z-score is z = (x-μ)/σ/√n where
x is the raw score
μ is the population mean
σ is the population standard deviation.
(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.
For x > 160 lb
z = 160 - 172/29/√36
z = 160 - 172/29/6
z = -2.48276
Probability value from Z-Table:
P(x<160) = 0.0065185
P(x>160) = 1 - P(x<160) = 0.99348
(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.
For x = 170 lb
z = 170 - 172/29/√81
z = 170 - 172/29/9
z = -0.62069
Probability value from Z-Table:
P(x = 170) = 0.2674
For x = 175 lb
z = 175 - 172/29/√36
z = 175- 172/29/6
z = 0.93103
Probability value from Z-Table:
P(x = 175) = 0.82408
The probability that they have a mean weight between 170lb and 175lb is calculated as:
P(x = 175) - P(x = 170)
0.82408 - 0.2674
= 0.55668
Prove that for any natural value of n the value of the expression (n+2)^2-(n-2)^2 is a multiple of 8.
Answers
Answer:
We have the expression:
(n + 2)^2 - (n - 2)^2
Let´s break the parentheses:
(n + 2)^2 = n^2 + 4*n + 4
(n - 2)^2 = n^2 - 4n + 4
Then:
(n + 2)^2 - (n - 2)^2 = (n^2 + 4*n + 4) - (n^2 - 4n + 4) =
= (n^2 - n^2) + (4 - 4) + (4n - (-4n)) = 4n - (-4n) = 8*n
Then for any natural value of n, 8*n will be a multiple of 8.
y = 230x + 100
Is this proportional or non proportional?
Answers
Proportional equations are of the form y = kx, for some fixed constant k. The k value is the constant of proportionality.
The +100 at the end is why we don't have a proportional equation.
Visually all proportional equations go through the origin, meaning the lines have y intercept of 0. For y = 230x+100, the y intercept is 100.
Which describes the missing number plotted on the number line?
A. the opposite of -4
B. the opposite of 4
C. the absolute value of -4
D. the absolute value of 4
Answers
rewrite using a single positive exponent 5^6/5^4
Answers
Answer:
5²Step-by-step explanation:
We can divide exponents by subtract 4 from 6. So, now we have 5^2 or 25.
The other way to solve to check our answer is to do the math.
5^6 = 15625
5^4 = 625
15625/625 = 25
So, we know we have the correct answer.
After the movie premiere 99 out of 130 people surveyed said they liked the movie.
What is the experimental probability that the next person surveyed will say he or she liked the movie?
What is the experimental probability that the next person surveyed will say he or she did not like the movie?
Answers
Answer:
99 over 130 multiplied by 100 over 1
which statement is true regarding the functions on the graph?
Answers
Answer:
f(3)=g(3)
Step-by-step explanation:
the only one i see is that
f(3)=g(3)
because the two functions intersect there
that means the two values are the same
please answer these questions
Answers
Step-by-step explanation:
you need to multiple first by second
Consider two bases B = {b1, b2, b3} and C = {c1, c2, c3} for a vector space V such that
b1 = c1 + 3c3, b2 = c1 + 4c2 - c3, and b3 = 5c1 - c2. Suppose vector x = b1 + 6b2 + b3. That is,
suppose space left square bracket bold italic x right square bracket subscript B space equals open square brackets table row 1 row 6 row 1 end table close square brackets . Find space left square bracket bold italic x right square bracket subscript B space, the coordinates of the vector x in basis C.
Answers
Helppp pleaseee, abc= dce. If ac=5 and bc=7 cd=?
Answers
Answer:
CD = 5
Step-by-step explanation:
Given that ∆ACB is congruent to ∆DCE, it follows that their corresponding angles and corresponding side lengths are congruent to each other. Thus:
AC is congruent to CD,
BC is congruent to EC, and
AB is congruent to DE.
Since AC = 5, therefore CD = 5.
GIVING BRAINLIEST AND STARS
13)
Using a map scale of 1/2 inch = 10 miles, what would be the distance on the map between two cities that are actually 120 miles
apart?
A)
6 inches
B)
8 inches
C)
10 inches
D)
12 inches
Answers
Answer:
A) 6 Inches
Step-by-step explanation:
1/2=10 to find how many inches we need to get 120 miles, you have to find the conversion rate.
Conversion rate is 120 ÷ 10 which equals 12.
Now we multiply the conversion rate (12) times 1/2 to get an answer of 6 inches.
i'd appreciate a brainliest :)
Marlye asked students in her school whether they prefer scary movies or comedies. She found that 35 students prefer scary movies while 65 students prefer comedies. What percent of the students questioned prefer scary movies? 30% 35% 50% 65%
2
SEE ANSWERS
Answers
Answer:
The answer is 35%
Step-by-step explanation:
If we add together 35 and 65 we get 100. This means altogether there are 100 kids in her school. Out of those 100 kids, 35 like scary movies. We can write this as the fraction 35/100. This is equivalent to 0.35 or 35%.
Answer:
35%
Step-by-step explanation:
35+65
= 100
[tex]\frac{35}{100} * 100[/tex]
= 35%