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2 years ago

Last semester, Mr. Dean had 8 students who built a sailboat in 160 working hours. The time that

Mathematics

1 answer:

sveta [45]2 years ago

4 0

Answer:

106.67 hours

Step-by-step explanation:

Total hours

160 * 8 = 1,280

Hours for group of 12

1280 / 12 = 106.6666666667

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Use the arc length formula to find the length of the curve y = 4x − 5, −1 ≤ x ≤ 3. Check your answer by noting that the curve is

Reptile [31]

Answer:

$4\sqrt{17}$

Step-by-step explanation:

Let's find the answer by using the arc length formula which is:

$\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^{2} } } \, dx$

First, let's find dy/dx which is:

y=4x-5

y'=4*(1)-0

y'=4, now let's use the formula:

$\int\limits^3_{-1} {\sqrt{1+4^{2}} } \, dx=\sqrt{17} *(3-(-1))=4\sqrt{17}$

Now, using the distance formula we have:

$d=\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }$

$y(-1)=4*(-1)-5=-9 \\y(3)=4*(3)-5=7$

So we have two points (-1, -9) and (3, 7) so:

$d=\sqrt{(3-(-1))^{2} +(7-(-9))^{2} }=4\sqrt{17}$

Notice both equations gave the same length $4\sqrt{17}$ .

5 0

3 years ago

Need help!!! which addition matches the problem...

Tom [10]

Answer:

The addition that matches the problem is the first one.

Step-by-step explanation:

The red line goes back 8 so it is a -8 and the blue line goes forward 4 so it is a postive 4.

4 + (-8) = -4

6 0

2 years ago

Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)

Citrus2011 [14]

Answer:

It is 3y = 4x + 10

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

${x}^{2} - xy + {y}^{2} = 7$

introduce dy/dx :

$\frac{d}{dx} ( {x}^{2} - xy + {y}^{2} ) = \frac{d}{dx} (7) \\ \\ 2x - (y + \frac{dy}{dx} ) + 2y \frac{dy}{dx} = 0$

make dy/dx the subject:

$2x - y - \frac{dy}{dx} + 2y \frac{dy}{dx} = 0 \\ \\ 2y \frac{dy}{dx} - \frac{dy}{dx} = y - 2x \\ \\ \frac{dy}{dx} (2y - 1) = y - 2x \\ \\ \frac{dy}{dx} = \frac{y - 2x}{2y - 1}$

At point (-1, 2):

$\frac{dy}{dx} = \frac{2 - 2( - 1)}{2(2) - 1} \\ \\ slope = \frac{4}{3}$

but a tangent has the same slope as the curve:

$y = mx + c$

m is the slope

c is the y-intercept

At (-1, 2):

$2 = ( - 1 \times \frac{4}{3} ) + c \\ \\ c = 2 + \frac{4}{3} \\ \\ c = \frac{10}{3}$

equation:

$y = \frac{4}{3} x + \frac{10}{3} \\ \\ { \boxed{3y = 4x + 10}}$

8 0

2 years ago

Read 2 more answers

Choose all the common denominators for 2/3 and 7/9. 6 9 18 27 30

n200080 [17]

Answer:

Step-by-step explanation:

2/3x2= 6/9, which makes it have a common denominator with 7/9.

7 0

2 years ago

Read 2 more answers

How do you solve this problem -g+2(3 g)=-4(g+ 1)?

alexgriva [62]

$-g+2(3 g)=-4(g+ 1)?\\-g + 6g = -4g - 4\\5g = -4g - 4\\9g = -4\\\\g = -\frac{4}{9}$

5 0

3 years ago