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2 years ago

jenna has 24 dimes and quarters in her purse. in total the coins are worth $3.60. How many of each coin does she have?

Mathematics

1 answer:

Paul [167]2 years ago

5 0

Answer:

Jenna has 24 Dimes and 6 Quarters

Step-by-step explanation:

Hopefully this helps

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago

Simplify 6 to the 3rd

elixir [45]

Answer:

Isnt it 2?

Step-by-step explanation:

7 0

3 years ago

A basketball player scored 26 times during one game. She scored a total of 51 points, two for each two-point shot and one for ea

gulaghasi [49]

She scored alot but she made 25 two point shots and one free throw

f+t+26
1f+2t=51
1x1=1 2x25=50 together that makes 51 points and she scored 26 times

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2 years ago

Read 2 more answers

Find an equation of the line. Write the equation using function notation.

Gemiola [76]

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Step-by-step explanation:

Given equation of line is:

$4y=x-8$

We have to convert the given line in slope-intercept form to find the slope of the line

So,

Dividing both sides by 4

$\frac{4y}{4} =\frac{x-8}{4}\\y = \frac{1}{4}x-\frac{8}{4}\\y = \frac{1}{4}x-2$

Let m1 be the slope of given line

Then

$m_1 = \frac{1}{4}\\$

Let m2 be the slope of line perpendicular to given line

As we know that produt of slopes of two perpendicular lines is -1

$m_1.m_2 = -1\\\frac{1}{4} . m_2 = -1\\m_2 = -1*4\\m_2 = -4$

The slope intercept form of line is given by:

$y = m_2x+b$

Putting the value of slope

$y = -4x+b$

to find the value of b, putting (3,-3) in equation

$-3 = (-4)(3) + b\\-3 = -12 +b\\b = -3+12\\b = 9$

Putting the value of b in the equation

$y = -4x+9$

Hence,

The equation of line perpendicular to 4y = x-8 passing through (3,-3) is:

$y = -4x+9$

Keywords: Equation of line, slope

Learn more about equation of line at:

#LearnwithBrainly

4 0

3 years ago

___ is 100 times as much as 80

Katarina [22]

8000 is 80*100. Use a calculator if you can't solve this in your head. c:

7 0

2 years ago

jenna has 24 dimes and quarters in her purse. in total the coins are worth $3.60. How many of each coin does she have?​

jenna has 24 dimes and quarters in her purse. in total the coins are worth $3.60. How many of each coin does she have?