Find the equation of the curve that passes through the point (x, y) = (0, 0) and has an arc length on the interval x is between 0 and pi over 4 inclusive given by the integral the integral from 0 to pi over 4 of the square root of the quantity 1 plus the cosine squared x, dx . (5 points)
Answer:
[tex]\displaystyle y=\sin(x),\text{ where } 0\leq x\leq\pi/4[/tex]
Step-by-step explanation:
The curve passes through the point (x, y) = (0, 0) and has an arc length on the interval [0, π/4] given by the integral:
[tex]\displaystyle \int_{0}^{\pi/4}\sqrt{1+\cos^2(x)}\, dx[/tex]
And we want to find the equation of the curve.
Recall that arc length is given by:
[tex]\displaystyle L=\int_a^b\sqrt{1+\Big(\frac{dy}{dx}\Big)^2}\, dx[/tex]
Rewrite our original integral:
[tex]\displaystyle \int_{0}^{\pi/4}\sqrt{1+(\cos(x))^2}\, dx[/tex]
So:
[tex]\displaystyle \frac{dy}{dx}=\cos(x)[/tex]
It follows that:
[tex]\displaystyle y=\sin(x)+C[/tex]
Using the initial condition:
[tex]0=\sin(0)+C\Rightarrow 0=0+C\Rightarrow C=0[/tex]
The equation for our curve is:
[tex]\displaystyle y=\sin(x),\text{ where } 0\leq x\leq\pi/4[/tex]
Ken wants to buy two shirts. The original price of the first shirt is $34, and the original price of the second shirt is $28. Ken will use one of the two discount coupons shown to buy the shirts. Coupon 1 Coupon 2 Buy one shirt at the original price and receive half off the price of a second shirt of equal or lesser value. Take 20% off the original price of each shirt, Based on this information, which statement is true?
Write the equation of the line graphed below.
Answer:
x=1
Step-by-step explanation:
Square Areas
The dots on the grid are all one unit apart.
1. The square shown here can be described
as a 3/5 square. Find its area.
.
Show all your reasoning
Answer:
The area will be "34 unit²".
Step-by-step explanation:
The diagram is missing throughout the given question. Below is the figure attached.
According to the question,
The side of squares will be:
= [tex]\sqrt{(5)^2+(3)^2}[/tex]
= [tex]\sqrt{25+9}[/tex]
= [tex]\sqrt{34} \ units[/tex]
Hence,
The area of square will be:
= [tex](side)^2[/tex]
= [tex](\sqrt{34} )^2[/tex]
= [tex]34 \ unit^2[/tex]
find l of the following cone
Answer:
[tex] l = \sqrt{261}\: in[/tex]
Step-by-step explanation:
Height of the cone h = 15 in
Radius of the cone r = 12/2 = 6 in
We need to find slant height (l) =?
[tex] \because l = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ \therefore l = \sqrt{ {6}^{2} + {15}^{2} } \\ \\\therefore l = \sqrt{36 + 225} \\ \\\therefore l = \sqrt{261} \\ [/tex]
Answer:
l = √261 in
Step-by-step explanation:
Hope this helps
Solve 3x - y = 3 and 2x - y = 2 by substitution method
Answer:
x = 1
y = 0
Step-by-step explanation:
3x - y = 3
2x - y = 2 , then y = 2x - 2
substitute for y:
3x - (2x - 2) = 3
combine like terms:
x + 2 = 3
subtract 2 from both sides of the equation:
x = 1
y = 2(1) - 2 = 0
Answer:
x=5, y=8
Step-by-step explanation:
let 3x-y=3 be [1]
and 2x-y = 2 be [2]
Change up [2] to:
2x=2+y
2x-2 = y and name this [3]
Sub [3] into [1]
3x-(2x-2)=3
3x-2x-2=3
x-2=3
x=5
Sub x=5 into [3]
2(5)-2=y
10-2=y
8=y
Jess has 60 ounces of an alloy that is 40% gold. How many ounces of pure gold must be added to this alloy to create a new alloy that is 75% gold?
Answer:
84 ounces of pure gold
Step-by-step explanation:
Jess has 60 ounces of an alloy that is 40% gold. How many ounces of pure gold must be added to this alloy to create a new alloy that is 75% gold?
Pure gold = 100% gold
Let the number of ounces of pure gold = x
Hence, we have the equation
40% × 60 ounces + 100%× x ounces = 75%(60 + x)ounces
= 0.4 × 60 + 1x = 0.75(60 + x)
= 24 + x = 45 + 0.75x
Collect like terms
x - 0.75x = 45 - 24
0.25x = 21
x = 21/0.25
x = 84 ounces
Therefore, we need 84 ounces of pure gold
84 ounces of pure gold must be added
The first is to write out the parameters
Jess has 60 ounces of alloy
40% of this alloy is pure gold
The number of ounces that should be added can be calculated as follows;
Let y represent the unknown
40/100(y)(60) + 100/100(y)= 75/100(60+y)
24 + y= 0.75(60+y)
25 + y= 45 + 0.75y
24 - 45= 0.75y -y
-21= -0.25y
y= 21/0.25
y= 84
Hence the number of ounces of pure gold required is 84 ounces
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PLEASE HELP! QUICK EASY POINTS!! LOOK AT THE IMAGE!
Answer:
0.2 and 11.8
Step-by-step explanation:
what is 3248x9853 plezzzzzzzzzzz
Answer: 32002544
Step-by-step explanation:
The measure of one interior angle of a parallelogram is 5 times the measure
of another angle. What's the measurement of the larger interior angle?
Answer:
Step-by-step explanation:
The sum of these adjacent angles must sum to 180 degrees (also the sum of all angles must be 360)
a+5a=180
6a=180
a=30
The larger angle is 5a so the larger angle is
5(30)=150 degrees.
i just need the Y blank answers please!!
|x-(-12)| if x>-12
ill give brainlyest if corect
Answer:
x+12
Step-by-step explanation:
:)
HELP ILL GIVE BRAINIEST THIS MY LAST QUESTION!
Jim and Regina can complete one job in 4 hours when working together. When working alone, Jim works twice as quickly as Regina.
• How long will it take each of them to do the job when working alone? Show all work supporting your answer.
• If Regina works as quickly as Jim, how long will it take both of them to do the job working together? Show all work supporting your answer.
Answer:
Jim = 6 hoursRegina = 12 hoursTogether at same rate = 3 hoursStep-by-step explanation:
Let Jim's speed is J and Regina's speed is R and the work is WWe have:
(J + R)*4 = WJ = 2RSubstitute J with 2R:
(2R + R)*4 = W12R = WRegina needs 12 hours to complete work
and
Substitute R with J/2:
(J + J/2)*4 = W 6J = WJim needs 6 hours to complete same work
If Regina works as quickly as Jim:
J + R = 2JThen
Jim can complete 1/6 of work in one hour, they both can complete twice work:
1/6*2 = 1/3Time to complete work:
1: 1/3 = 3 hoursAnswer:
Honestly, Mark above person answer as brainliest..okay
Use 3.14 for pi and round to the nearest tenth.
Answer:
3.1
Step-by-step explanation:
if the last number is less thank five round down
The skateboard ramp has a slope of 2/5 if the height is 6 what is the width?
Answer:
its 5y−30
2
Step-by-step explanation:
Because lets put this problem in slope form. The form is Y=mx+b
ok now lets put it with the number Y=2/5+6
describe the following number patterns in your own words and state the constant difference or constant ratio if there is one
Step-by-step explanation:
awq-pzcq-mje
girls
come
to
see
my
22cm
sperm
fast
girl
An item is regularly priced at $80 Barbado add a discount of 25% off the regular price how much did Bob pay
Answer: $60
Step-by-step explanation:
Given
The price of an item is $80
The discount on it is 25%
Net payable price =Regular Price- discount
[tex]\Rightarrow \text{Net Payable Price(P)}=80-25\%\ \text{of}\ 80\\\Rightarrow P=80(1-0.25)=80\times 0.75\\\Rightarrow P=\$60[/tex]
I WILL GIVE BRANLIEST HELP FAST DUE IN 10 MINS 56yx^3-32yx+16y
Answer:
8y(7x^3-4x+2)
Step-by-step explanation:
Group and factor out the greastest common factor then combine
Answer:
this is my alt here ya go champ
Step-by-step explanation:
There are 20 boys in Mrs. Shaw’s 3rd-period class. 11 of the boys are from Benignus. What percent of the boys came from Benignus?
please hurry
6th grade math
Maggie has $16 to spend on lunch for the week. she has spent $4 so far. which inequality shows how much she can spend for the rest of the week?
PLEASE HELP ASAP
An isosceles trapezoid has an area of 25 square units and a height of 5 units. Find the sum of the bases of the trapezoid.
Complete your work in the space provided.
Answer:
5 units because 5 times 5 is 25
20 POINTS!!!!!!!!! pls answer asap
Answer:
FD = 26Step-by-step explanation:
CD = ED --- (secant property)
so, ==>>
13x - 16 = 4x + 11
13x - 4x = 11 + 16
9x = 27
x = 27÷9
x = 3
side ED = 4x + 11 = 4×3 + 11
side ED = 23
side FE = 12
ΔFED = 90° ...... (tangent secant property)
so.........
FE² + ED² = FD² ......... ( by pythagoras theorm)
12² + 23² = FD²
144 + 529 = FD²
673 = FD²
√673 = FD
26 = FD
Answer:
26
Step-by-step explanation:
4. Asia is designing a triangular-shaped window with a height of 15 inches and
an area of 135 square inches. What is the length of the base of the window?
Answer:
18in
Step-by-step explanation:
Given data
Height h= 15 in
Area= 135 in^2
The expression for the area is given as
Area= 1/2 Base * Height
substitute
135= 1/2* Base*15
135= 7.5 Base
Base= 135/7.5
Base= 18 in
Hence the base is 18in
What is the scale factor of the dilation from A to B?
Answer:
1
Step-by-step explanation:
The scale factor of the dilation from A to B is, 1.67
What is the scale factor ?Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.
For example, Two spheres look similar but could have different radii.
Given that,
Two parallelograms
A & B
First one has side length = 4.5 unit
Second one has side length = 7.5 unit
For calculating scale factor, we need to found ratio of two sides length
Scale factor = 7.5/4.5
= 1.66666
Hence, the scale factor is 1.67
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Venita is sewing new curtains. The table below shows the relationship between the number of stitches in a row and the length of the row.
Sewing
Number of stitches
Length (cm)
5
1
15
3
20
4
30
6
What is the relationship between the number of stitches and the length?
Answer:
The number of stitches is 5 times the length.
Step-by-step explanation: i took edge
Find the slope of the line graphed
Answer:
I believe it is 2
A coat is on sale for 30% off the original price of 120$.what is the amount of discount
Answer:
36
Step-by-step explanation:
You do 120 multiplied by .3 to get 36. This makes the discount amount is $36 which also means you only pay $84 for the coat.
Help!!
what's 7e-9-3e for e=6?
Answer:
15
Step-by-step explanation:
7e (7×6) = 42
42 - 9 = 33
3e (3×6) = 18
33 - 18 = 15
write a polynomial function in standard form with zeros at -1 -4 and 2
Pleasee PLEASE PLEASE SOMEONE HELP ME
Answer:
y= x^3+3x^2-6x-8
Step-by-step explanation:
What is the area of this figure?
Enter your answer in the box