Answer:
[tex]y = -x -2[/tex]
Step-by-step explanation:
Slope-Intercept form of the line
Any given line with slope m and y-intercept b can be written as:
y=mx+b
We need to find the equation of a line parallel to
2x + 2y = 6
Dividing by 2:
x + y = 3
Solving for y:
y = -x + 3
Comparing with the slope-intercept form of the line:
m = -1
Parallel lines have the same slope, thus the required line must have a slope m = -1.
Since we have a point through which the line passes, we use the point-slope form:
y - k = m ( x - h )
Where (h,k) is the point.
The required equation of the line is:
y - (-5) = -1 (x - 3)
Operating:
y + 5 = -x + 3
Solving for y:
[tex]\boxed{y = -x -2}[/tex]
Find the volume common to two spheres, each with radius r, if the distance between their centers is r/2. [Hint: It may be helpful to look at the previous question and see how it relates to this one. ] intersectingspheres
Answer:
The volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]
Step-by-step explanation:
Let r be the radius of each sphere
We are given that distance between their centers is [tex]\frac{r}{2}[/tex]
Let [tex](\frac{-r}{4},0)[/tex] be the center of sphere 1 and [tex](\frac{r}{4},0)[/tex]be the center of sphere 2 .
Using the disk points
a=0 and b =[tex]\frac{3r}{4}[/tex]
[tex](x+(\frac{r}{4}))^2+y^2=r^2\\V=2 \int_{0}^{\frac{3r}{4}} \pi y^2 dx\\V=2 \int_{0}^{\frac{3r}{4}} \pi [r^2-(x+(\frac{r}{4}))^2]dx\\V=\frac{27 \pi r^3}{32}[/tex]
Hence the volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]
In attached diagram, we can see 2 circumferences with radius r, and separated centers by r/2.
The solution is:
V = (11/12)×π×r³
Let´s call circumferences 1 and 2, by symmetry, rotating area A will produce a volume V₁ identical a V₂, Obtained by rotating area B ( both around x-axis), then the whole volume V will be:
V = 2× V₁
V₁ = ∫π×y²×dx (1)
Now
( x - r/2)² + y² = r² the equation of circumference 1
y² = r² - ( x - r/2)²
Plugging this value in equation (1)
V₁ = ∫π×[ r² - ( x - r/2)²]×dx with integrations limits 0 ≤ x ≤ r/2
V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx
V₁ = π× [ r²×x - x³/3 + (r/2)²×x - (1/2) ×r×x²] evaluate between 0 and r/2
V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) ×r×x²]
V₁ = π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ - (1/2) ×r×(r/2)²]
V₁ = π× [ (5/8)×r³ - r³/24 - r³/8]
V₁ = π× (11/24)×r³
Then
V = 2× V₁
V = 2×π×11/24)×r³
V = (11/12)×π×r³
Related Link : https://brainly.com/question/14301190
Tim's holds a fishing line at the surface of a lake, and it sinks 10 feet below the surface of the water. Tim then pulls the lure up 4 feet.which of the following statements about this situation are true?select all that apply
Answer:
Where are the answers to choose from?
x/5-g=a isolate x PLS
Which relation is not a function?
Please help it is a quiz and I really need help! 5:06pm est answer as fast as you can!
Answer:
b
Step-by-step explanation:
Why did I get this wrong?
Step-by-step explanation:
12 / x¹⁴ = 12x⁻¹⁴
Integrate using power rule.
-12/13 x⁻¹³
-12 / (13x¹³)
You forgot the negative sign.
What is the volume of a sphere with a radius of 7 centimetres?
Use 3.14 for pi. Round your answer to the nearest hundredth. Use the formula provided.
V=
1077.02 cm3
1436.03 cm3
1975.43 cm3
11,494.04 cm3
Answer:
[tex]V=1436.03 \ cm^3[/tex]
The second choice provides the correct answer.
Step-by-step explanation:
The Volume of a Sphere
The volume of a sphere of radius r is given by:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]
The radius of the sphere is r=7 cm, thus:
[tex]\displaystyle V=\frac{4}{3}\cdot 3.14\cdot 7^3[/tex]
[tex]V=1436.03 \ cm^3[/tex]
Note: We have used an approximated value for pi=3.14.
The volume of the sphere rounded to the nearest hundredth is
[tex]\boxed{V=1436.03 \ cm^3}[/tex]
The second choice provides the correct answer.
-3x/2+4=16
What is x?
Answer:
-8
Step-by-step explanation:
-4 both sides & 16-4 is 12.. -3/2x equals 12 so to solve for x, you would multiply 2 by both sides. You end w -3x equals 24. You then divide -3 both sides and 24/-3 is -8... hopee that helps? :)
49.67 to the nearest ten
answer:
50
explanation:
Please help!
The access code to a houses security system consists of 8 digits. How many different codes are available if each digit can NOT be repeated?
Country A is ten to the third power times greater than Country B. Country A has a population of 230,000,000. What is the population Of Country B. Help Pls
If You Know The Answer Help :)
Answer:
0.3
Step-by-step explanation:
Answer:
3/20
Step-by-step explanation:
1/5=4/20
7/20-4/20=3/20
Hope this helps!
A bride is choosing a dress for her bridesmaids. If there are 4 styles, 7 colors, and 5 fabrics, in how many ways can she select the bridesmaids' dress?
Answer: 60
Step-by-step explanation: multiply 4,7,and 5
She can select the bridesmaids' dress in 140 possible ways.
What is Permutation?Permutation represents each of the several possible ways in which a set or number of things can be ordered or arranged.
Given is a bride who is choosing a dress for her bridesmaids which are available in 4 styles, 7 colors, and 5 fabrics.
Now, for every possible style there exist a dress for that color. So, with 4 styles and 7 colors, the total number of possible dresses will be = 7 x 4 = 28. Now, for these 28 dresses, their are 5 different fabric available, so the total number of possible ways or dresses from which she can select the dress are = 28 x 5 = 140
Therefore, she can select the bridesmaids' dress in 140 possible ways.
To solve more questions on Arrangements and selections, visit the link below-
https://brainly.com/question/16721336
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9x - 4= 2x + 3
-—-——-—-
Answer:
x = 1
Step-by-step explanation:
9x−4=2x+3 Move all terms containing x to the left side of the equation.
7x−4=3 Move all terms not containing x to the right side of the equation.
7x=7 Divide each term by 7 and simplify. x = 1
Write an equation for a line parallel to y = 5x + 1 and passing through the point (3,11)
Answer:
Here's the parallel line: y = 5x - 4
An investment account earns 4% the first year, 5% the second year, and X% the third year. Find X if the three year average interest rate is 10%.
Answer:
The answer is 1 percent because if you add the 5% and 4% you get 9% and all there is left of the average interest 10 and get 1
Step-by-step explanation:
May i please get Brainiest
--0.5x – 3 = 4 anybody know the awnser what does x =
Answer:
- 14
Step-by-step explanation:
Step 1:
- 0.5x - 3 = 4 Equation
Step 2:
- 0.5x = 7 Add 3 on both sides
Step 3:
x = 7 ÷ - 0.5 Divide
Answer:
x = - 14
Hope This Helps :)
what is the area of a rectangles with the side lengths 5 inches and 4/3 inches?
Answer: 20/3 square inches
Step-by-step explanation:
Area = length*width
length = 5 in.
width = 4/3 in.
A = 5 * (4/3) = 20/3 in^2
can you divide 2 by 9 explain your response
Answer: Yes you can but it would be the same as dividing 10 by 3, it would just be a repeating fraction
Answer:
I can’t divide 2 by 9 because the number 9 is greater than 2. In other words, there are no 9s in 2
Step-by-step explanation:
All six digits in the number are even one digit is used twice all other digits are used once the ones digit is 4 times the hundreds digit the tens digit id the difference of the ones digit and hundreds digit the same digit is in the tens place and hundreds thousands place the thousands digit is not zero
Answer:
rffrefr
Step-by-step explanation:
Express as a trinomial.
(x + 1)(3x − 2)
PLEASE HELP :)
Answer:
3x^2+x-2
Step-by-step explanation:
Write out the correct word form of each number.
10) 8,924,600.32
11) 707.91
12) 641,971.44
does 9.03 + 10.71 – 6.8 =13.94
Answer:
No
Step-by-step explanation:
Let's break this down...
9.03+10.71 is 19.74 and subtracted by 6.8 it will be 12.94 not 13.94 so it is not correct
So the answer is No
Hope this helps!
Answer:
No, it is 12.94
Step-by-step explanation:
9.03 + 10.71 = 19.74, 19.74 - 6.8 = 12.94
If f(x) = 7x, which of the following is the inverse of f(x)?
O A. f'(X) = x + 7
B. f1(x) = x - 7
O c. f'(x)
O d. f'(X) = 7x
SUBMIT
Answer:
x/7
Step-by-step explanatio
Please help ASAP
Thank you
if Billy has three and four fifths of cake and Sam eats 2/3 of it how much cake does Billy have left
Answer:
3 and one third
Step-by-step explanation:
(3 1/3)
Please help me answer this
Answer:
the first.option is the right answer
On interval 0 ≤ x < 2π, where are the x-intercepts of y = cos(2x)?
A. pi/2 and 3pi/2
B. 0, pi, and 2pi
C.pi/2, pi, and 3pi/2
D.pi/2, 3pi/4, 5pi/4, and 7pi/4
Answer:
Choice D:
π/2, 3π/4, 5π/4, and 7π/4
Step-by-step explanation:
correct on edg
The solution of the equation y = cos(2x) will be π/4, 3π/2, 5π/4, and 7π/4. Then the correct option is D.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
y = cos(2x)
The x-intercept of the equation in the interval 0 ≤ x < 2π will be given as,
y = 0
cos(2x) = 0
cos 2x = cos (n + 1) π/2
2x = (n + 1)π / 2
x = (n + 1)π / 4
x = π/4, 3π/2, 5π/4, 7π/4
The solution of the equation y = cos(2x) will be π/4, 3π/2, 5π/4, and 7π/4. Then the correct option is D.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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If 120 customers have bought tickets today, how many free tickets has the manager given away
if a coin is flipped 4 times what is the probability of it landing on heads 3 times and tails 1
Answer:
(`1/4)^4
Step-by-step explanation:
Since the probability of landing on a head is theoretically the same as that of landing on tails, and since the four flips are entirely independent of one another, the desired probability is
(1/2)^4 or 1/16
Haper is saving money to buy a new camping tent. Each week he double the amount he saved the previous week. If he saved 1$ the first week how much will he save in 7 weeks
Answer: $49
Step-by-step explanation: if there are 7 days in a week and he is saving for 7 weeks, its 7 x 7= 49
Answer:
64$ if he doinles
Step-by-step explanation:
1,2,4,8,16,32,64