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2 years ago

A car dealership purchased a car for $15,000. They mark up the price by 35%. What is the retail price of the vehicle

Mathematics

1 answer:

Snowcat [4.5K]2 years ago

4 0

Answer: the answer is 20,250

Step-by-step explanation:

35% of 15,000 = 5,250

15,000+5250 = 20,250

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Evaluate the surface integral. s (x + y + z) ds, s is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 +

Stolb23 [73]

$S$ is given to be parameterized by

$\mathbf r(u,v)=\langle x(u,v),y(u,v),z(u,v)\rangle=\langle u+v,u-v,1+2u+v\rangle$

with $0\le u\le3$ and $0\le v\le2$ . We have

$\mathbf r_u=\langle1,1,2\rangle$
$\mathbf r_v=\langle1,-1,1\rangle$
$\mathbf r_u\times\mathbf r_v=\langle3,1,-2\rangle$
$\left\|\mathbf r_u\times\mathbf r_v\right\|=\sqrt{14}$

The surface integral is then

$\displaystyle\iint_S(x+y+z)\,\mathrm dS=\iint_S(x(u,v)+y(u,v)+z(u,v))\left\|\mathbf r_u\times\mathbf r_v\right\|\,\mathrm du\,\mathrm dv$
$=\displaystyle\sqrt{14}\int_{u=0}^{u=3}\int_{v=0}^{v=2}((u+v)+(u-v)+(1+2u+v))\,\mathrm dv\,\mathrm du$
$=\displaystyle\sqrt{14}\int_{u=0}^{u=3}\int_{v=0}^{v=2}(4u+v+1)\,\mathrm dv\,\mathrm du$
$=\displaystyle\sqrt{14}\left(8\int_{u=0}^{u=3}u\,\mathrm du+3\int_{v=0}^{v=2}v\,\mathrm dv+6\right)$
$=\displaystyle\sqrt{14}\left(8\int_{u=0}^{u=3}u\,\mathrm du+3\int_{v=0}^{v=2}v\,\mathrm dv+6\right)$
$=48\sqrt{14}$

4 0

3 years ago

Prove by contradiction that the interval (a,<br> b.has no minimum element.

Snowcat [4.5K]

Assume (a,b) has a minimum element m.

m is in the interval so a < m < b.

a < m

Adding a to both sides,

2a < a + m

Adding m to both sides of the first inequality,

a + m < 2m

2a < a+m < 2m

a < (a+m)/2 < m < b

Since the average (a+m)/2 is in the range (a,b) and less than m, that contradicts our assumption that m is the minimum. So we conclude there is no minimum since given any purported minimum we can always compute something smaller in the range.

8 0

3 years ago

What is the volume of this solid? Use 3.14 for pi. 37.68 cm³ 138.16 cm³ 169.56 cm³ 207.24 cm³ A solid consisting of a cone on to

yulyashka [42]

Volume of Solid = Volume of Cylinder + Volume of Cone
Volume of Cylinder = πr²h
v= 3.14 * (3)² * 6
v = 169.56

Volume of Cone = πr² h/3
v = 3.14 * (3)² * 4/3
v = 37.7

Now, V = 169.56 + 37.7 = 207.26 cm³

Hope this helps!

8 0

2 years ago

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Irina-Kira [14]

Y=2x-1

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3 years ago

HELP LOOK AT THE SCREENSHOT<br><br> Find the value of x. (SHOW WORK)

Vanyuwa [196]

Answer: x = 2

=============================================================

Explanation:

Refer to the diagram below.

I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).

Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)

Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.

The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.

----------------------

Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.

The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10

Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.

----------------------

Now let's solve for x

6x-10 = 3x-4

6x-3x = -4+10

3x = 6

x = 6/3

x = 2

4 0

3 years ago