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2 years ago

15

Willy rents a bike for 7 days. The charge is $15 plus the $0.08 per mile. He wants to spend exactly $35. How many miles can he r

ide the bike? *

1 answer:

Burka [1]2 years ago

3 0

Answer:

Willy can ride the bike for 250 miles.

Step-by-step explanation:

$35 - $15 = $20

$0.08 × 12.5 = $1

$1 per 12.5 miles

$20 × 12.5 = 250

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in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Nimfa-mama [501]

Answer:

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

Step-by-step explanation:

Let $\vec u$ and $\vec a$ , from Linear Algebra we get that component of $\vec u$ parallel to $\vec a$ by using this formula:

$\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a$ (Eq. 1)

Where $\|\vec a\|$ is the norm of $\vec a$ , which is equal to $\|\vec a\| = \sqrt{\vec a\bullet \vec a}$ . (Eq. 2)

If we know that $\vec u =(2,1,1,2)$ and $\vec a=(4,-4,2,-2)$ , then we get that vector component of $\vec u$ parallel to $\vec a$ is:

$\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

Lastly, we find the vector component of $\vec u$ orthogonal to $\vec a$ by applying this vector sum identity:

$\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}$ (Eq. 3)

If we get that $\vec u =(2,1,1,2)$ and $\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$ , the vector component of $\vec u$ is:

$\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

$\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

4 0

2 years ago

Which equation shows y=−1/2x+4 is in standard form?

adelina 88 [10]

Answer:

B. x + 2y = 8 is your answer.

Step-by-step explanation:

So this is what you do:

y = -1/2x + 4 <u>You are going to add -1/2 to the other side.</u>

y + 1/2x = 4 <u>You are going to multiply the equation by 2.\</u>

B. x + 2y = 8 is your answer.

8 0

2 years ago

Pls can someone pls help me <br> Please show your work

Lana71 [14]

Answer:

x = 8

I dunno what the question is in the first place, but I assume you are solving for x.

Step-by-step explanation:

The two given angles are equivalent because they are parallel and they have a line that intersects.

The line creates two angles on each side of each line, which is 120 or 60 because there are 180 degs on a straight line.

The obtuse side is 120, and the -8 + 16x is also on an obtuse angle, showing that they are equal.

120 = -8 + 16x

128 = 16x

8 = x

x = 8

7 0

1 year ago

Which of the following best describes the ordered pairs (-3,-6),(0,-9),(-3,-14),(7,-16)

Genrish500 [490]

Well...their relations but not functions

5 0

2 years ago

The roof of a grain silo is in the shape of a cone. The inside radius is 20 feet, and the roof is 10 feet tall. Below the cone i

nirvana33 [79]

Answer:

41887.90 cubic feet

Step-by-step explanation:

We need to find the volume of the silo.

We simply need to find the volume of the cylindrical part and the conical part and add them together.

The body of the silo is a cylinder with height of 30 ft and radius of 20 ft and the roof is a cone with height 10 ft and radius 20 ft.

The volume of a cylinder is given as:

$V = \pi r^2h$

The volume of a cone is given as:

$V = \frac{1}{3} \pi r^2H$

where r = radius of cylinder and cone

h = height of cylinder

H = height of cone

Adding them together, we have that the volume of the silo is:

$V = \pi r^2h + \frac{1}{3} \pi r^2H$

$V = \pi r^2 (h + \frac{1}{3}H)\\ \\V = \pi * 20^2 (30 + [\frac{1}{3}* 10]) \\\\V = 1256.64 ( 30 + 3.33)\\\\V = 1256.64(33.33)\\\\V = 41887.90 ft^3$

The volume of the silo is 41887.90 cubic feet.

5 0

2 years ago