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]
Richard's mom gave him $25.00 on Monday morning to use on lunches. At his school, the school lunch costs $1.50, which he bought Monday through Thursday. On Friday, he decided to buy 3 slices of pizza instead of buying the school lunch. If the pizza costs $1.40 per slice, then how much of the money is left at the end of the school week?
Answer:
Lfjbefibqeuifbiw
Step-by-step explanation:
d sdf sjfjs
Given the vertex form of a parabola
Carly had some markers. After she bought 16 more, she had 40 markers. How
many markers did Carly start with?
Answer:
24 markers
Step-by-step explanation:
24+16=40
40-16=24
Mrs. Squire had her class share some of the things they did over summer break. The scatter plot below shows the number of books students read and the number of days they went swimming. Which best describes the type of association shown in this scatter plot?
Answer:
Step-by-step explanation:
Determine if two triangles are congruent. If they are, state how you know.
A: SSS
B: SAS
C: HL
D: AAS
help me ASAP please!:(
Help me pls wdadsada
Answer:
one blue triangle is equal to 4
x = 4
Step-by-step explanation:
ok so lets say one red circle is equal to y so
y = 2
there is 4 circles so it would be
4y = 4 * 2 = 8
then the blue triangles are x and are equal to
2x = 2 * x = ?
8 / 2 = x = 4
x = 4
Use simple interest to find the ending balance. $215 at 8% for 8 years
Answer:
$ 352.6
Step-by-step explanation:
SI = P (1 + rt)
= 215 [ 1 + (0.08) x 8]
= 215 (1 + 0.64)
= 215 (1.64)
= $ 352.6
The total cost of a pair of shoes and a hoodie is $150 the hoodie cost $100 more than the pair of shoes how much does each item cost?
Answer:
shoes = $25
hoodie = $125
Step-by-step explanation:
total cost = $150
hoodie = x + 100
shoes = x
x + x + 100 = 150
2x = 150 - 100
x = 50/2
x = 25
shoes = $25
hoodie = $125
add them up and u get the price of the shoe 125+25= $150
Solve for k:
k over 6.12 = 8.7
1. k = 53.244
2. k = 1.42
3. k = 2.58
Answer:
1. k=53.244 or k=13311/250
Which expression uses the greatest common factor and distributive
property to write 18 + 24 as a product? Circle the letter of the
correct answer.
A 2(9 + 12)
B 8(10 + 16)
C 6(3) + 6(4)
D 6(3+4)
Lily chose A as the correct answer. How did she get that answer?
Answer: she got that because when you multiply 2 by 9 you get 18 and when you do 2 times 12 you get 24. Choice à is just a disturbuted version of 18+24
Step-by-step explanation:
Answer:
D. 6(3 + 4)
Step-by-step explanation:
because 18 + 24 = 42 and 6(3 + 4) = 42 as well
Out of 250 randomly selected U.S. men in the 35– 44 age group, about how many would you expect to have a total cholesterol level greater than 260 milligrams per deciliter of blood?
Answer:
i think this is the one
Step-by-step explanation:
The dashed segments in these drawings represent the ... Select all the statements that are true about bases and heights in a ... Find the area of the parallelogram and record it in the last column of the table. ... Figure 1.2.2.6: 2 copies of the same parallelogram. On the ... Definition: Parallelogram.
Gill earned $10 on Thursday,$20 on Friday,and $15 on Saturday selling necklaces.He sold each necklace for the same amount.What is the most he could have charged for each necklace?
Answer:
20 dollars.
Step-by-step explanation:
Look at the largest number.
Answer: pretty sure it is 5
Find the quotient. Express your answer as a mixed number in simplest form.
334 ÷ 112
Answer:
2 and 55/56
Step-by-step explanation:
334/ 112= 2.982142857 or 2 and 55/56
Use the simple interest formula to find the interest earned and the ending balance. I = Prt
1. $270 at 9% for 3 years
Answer:
$72.90 is the interest earned
Step-by-step explanation:
The appropriate formula is i = prt, where r is the annual interest rate expressed as a decimal fraction.
Here, i = ($270)(0.09)(3 yr) = $72.90 is the interest earned
Show all your work! Thank you!
Answer:
a
Step-by-step explanation:
1+1=2 2+2=4 meaning its 9$ for the cheesecake and 10 for the apple pie
find the value of given expression
[tex] \sqrt{899 + 1} [/tex]
Answer:
30 is the answers for the question
PLEASE HELP
A number b increased by 4 is greater than or equal to 15.
Answer:
b ≥ 11
Step-by-step explanation:
b + 4 ≥ 15
b ≥ 15 - 4
b ≥ 11
Find the volume of a right circular cone that has a height of 2.7 ft and a base with a diameter of 14.4 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
20.4 cubic feet
Step-by-step explanation:
formula for the volume of a cone is (r^2xhxpi)/3
so, r= 14.4/2
(7.2x2.7xpi)/3
The volume of a right circular cone is 146.49 cubic foot.
What is the volume of a right circular cone?The Volume of Right Circular Cone formula is defined as The volume of a cone is one-third of the product of the area of the base and the height of the cone.
The volume of a right circular cone is given by;
[tex]\rm Volume=\dfrac{1}{3}\pi r^h\\\\r = radius, \ h = height\\[/tex]
The volume of a right circular cone that has a height of 2.7 ft and a base with a diameter of 14.4 ft.
The radius of the cone is;
[tex]\rm Radius=\dfrac{diameter}{2}\\\\ Radius=\dfrac{14.4}{2}\\\\ Radius=7.2[/tex]
The volume of a right circular cone is;
[tex]\rm Volume=\dfrac{1}{3}\pi r^h\\\\ Volume=\dfrac{1}{3}\times 3.14 \times (7.2)^2\times 2.7\\\\Volume=146.49[/tex]
Hence, the volume of a right circular cone is 146.49 cubic foot.
Learn more about circular cone here;
https://brainly.com/question/14735698
#SPJ2
I really need help...Will mark brainiest
Answer:
89999
Step-by-step explanation:
Find the interest
earned:
$26,000 for 36 months
at 7.5% annual
compound interest
Answer:
Interest = $6,300 (Approx.)
Step-by-step explanation:
Given:
Amount deposit (P) = $26,000
Number of month = 36 month
Number of year (n) = 36 / 12 = 3 year
Rate of interest (r) = 7.5% = 0.075
Find:
Interest earned
Computation:
Interest = p[(1+r)ⁿ-1]
Interest = 26,000[(1+0.075)³-1]
Interest = 26,000[(1.075)³-1]
Interest = 6,299.71
Interest = $6,300 (Approx.)
Wanda went to the candy store and bought 2 pounds of candy. If 4/5 of Wanda's candy was chocolate, how many pounds of chocolate candy did Wanda buy?
Answer:
1.6 pounds
Step-by-step explanation:
Hope this helped have a great day!!
Answer:
Ummmmm
Step-by-step explanation:
I am a little confused on the way you worded the question however *not guaranteed this is the right answer let me know if it is* but I'm just going to see what I can find using this very confusing question. Next time please try to word the question better but please give me a heart for trying.
She bought 2 pounds of chocolate candy and if its supposed to be separate then £0.40p
Please at least answer one!! Will mark brainiest
Step-by-step explanation:
Hi bro.....
I think that is good :)
Answer:
Your a goat.
Step-by-step explanation:
Pat has spent 48 minutes reading, 1 hour and 17 minutes playing baseball in the yard, 65 minutes playing soccer, and 39 minutes watching tv. Show your work Part A. How many minutes did pat spent playing sports
Answer:
the total minutes spent on playing sports is 142 minutes
Step-by-step explanation:
The computation of the minutes spent in playing sports is shown below:
= Baseball + soccer
= 1 hour 17 minutes + 65 minutes
= 77 minutes + 65 minutes
= 142 minutes
Hence, the total minutes spent on playing sports is 142 minutes
Nine times the sum of a number and 2 is 8. Use the variable x for the unknown number
Find the distance between (-2, 3) & (-7, -7). Round to the nearest tenth.
Answer:
11.2 units
Step-by-step explanation:
From (-7, -7) to (-2, 3) is 5 units horizontally and 10 units vertically. Thus we have a right triangle with sides 5 and 10 respectively. The length of the hypotenuse of this triangle is the distance between (-2, 3) & (-7, -7):
d = √(5² + 10²) = √(25 + 100) = √125 = √25√5, or 5√5.
This is approximately 11.2 units
[tex]{ \sf{find \: the \: distance \: between \: ( - 2,3)and \: ( - 7, - 7).}} \\ { \sf{round \: to \: the \: nearest \: tenth}}[/tex]
[tex]{ \sf{ \red{distance = \sqrt{( {x2 - x1})^{2} + ( {y2 - y1})^{2} } }}} \\ \\ { \sf{x1 = - 2}} \\ { \sf{x2 = - 7}} \\ { \sf{y1 = 3}} \\ { \sf{ y2 = - 7}}[/tex]
[tex]{ \sf{ \green{ distance = \sqrt{ {( - 7 - ( - 2)})^{2} + {( - 7 - 3)}^{2}}}} } \\ \\ { : {\implies{ \green{ \sf{distance = \sqrt{ {( - 5)}^{2} + {( - 10)}^{2} } }}}}} \\ \\ { : { \implies{ \green{ \sf{distance = \sqrt{25 + 100}}}}}} [/tex]
[tex]{ : { \implies{ \sf{ \green{distance = \sqrt{125}}}}}} \\ \\ { : { \implies{ \green{ \sf{distance = 5 \sqrt{5}}}}}} \\ \\ { : { \implies{ \green{ \sf{distance = 5 \times 2.236}}}}}[/tex]
[tex]{ : { \implies{ \underline{ \green { \sf{distance = 11.18= 11.2}}}}}}[/tex]
Is it the first one the second one the third one the fourth one ??not to be rude but please hurry !!! 20 points !!!
Answer:
5/6 ÷ 1/12 = 10
Step-by-step explanation:
5/6 ÷ 1/12 = 5/6 x 12/1 = 60/6 = 10
Proof:
5/6 tank = 10/12 tank
If each trip takes 1/12 tank, then 10 ÷ 1 = 10 trips
PL Z HELP 30 points brainliest
Kenneth sold $26,000 worth of computers in eight days. At this rate, how many dollars worth of computers can he sell in 10 days?
Answer:
$32500
Step-by-step explanation:
26,000/8=3250
325010x10=32500
What is the equation for the line of symmetry in this figure?
Answer:
Step-by-step explanation:
Y-axis is the line of symmetry as it divides the figure into two equal parts
PLEASE PLEASE HELP!!!!
Answer:
I think acute
Step-by-step explanation:
1. By what factor did the medicine decrease in the first hour and a half? Explain how you know.
Answer:
4/9
Step-by-step explanation:
At t = 0 ; volume = 270
At t = 1.5 ; volume = 80
y = P(1 - r)^t
y =ab^x (exponential)
a = initial amout at t = 0
y = final amount
t = 1.5
80 = 270b^t
80/270 = b^t
8/27 = b^1.5
8/27 = b^3/2
b^3/2*2/3 = (8/27)^2/3
Cube root of 8/27 = 2/3
Square of 2/3 = (2/3)^2 = 4/9