Answer:
the circumfrence is the diameter times pi so if the diameter was 3 you would time that by 3.14 to get the circumfrence hope that helps
Step-by-step explanation:
The circumference of the scaled copy is half the circumference of the original circle.
The area of the scaled circle is half the area of the original circle.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
Let the radius of the circle = r
The circumference of the circle = 2πr
The area of a circle = πr²
Now,
Scale factor = Original circle / Scaled circle
Now,
Scale factor = 2
2 = Circumference of the Original circle / Circumference of the Scaled circle
Circumference of the Scaled circle = (1/2) Circumference of the Original circle
Again,
Scale factor = 2
2 = Area of the Original circle / Area of the Scaled circle
Area of the scaled circle = (1/2) Area of the original circle
Thus,
The circumference of the scaled copy is half the circumference of the original circle.
The area of the scaled circle is half the area of the original circle.
Learn more about scale factors here:
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The difference of 2 numbers is 7. The sum of those numbers is 23. What are the 2 numbers?
Let's write this question as a systems of equations to solve.
x-y=7 (the difference)
x+y=23 (the sum)
Through the process of elimination we get
2x=30
x=15.
With that value of x, we can plug it back into any of the previous equations to get the value of y.
(15)-y=7 (Solve for y)
y=8.
The two numbers are 15 and 8.
The cost of 3 scarves is $26.25. What is the unit price? (cost per scarf)
$8.75 because 26.25 divided by 3 equals $8.75.
hope this helps
A veterinarian prescribes Benadryl for a dog with allergies. The recommended dosage is 3 mg per kg per day to be given in two doses. If your golden retriever weighs 67 lbs., how much Benadryl should he get in each dose? Round to nearest milligram.
Answer:
Each dose should be of 5.05 milligrams.
Step-by-step explanation:
To solve the present problem, it is necessary to first establish the equivalence between pounds and kilograms. Thus, 1 pound is equal to 0.453 kilograms. Therefore, the dog weighs about 30.35 kilograms (67 x 0.453), with which, since 3 milligrams must be applied for each kilogram of the animal's weight, 10.1 milligrams of Benadryl (30.35 / 3) should be applied.
Now, since Benadryl is applied in two doses, each of these doses should be 5.05 milligrams (10.1 / 2).
Joe marked up all the shoes in his store by 15%. If a pair of shoes originally cost $45, what was the price after the markup?
Answer:
The price would be $51.75.
Step-by-step explanation:
Since Joe is marking up by 15%, the price will increase for the pair of shoes. Multiply 45 by 1.15 since you are increasing the price by 15% to get your final answer which is $51.75.
It Snowed 1/2 inch on Saturday and 1 3/5 inches on Sunday. How much did it snow altogether, total?
Answer:
Fraction form: it snowed 2 1/10 inches in total, decimal form: in other words it snowed 2.1 inches.
Step-by-step explanation:
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.
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]
the measure of the angle is..
Answer:
149
Step-by-step explanation:
149 and the angle beside b are supplementary (Let's call it A)
180-149=A=31
180-31=149
149=B
Find the value of the variable that results in congruent triangles
1.
Answer:
x = 26
Step-by-step explanation:
m<B = m<E = (x + 17)°
180 - (25 + 112) = (x + 17) (sum of ∆)
180 - 137 = x + 17
43 = x + 17
Subtract both sides by 17
43 - 17 = x
x = 26
Use special right triangle ratios to find the length of the hypotenuse. Right Triangle Trig.
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)
"Five less than
the quotient of
a number and
3 is -7°
A. 5 - X/3-7
B. -7 +x/3
C. X3 - 5 =-7
D. 5 - 4/2 = -7
0.50(61 + 3s)
Use the Distributive Property to expand the expression.
Answer:
30.5 + 1.5s
Step-by-step explanation:
Identify proportional relationships
Does the following table show a proportional relationship between the variables g and h?
g
3
6
9
9
36
81
Answer:
sure easy man the carrot is blue and green and orange there naswer soled
4,0000000000×10,00000000
Answer:
yes 40
Step-by-step explanation:
she got it correct
HELP PLEASE I GIVE BRAINLIEST
Answer:
30
Step-by-step explanation:
Perimeter of rectangle = 5y - 1 + 4y + 2 + 5y - 1 + 4y + 2
= 18y + 2
18y + 2 = 128
18y = 128 - 2
= 126
y = 126 ÷ 18
y = 7
Length of AD = 4y + 2
= 4(7) + 2
= 28 + 2
= 30
I NEED REAL HELP PLEASEE!!! a store has televisions on sale for 20% off the original price. The original price of a television is 150 before the sale what will be the sale price of the television set
a. 142.50
b.135
c.130
d.127.50
e.120
Answer:
120Step-by-step explanation:
E
Answer:
$120
Step-by-step explanation:
which statement is true regarding the functions on the graph?
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
1 1/6 as an improper fraction
Answer:
The mixed number 1 1/6 converted into an improper fraction is 7/6.
Step-by-step explanation:
The improper fraction representation after converting of 1 1/6 is 7/6 where numerator is 7 and denominator is 6
To convert a mixed number to an improper fraction, we follow these steps:
Multiply the whole number by the denominator of the fraction.
In this case, multiply 1 (the whole number) by 6 (the denominator), which gives 6.
Add the numerator to the result obtained in step 1.
The numerator in this case is 1. Adding 1 to 6 gives 7.
Place the result from step 2 as the numerator of the fraction, and keep the denominator the same.
The denominator remains 6.
Therefore, the improper fraction representation of 1 1/6 is 7/6.
Learn more about converting fractions here:
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Find the value of x → x² = (Q - A)(Q - B)(Q - C) ….. (Q - Z)
Answer:
[tex]\boxed{0}[/tex]
Step-by-step explanation:
x² = (Q - A)(Q - B)(Q - C) ... (Q - Z)
x² = (Q - A)(Q - B)(Q - C) ... (Q - P)(Q - Q)(Q - R) ... (Q - Z)
x² = (Q - A)(Q - B)(Q - C) ... (Q - P)(0)(Q - R) ... (Q - Z)
x² = 0
x = 0
Answer:
t8y8 uv7g7 ug8 ugy ug h 7 v jvu utyc7 . hit u ut taj h
Step-by-step explanation:
fucjvjvi j jvu jvivu igigi ivigi iigihi ivigi igih
In preparation for the school play, the number of adult tickets sold by the ticket office was 5 less than twice the number of children's tickets. They sold 95 adult tickets. Write an equation you can use to find how many children's tickets were sold.
Answer:
3
Step-by-step explanation:
i think 5-2
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.
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]
In the lab, Karen has two solutions that contain alcohol and is mixing them with each other. She uses 3 times as much Solution A as Solution B. Solution A is 10% alcohol and Solution B is 15% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 180 milliliters of pure alcohol?
Answer:
She uses 162 millitiers if Solution B.
Step-by-step explanation:
180 - 10% = 162
Solution A = 18 milliliters
Soultion B = 162 millitiers
write the decimal 2.10 as a percent
Answer:
210%
Step-by-step explanation:
dat was too easy
Answer:
210% or 21% or 2.10%
its all about what 2.10 is out of (example: /1=210% /10= 21% /100=2.1%
edit: if your wondering what the "/" means it means " out of" (example: 1 out of 100 is 1%)
HELPPP I NEED AN ANSWER ASAP
Answer:
2, 4, and 6 (b, d, f)
Step-by-step explanation:
dont really know how to explain
Is this a function???
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
If you rotate figure GTR 270° clockwise about the origin. What will be the coordinates of G’T’R’ (Please Help I need this done in five minutes.)
Answer:
C. G' (4,-7), R' (2,-3), T'(6,-4)
Step-by-step explanation:
Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.
Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
A, 2 5/8 cups
Step-by-step explanation:
Since six dozen brownies is three times as much as two dozen, we can multiply 7/8 cups by 3. 3 x 7/8 = 21/8 If we simplify this fraction, it is 2 5/8. Therefore the answer is A, 2 5/8 cups.
Find the are of the semi circle.Either enter an exact answer in terms of pie or use 3.14 and enter your answer as a decimal.The raduis is 4
...............................
Answer:
What dose this mean
Step-by-step explanation:
Thx for the free points
24 = 3y Solve for y and show work
Answer:
y=8
Step-by-step explanation:
because 3×8 is 24
and 8 would be the missing number
20) Find the length of a side of a square with a
diagonal length of 100 cm.
Answer:
about 7.0710678cm
Step-by-step explanation:
it's a square so the sides are equal.
the diagonal is 100cm
This makes a right triangle with two sides
since the sides are equal, they both are equal to the square root of 50, which is half of 100
the square root of 50 is about 7.0710678cm