hi
area of circle is π* radius²
as radius is half diameter, and as diameter is 22 , so radius is 22 /2 = 11 cm
so area is 11²π and 11² = 121 then area is 121π
as it is say to use 3.14 for pi , then 121*3.14 = 379.94
but 379.94 is the area of the whole circle , and we only have half.
so : 379.94 / 2 = 189.97
area of semi circle is 189.97
Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = t i t2 j 2 k
The velocity of a particle = i + 2t j
The acceleration of a particle = 2 j
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
Here,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
We have to find, the velocity, acceleration, and speed of a particle with the given position function.
What is Velocity of a particle with the given position function?
The instantaneous velocity v(t) of a particle is the derivative of the position with respect to time. That is, v(t)=dx/dt.
Now,
The position function is, [tex]r (t ) = ti + t^{2} j +2k[/tex]
The velocity of a particle = [tex]\frac{d r(t)}{dt}[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
The acceleration of a particle = [tex]\frac{d^{2} r(t)}{dt^{2} }[/tex]
[tex]r (t ) = ti + t^{2} j +2k[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]\frac{d^{2} r(t)}{dt^{2} }= 2j[/tex]
The speed of a particle = [tex]| \frac{d r(t)}{dt}| = |v(t)|[/tex]
[tex]\frac{d r(t)}{dt} = i + 2t j[/tex]
[tex]|v(t)|=\sqrt{1 + 4t^{2} }[/tex]
Hence, The velocity of a particle = [tex]i + 2t j[/tex]
The acceleration of a particle = [tex]2 j[/tex]
The speed of a particle = [tex]\sqrt{1 + 4t^{2} }[/tex]
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Consider the points p such that the distance from p to a ( 1,5,3) is twice the distance from p to b (6, 2, 2) . show that the set of all such points is a sphere, and find its center and radius
The set of all such points is a sphere center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9
what is the sphere?
sphere, The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.The standard form of the equation of a sphere with center (a ,b ,c) and radius r is
( x -a)² + ( y-b)² + ( z - c)² = r²
We let P = ( x, y,z ) be an arbitrary point which satisfies the given conditions. Then
[tex]\sqrt{(x - 1)^{2} + ( y - 5)^{2} + (z - 3)^{2} } = 2 \sqrt({x - 6)^{2} + ( y - 2 )^{2} +( z - 3)^{2} }[/tex]
Squaring both sides of this equation and simplifying yields
( x - 1)² + ( y - 5)² + ( z -3)² = 4 [ (x - 6)² + ( y- 6 )² + ( z - 3)²
( 3x² - 46x + 143 ) + ( 3y² - 38y + 119 ) + ( 3z² - 18z + 27 ) = 0
Next, we complete the square for each variable to obtain
( x - 23/3)² + ( y - 19/3)² + ( z - 3 )² = 332/9
Thus the set of all such points P forms a sphere, with
center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9
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Which choice is a term in this expression? 3x − 7(x + 4)
The term in the given expression is -3x − 7(x + 4) (A) -3x.
What exactly do we mean by expressions?A finite combination of symbols that is well-formed according to context-dependent rules is referred to as an expression or mathematical expression.A mathematical expression is a phrase that has at least two numbers or variables, at least one mathematical operation, and at least one mathematical operation.Addition, subtraction, multiplication, and division are all considered math operations.The structure of an expression is as follows: An expression is (Number/variable, Math Operator, Number/variable).Term:
Terms are expression parts that are separated by + or - signs.Because it is separated from the rest of the expression by a - sign, -3x is a term.Therefore, the term in the given expression is (A) -3x.
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The correct question is given below:
Which choice is a term in this expression? -3x − 7(x + 4)
A pair of cars, 70 miles apart, begin at the same time to run toward each other. If car A
from city A runs at a rate that is 5 mph faster than car B from city B, and if they meet 2
hours later, how far is the place they meet away from city A?
Answer: car a must be meet to cannot be so your aner is a
Step-by-step explanation:
Irwin has flowering plants in 15% of his garden. Which of the following is equivalent to 15%?
Answer: Im not sure
Step-by-step explanation:
You didnt list the options therefore i cant answer this for you. :I
how can you see immediately that two integers add up to 1?
The numbers have absolute values that differ by 1, and the number with the larger absolute value is positive.
Helpppp...
[tex]{e}^{x} = {2e}^{ - x} [/tex]
Pls gv explaination to the solution
A number is chosen at random from the numbers 1-10. What is the probability of selecting the number 7 or a number less than 4?
Answer:
3/25
Step-by-step explanation:
CH#6 LINES & ANGLES
I. In fig. the values of x and y are equal to:
(a) 130⁰
(b) 150⁰
c) 160⁰
(d) 135⁰
Please help solve this equation. -3(5w-3y-2)
Answer:
-15w+9y+6
Step-by-step explanation:
I think that you are asking to simplify the expression. An equation has an equal sign and I do not see one.
We need to distribute the -3 to everything inside of the parentheses.
A negative times a negative is a positive.
A negative times a positive is a negative.
-3(5w-3y-2)
-3(5w) -3(-3y) -3(-2)
-15w + 9y + 6
Hi!
To simplify this, use the Distributive Property:
[tex]\tt{a(b+c)=ab+ac}[/tex] | Basically, we distribute a so that it gets multiplied by b and c.Now, let's simplify the given expression:
[tex]\dashrightarrow\sf{-3(5w-2y-2)}[/tex]
Like the property said, We should distribute -3 so that it's multiplied by each term:
[tex]\bullet\dashrightarrow\sf{-15w+9y+6}[/tex]
Therefore,
[tex]\bullet\dashrightarrow\stackrel{\heartsuit}{\boxed{\boxed{\boldsymbol{-15w+9y+6}}}}}\dashleftarrow\bullet[/tex]
Good luck.- stargazing :')
PLEASE HELP ME!
WILL GIVE BRAINLIEST!
Please help! Find the value of FG. The drawing is not to scale. EF=11 and EG=21
The value of FG is 32.
The drawing is attached with this.
Given that,
Value of EF = 11
Value of EG = 21
From the above given data we can assume that F and G be the corner points.
E is the point lie between F and G.
We have to find the value of FG. It may be a straight line.
So,
Value of FG = Value of EF + Value of EG
FG = 11 + 21
FG = 32
That is, the value of FG is 32.
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can anyone help me with this question please asap !! thank you in advance !!!!!
Answer:
31/35
Step-by-step explanation:
3/5 + 2/7 = (3 × 7) / (5 × 7) + (2 × 5) / (7 × 5)
= 21/35 + 10/35
= 31/35.
What is the answer to this problem ?
Answer:
11
Step-by-step explanation:
Plug 4 into the x, 6(4) = 24
24 - 13 = 11
2/3 of the students in class are male. If 18 of the students are male, how many students are in the class
Answer:
27 students
Step-by-step explanation:
Split 18 into 2 to find 1/3. 18/2= 9
9= 1/3
18= 2/3
27= 3/3 or 1
Answer:
There are 27 students.
Step-by-step explanation:
Given that,
→ 2/3
→ 18 ÷ 2
→ 9 = 1/3
Now the number of students are,
→ x = (2/3) + (1/3)
→ x = 18 + 9
→ [ x = 27 ]
Hence, there are 27 students.
solve the literal equation for y
4x+1=9+4y show steps please i am confused
The solution to the literal equation is y = x - 2.
What is the solution to inequality?To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.
From the given information:
4x + 1 = 9 + 4y
To solve for y, we have to switch the sides:
9 + 4y = 4x + 1
Subtract 9 from both sides
9 - 9 + 4y = 4x + 1 - 9
4y = 4x - 8
Divide both sides by 4
[tex]\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}[/tex]
y = x - 2
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Three numbers are in the ratio 2:5:7 and their lcm is 490 find the square root of the largest number
Answer:
49
Step-by-step explanation:
The ratio of three numbers = 2:5:7
Then the numbers are 2x,5x and 7x
Given that the LCM of these numbers = 490
LCM of 2x,5x,7x is 2×5×7×x = 70x
Then, we have 70x = 490
x = 7
Hence, the numbers are 14, 35 and 49
Largest number = 49
∴The square root of the largest number = 7
▼
What, approximately, is the percent uncertainty for the measurement given as 1.59 m²?
Answer: The approximately percent uncertainty for the measurement is 0.62%.
Step-by-step explanation:
The given parameters:
Area of the measurement, A = 1.59 m²
The uncertainty in the measurement of the area = ±0.01 m²
The approximately percent uncertainty for the measurement is calculated as follows;
[tex](0.01/1.59)*100[/tex] %
=0.62%
Thus, the approximately percent uncertainty for the measurement is 0.62%.
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Answer: 0.6 percent.
Step-by-step explanation: to find the uncertainty , we will take that absolute uncertainty _0.01 divided by the measurement of 1.59 _ times by a hundred percent and we get 0.6 percent.
Kyrie and Jayla were trying to describe parts
of the expression (5p+ 3)(p+1).
Jayla said, "The entire expression is the
sum of 5 terms."
Kyrie said, "The entire expression is the
product of 4 factors."
Step-by-step explanation:
did you leave something out ?
(5p + 3)(p + 1) = 5p×p + 5p×1 + 3×p + 3×1 =
= 5p² + 5p + 3p + 3 = 5p² + 8p + 3
at no point do we have 5 terms to sum up. but 4 and then finally 3, yes.
but we always have also additions, not only multiplications (products).
so, none of the 2 options is correct.
we could, of course. start with the initial expression, that shows the product of 2 factors and multiply by 1×1
(5p + 3)(p + 1)×1×1
then we have the expression as product of 4 factors.
in the same way we could bump up the sum scenario by adding one or 2 0s : tadah ! sum of 5 terms.
I strongly suspect there is something missing in the problem description.
Answer:
Neither is correct.
Step-by-step explanation:
How to I do part (ii)?
Answer:
Step-by-step explanation:
7(i)
[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=\frac{dx}{dx} *(3x-5)^\frac{5}{3}+x*\frac{d}{dx} \{(3x-5)^\frac{5}{3} \}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=1*(3x-5)^\frac{5}{3} +x*\frac{5}{3}*(3x-5)^{\frac{5}{3} -1}*\frac{d}{dx} \{(3x-5)\}\\\\ \frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +\frac{x*5*(3x-5)^{\frac{2}{3}}*3 }{3} \\\\\frac{d}{dx}\{x*(3x-5)^\frac{5}{3} \}=(3x-5)^\frac{5}{3} +5x*(3x-5)^\frac{2}{3} \\\\[/tex]
[tex]\displaystyle\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3}*((3x-5)^{\frac{5}{3}-\frac{2}{3}} + 5x)\\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5)^\frac{3}{3}+5x) \\\\\frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(3x-5)^\frac{2}{3} *(3x-5+5x)\\\ \frac{d}{dx}\{x*(3x-5)^\frac{2}{3} \}=(8x-5)*(3x-5)^\frac{2}{3}[/tex]
7(ii)
[tex]\int\limits {(x*(3x-5)^\frac{2}{3}) } \, dx \\Let\ \sqrt[3]{3x-5} =u\\Hence,\\(\sqrt[3]{3x-5})^3=u^3\\ 3x-5=u^3\\3x-5+5=u^3+5\\3x=u^3+5\\[/tex]
Divide both parts of the equation by 3:
[tex]\displaystyle\\x=\frac{u^3+5}{3}\\\\dx=\frac{d}{du} \{\frac{u^3+5}{3}\} \\dx=\frac{3u^2}{3} du=\\\\dx=u^2du\\Hence,\\\\\int\limits {\frac{u^3+5}{3}* u^2*u^2} \, du =\\\\\int\limits {\frac{u^3+5}{3} *u^4} \, du =\\\\\int\limits {\frac{u^7+5u^4}{3} } \, du =\\\\\frac{1}{3} \int\limits {u^7} \, du +\frac{1}{3}\int\limits {5u^4} \, dxu =\\\\[/tex]
A plane leaves the airport and travels east for 2.5 hours at a speed of 240 miles per hour. It then travels south for 500 miles. a)Calculate the distance of the plane from the airport. b)Calculate the bearing of the plane from the airport.
a) The distance of the plane from the airport is approximately 781.025 miles.
b) The bearing of the airplane in standard position is approximately 320.194°.
How to calculate the distance and the bearing of the bearing from the airport
Let the location of the airport be the origin and the orthogonal axes are oriented to the east and north, respectively. Beside, let consider that the plane moves at constant speed. a) Thus, the distance of the plane can be found by using the Pythagorean Theorem:
d = √[[(240 mi / h) · (2.5 h)]² + (500 mi)²]
d ≈ 781.025 mi
b) And the bearing in standard position is determined by the following inverse trigonometric function:
θ = tan⁻¹ [(- 500 mi) / [(240 mi / h) · (2.5 h)]]
θ ≈ 320.194°
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A scale that allows one to determine only if there is more, less, or an equal amount of the attribute in comparison to another observation is called a(n) _____ scale.
Ordinal is the answer.
In the given statement is:
A scale that allows one to determine only if there is more, less, or an equal amount of the attribute in comparison to another observation is called a(n) ____ scale.
Ordinal Scale is the 2nd level of measurement that reports the ranking and ordering of the data without actually establishing the degree of variation between them. Ordinal level of measurement is the second of the four measurement scales. "Ordinal" indicates "Order".
Hence, The answer is Ordinal
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Is the relationship between the side length of a square and its area proportional?
The relationship between the length of a side and the area is non proportional.
The answer is non proportional because the side length is x,
so is the other side lengths.
The side lengths are all equal and to find area you do x squared or x times x.
So they are not proportional because there will be different numbers for each.
For example. X= 2, area ( x squared ) is 4.
Hence, The relationship between the length of a side and the area is non proportional.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In a square, we need to find the relationship between the length of a side and the area.
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Please help me with this question I'm so confused
Answer:
x is equal to 15.
Step-by-step explanation:
In this problem, it is said that ΔABC ~ ΔXYZ. This means that the shapes are the same, however they are not the same size. Here the problem is asking for the value of x when the triangle is scaled up.
Look on the triangles for where there are values on both ABC and XYZ. Notice that the hypotenuse for both triangles have a value.
The hypotenuse of triangle XYZ is 10, while the hypotenuse of triangle ABC is 25. Dividing both of those results by 10 results in a 1:2.5 ratio, meaning that the values of triangle ABC are 2.5 times larger than the values of triangle XYZ.
Knowing this, take the value of XZ on triangle XYZ, and multiply it by 2.5 to get the value of AC on triangle ABC, or x.
6 * 2.5 = 15
The value of x is 15.
Answer:
x = 15
Step-by-step explanation:
Since the triangles are similar that means that the sides are proportional. There are a couple of ways to find x. One way is to find the scale factor. We can use the two corresponding sides that we know. 25 and 10 are corresponding sides. They are both the hypotenuse of their triangles or you can say that they are both the side across from the 90 degree angle.
There is some number that I can multiple 10 by to get 25. This is my scale factor. This is how I can find it.
Let s = the scale factor.
10s = 25 Divide both sides of the equation by 10
s = 2.5 This means that each side of the larger triangle is 2.5 times longer than each side of the original triangle.
To find x. Find is corresponding side on the right and take that length and multiple it by 2.5
6 x 2.5 = 15
Another way is to set up a proportion.
[tex]\frac{10}{6}[/tex] = [tex]\frac{25}{x}[/tex] I could cross multiply and solve for x
10x = (6)(25)
10x = 150 Divide both sides by 10
x = 15
Danae is choosing between two jobs. One job pays an annual bonus of $1,500 plus $120 per day workec second job pays an annual bonus of $2,500 plus $110 per day worked. Which equation can be solved to after how many days, d, Danae would make the same amount of money regardless of the job she choose
Answer: 120d + 1,500 = 110d + 2,500
Step-by-step explanation:
Answer:
$1,500 + 120d = $2,500 + 110d
Step-by-step explanation:
Just in case you want the solution as well:
10d = 1000
d = 100
8 Simplify: 7x² + 4x-x²
[tex] \: \Large \mathbb{SOLUTION:}[/tex]
[tex] \: \: \rm{ {7x}^{2} + 4x - {x}^{2}}[/tex]
[tex] \: \: \text{Reorder and gather like terms}[/tex]
[tex] \: \: \rm{( {7x}^{2} - {x}^{2} ) + 4x}[/tex]
[tex] \: \: \text{Collect coeffiecients of like terms}[/tex]
[tex] \: \: \rm{(7 - 1) {x}^{2} + 4x}[/tex]
[tex] \: \: \text{Calculate the sum or difference}[/tex]
[tex] \: \: \rm{ \underline{ \underline{ {6x}^{2} + 4x}}}[/tex]
[tex] \rm{6x {}^{2} + 4x}[/tex]
Solution:Collect like terms
[tex] \red{7x {}^{2} } + 4x \red{ - x {}^{2} }[/tex]
[tex] \red{6x {}^{2} } + 4x [/tex]
Use the equation y-6= to fill in the missing values in the table below
Using the given equation, the missing values in the table are:
x y
32 14
12 9
0 6
-8 4
-36 -3
How to Apply an Equation?Given the equation, y - 6 = x/4, we can rewrite the equation as:
y = x/4 + 6
For x = 12, we have:
y = 12/4 + 6 = 3 + 6
y = 9
For x = 0, we have:
y = 0/4 + 6 = 0 + 6
y = 6
For y = 4, we have:
4 = x/4 + 6
4 - 6 = x/4
-2 = x/4
-8 = x
x = -8
For y = -3, we have:
-3 = x/4 + 6
-3 - 6 = x/4
-9 = x/4
-36 = x
x = -36
Thus, using the given equation, the missing values in the table are:
x y
32 14
12 9
0 6
-8 4
-36 -3
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Express 21 as a product of prime
factors
Answer:
21=1×21 or 3×7
Step-by-step explanation:
21 is a composite number.factors of 21:1,3,7,21.
Prime factorization:21=3×7.
since 3 and 7 are the only prime numbers ...
Thanks!!
Which value of v makes 12=12+v-8/2 a true statement?
Answer:
Step-by-step explanation:
12 = 12 + v - (8/2)
12 = 12 + v - 4
12 - 12 = v - 4
v = 4
As treasurer of her school's 4H club, Carol wants to buy gifts for all
11 members. She can buy t-shirts for $5 and sweatshirts for $12.
The club has $118 to spend and Carol wants to spend all of the
money. How many of each type of gift should she buy?
Using algebraic expressions and equations, Carol should buy 2 t-shirts and 9 sweatshirts.
We can set up an algebraic expressions and equations to determine how many of each type of gift should Carol buy.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
1. Write an equation for the total number of members.
x + y = 11 (equation 1)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
2. If each t-shirt costs $5 and each sweatshirt costs $12, write an equation for the total amount spent buying the gift.
$5(x) + $12(y) = $118 (equation 2)
where x is the number of members who will get t-shirt
y is the number of members who will get sweatshirt
3. Rewrite equation 1 as an equation of y in terms of x.
x + y = 11 (equation 1)
y = 11 - x
4 . Plug in the expression for y in equation 2 and solve for x.
$5(x) + $12(y) = $118 (equation 2)
5x + 12(11 - x) = 118
5x + 132 - 12x = 118
-7x = -14
x = 2
5. Substitute the value of x in either equation 1 or 2 and solve for x.
x + y = 11 (equation 1)
2 + y = 11
y = 11 - 2
y = 9
Hence, Carol should buy 2 t-shirts and 9 sweatshirts.
Checking,
2 + 9 = 11
Each member will receive a gift.
2($5) + 9($12) =$118
Carol will be spending $118 for the gifts.
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