As per the given equation, the length of the arc of the curve from point p to point q is 1.8973
Here we have given the equation y = 1/2 x².
Then the the length of the arc of the curve from point p to point q is calculated by using the formula,
=> [tex]\int\limits^q_p {\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]
Here we have to extract the value of (x1, x2) from the given coordinates, then we get,
=> (x1, x2) = (-3, 3)
Now, we have to find the derivative of y, then we get he value as,
=> dy/dx = x
So, the length is calculated as,
=> [tex]\int\limits^3_{-3} {\sqrt{1+x^2} } \, dx[/tex]
As per the power rule of derivative, then reduced form of the equation is written as.
=> [x/√x²+1]₋₃³
When we apply the value of x as the given limit, then we get,
=> [3/√3²+1] - [(-3)/√(-3)²+1]
=> [3/√10] + [3/√10]
=> 6/√10
=> 1.8973
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I NEED HELP!
The function f(x) is a quadratic function and the zeros of f(x) are - 2 and 5. The y-intercept of f(x) is 30. Write the equation of the quadratic polynomial in standard form.
f(x)=___________
Answer:
Step-by-step explanation:
First of all you have to put the zeros into factor form.
y1 = (x + 2)(x - 5)
Notice that the x changes sigh. You say that the zeros are -2 and 5. To get y1 to go to zero, you must make x the opposite sign of what you are given.
Now you have to expand the factored form to get the standard form
y = x^2 + 2x - 5x - 10
y = x^2 - 3x - 10
That's not the right answer.
f(0) = 30 but you have - 10 at the end so you have to multiply the factored form by - 3
-3(f(x)) = -3(x + 2)(x - 5)
-3(f(x)) = -3(x^2 - 3x - 10)
f(x) = -3x^2 + 9x + 30
f(0) = -3(0)^2 + 9(0) + 30
f(0) = 30
The quadratic still has roots of (x +2)(x - 5) but that 3 makes the y intercept = 30.
See the graph below.
Janet and Artie want to play tug-of-war.
Artie pulls with 200 pounds of force while
Janet pulls with 60 pounds of force. In
order to make this a fair contest, Janet
enlists the help of her friends Trudi, Sherri,
andyBridget who pull with 20, 25, and 55
pounds respectively. Write an inequality
describing the minimum amount Janet's
fourth friend, Tommy, must pull to beat
Artie.
Answer:
Tommy would have to pull at least 40.0000000..... something to beat Artie but the closest whole number is 41 becouse it has to be over 200
Step-by-step explanation:
200 /= 60 + 20 +25 + 55 + x
200/= 160 + x - 160 both sides
40 = x
Mrs. Kirsch went shopping at a department store. The store is having a sale, discounting all items by 30% off the marked price. She decides to buy an item originally marked $85.95. She also had to pay 6% sales tax. What is the sales tax on the item? What is the final cost (sale price plus tax) of her purchase?
Answer:
63.76
Step-by-step explanation:
85.95-30% 60.16
60.16+6% 63.76
answer this question! i am having some trouble in khan..
please help me, I lost my answer
If a triangle with the angles of 72 degrees, 62 degrees, and 46 degrees and one of the side lengths is 40, what would the length of the other two side be?
Answer:
The length of the other two sides are: 43.09 and 32.60
Step-by-step explanation:
Let the given side of the triangle be b(= 40), and the angles be;
A = [tex]72^{o}[/tex], B = [tex]62^{o}[/tex]and C = [tex]46^{o}[/tex].
Applying the Sine rule,
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]
So that,
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]
[tex]\frac{a}{Sin 72}[/tex] = [tex]\frac{40}{Sin62}[/tex]
a = [tex]\frac{0.9511*40}{0.8829}[/tex]
= 43.0898
a = 43.09
Also,
[tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{40}{Sin62}[/tex] = [tex]\frac{c}{Sin46}[/tex]
c = [tex]\frac{0.7193*40}{0.8829}[/tex]
= 32.5881
c = 32.60
The length of the other two sides are: 43.09 and 32.60
Susan deposits $100 into a savings account that earns simple interest at a rate of 5%. If she makes no withdrawals, how much total interest has Susan's savings account earned after 5 years?
Answer:
Interest is $25
Step-by-step explanation:
Formula to find interest:
I = Prt
Given:
P = 100
r = 5% or 0.05
t = 5
Work:
I = Prt
I = 100(0.05)(5)
I = 5(5)
I = 25
Help! The picture is with it to see the question
Answer:
8
Step-by-step explanation:
sqrt8*sqrt8 = sqrt8^2 = 8
Please help I have tried so hard
28.4 grams = ? ounces
Can someone please help me with math.
Answer:
the answer to the questions are c,b,a
4x – 8
Please helppp
-2
Divide each term (-4x = 8 by -4)
Cancel the common factor of -4
x = 8/-4
THEN DIVIDE
x=-2
please help me and no links this is due in 10 mins ill give you the crown
Answer:
angle Q is 68°
angle R is 112°
explain how you can tell whether a group of ratios represents a proportional relationship. PLEASE HELP
PLSSSS DO NOT GIVE ME FILES
Read the sentences.
Some people train by climbing and swimming. Others train with running, biking, and weightlifting.
Select the sentence that correctly combines these sentences using semicolons.
Some people train by climbing and swimming, others train with running; biking; and weightlifting.
Some people; train by climbing and swimming, others train with running, biking, and weightlifting.
Some people train by climbing and swimming; others train with running; biking; and weightlifting.
Some people train by climbing and swimming; others train with running, biking, and weightlifting.
The diagram shows a right-angled triangle.
All the measurements are in centimetres.
The area of the triangle is 18cm^2
Work out the length of the shortest side of the triangle.You must show all your working
Answer:
short side = 4
Step-by-step explanation:
area = 1/2BH
18 = 1/2(x - 1)(x + 4)
18 = 1/2(x² + 4x - x - 4)
multiply both sides of the equation by 2:
36 = x² + 3x - 4
x² + 3x - 40 = 0
(x + 8)(x - 5) = 0
x = 5
short side = 5 - 1 = 4
The shortest length of the right angled triangle is 4 cm.
Area of a triangle:area = 1 / 2 bhwhere
b = base
h = height
Therefore,
area = 18 cm²
18 = [tex]\frac{1}{2}[/tex] × (x - 1)(x + 4)
36 = (x - 1)(x + 4)
x² + 4x - x - 4 = 36
x² + 3x - 4 = 36
x² + 3x - 4 - 36 = 0
x² + 3x - 40 = 0
x² - 5x + 8x - 40 = 0
x(x - 5) + 8(x - 5) = 0
(x + 8)(x - 5) = 0
x = -8 or 5
we can only use positive numbers.
Therefore,
x = 5
The shortest sides is definitely one of the 2 legs . The hypotenuse of a triangle is the longest side.
Therefore,
h = x - 1 = 5 - 1 = 4 cm
b = x + 4 = 5 + 4 = 9 cm
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Solve.
Pls need help
Answer: try C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
It's c because you multiply 3 1/8 by 3 and 3 1/4 by 4 and 3 1/2 by 1.
ill give brainiest - please help ASAP with WORK FOR IT please and thank you!! :)
3 pages, with work pleasee
Answer:
isosceles trapezoidtrapezoidrhombussquarerectangleparllelogramquadrilateral10x+18+62=180 co interior angle10x=180-80
x=100/10=10
:.x=10
9.
8x+2=7x+14 corresponding angle of parallelogram are equal
8x-7x=14-2
x=12
10.
4x+4=5x+1 corresponding sides of parallelogram are equal
4-1=5x-4x
x=3
11.
4+3x=19corresponding sides of parallelogram are equal
3x=19-4
x=15/3
x=5
Name the inequality!
If each square in the following floor plan represents 2.5 feet, what are the dimensions of the living room?
BRAINLIEST-
Find the volume of the figure
Answer:
4080cm²
Step-by-step explanation:
Please help me thank you!
The function ƒ(x) = 2x − 2 indicates:
a shift to the right of 1 unit.
a shift to the left of 2 units.
a shift to the right of 2 units.
None of these choices are correct.
Answer:
None of the choices are correct
Step-by-step explanation:
This is because it should be going down if it was subtracting but no answer says that so
Yo pls help me out, the question is on the picture.
ill mark brainliest if its correct. NO LINKS!
Margaret owns (5/6) of a section of land. She planted corn on (1/4) of her land. What fraction of the entire section is planted with Margaret’s corn?
Answer:
3/5
Step-by-step explanation:
subtract the fractions then turn the decimal into a fraction.
I need help fast please
Answer:
-2/3
Step-by-step explanation:
8^(x+2) =8^-2x
since the base are the same we deal with the exponent
x+2=-2x
x= -2/3
Find the area of the shaded region. Round to the nearest hundredth
Answer:
Area of the shaded region = 450.52 square inch
Step-by-step explanation:
Area of the shaded region = Area of the circle - Area of the right triangle inscribed in the semicircle
By applying Pythagoras theorem in the given right triangle,
(Hypotenuse)² = (leg 1)² + (leg 2)²
= (21)² + (20)²
Hypotenuse = [tex]\sqrt{441+400}[/tex]
= [tex]\sqrt{841}[/tex]
= 29
Since, hypotenuse of the right triangle is the diameter of the circle.
Therefore, radius of the circle = [tex]\frac{29}{2}[/tex]
= 14.5 in.
Area of the circle = πr²
= π(14.5)²
= 660.519
≈ 660.52 in²
Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(21)(20)[/tex]
= 210 in²
Area of the shaded region = 660.52 - 210
= 450.52 square inch
solve for x . Leave your answer in the simplest form
Hello!
Here we are given a composite shape, meaning that we can divide this shape up into ways that we are given formulas to solve for legs and such.
I can see here that this can be divided into a triangle and a rectangle using a horizontal line.
The leg lengths of this triangle would be 9, because it is congruent to the bottom side of the rectangle, and 7, because it is the left side minus the right side.
This would also make a right triangle, meaning we could solve for the hypotenuse utilizing the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
[tex]6^2+7^2=c^2[/tex]
[tex]36+49=c^2[/tex]
[tex]c^2=85[/tex]
[tex]c=\sqrt{85}[/tex]
Which is in simplest radical form.
Hope this helps!
16. The boys' soccer to a bouchoccer ball conoccer balls for $391. If the team bought a total of 17
soccer balls, how much did each soccer ball cost?
A. $21
B. $23
C. $374
D. $408
Answer:
The answer is B $23.
Step-by-step explanation:
You take 391 and divide it by 17
391/17=23
Hope this helps!
Find the x and y intercept of y=0.5x^2-3x.
Step-by-step explanation:
i don't have a step by step explanation so here you go the answer
help!! tell whether the triangle is a right triangle- i don’t need an explanation thank you!!
Answer:
1.) Right triangle
2.) Not right triangle
3.) Not right triangle
4.) Not right triangle
5.) Right triangle
6.) Right triangle
Step-by-step explanation:
The ones that are a right triangle have at least one angle that has an L shape