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Arada [10]
2 years ago
13

When the cost of a car is multiplied by 0.05 the result is $1750, find the cost of the car?

Mathematics
1 answer:
Viktor [21]2 years ago
3 0
The answer is $35,000
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What percentage is .0019951
ICE Princess25 [194]
The most exact answer would be 0.19951% but the approximate answer would be 0.2%.
8 0
2 years ago
Read 2 more answers
Find the area of the region that lies inside the first curve and outside the second curve.
marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the  the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = \dfrac{1}{2}

\theta = -\dfrac{\pi}{3}, \ \  \dfrac{\pi}{3}

Now, the area of the  region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \  \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \  5^2 d \theta

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \  \theta  d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \   d \theta

A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  \dfrac{cos \ 2 \theta +1}{2}  \end {pmatrix} \ \ d \theta - \dfrac{25}{2}  \begin {bmatrix} \theta   \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}

A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  {cos \ 2 \theta +1}  \end {pmatrix} \ \    d \theta - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}}    \ \ - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{2 \pi}{3} \end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3})  \end {bmatrix} - \dfrac{25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} +   \dfrac{\pi}{3}  \end {bmatrix}- \dfrac{ 25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3}   \end {bmatrix}- \dfrac{ 25 \pi}{3}

A =    \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx
7 0
3 years ago
Who can help me to solve these questions please?
ankoles [38]

Using the given information, length of QR = 16.6 cm

The area of the trapezium is 304.5 cm²

<h3>Calculating area of a trapezium</h3>

From the question we are to calculate the length of QR and the area of trapezium PQRS

In the given diagram,

Let the midpoint of PS be T

Then, we can write that

|OP|² = |OT|² + |PT|²  (<em>Pythagorean theorem</em>)

|OP| = radius = 13 cm

|PT| = 1/2 × PS = 1/2 × 24 cm = 12 cm

∴ 13² = |OT|² + 12²

169 = |OT|² + 144

|OT|² = 169 -144

|OT|² = 25

|OT| = √25

|OT| = 5 cm

Also, let the midpoint of QR be U

Then, we can write that

|OQ|² = |OU|² + |QU|² (<em>Pythagorean theorem</em>)

|OQ| = radius = 13 cm

From the given information,

The distance of QR from O is twice the distance of PS from O

∴ |OU| = 2 × |OT|= 2 × 5 cm = 10cm

Thus,

13² = ||² + 12²

169 = 10² + |QU|²

|QU|² = 169 -100

|QU|² = 69

|QU| = √69

|QU| = 8.3 cm

Now,

Length of QR = 2 × |QU| = 2 × 8.3 cm

Length of QR = 16.6 cm

b)

Area of the trapezium = 1/2(|QR| + |PS|) × |TU|

Area of the trapezium = 1/2(16.6 + 24) × 15

NOTE: |TU| = |OT| + |OU|

Area of the trapezium = 1/2(40.6) × 15

Area of the trapezium = 20.3 × 15

Area of the trapezium = 304.5 cm²

Hence, the area of the trapezium is 304.5 cm²

Learn more on Calculating area of trapezium here: brainly.com/question/3435635

#SPJ1

7 0
2 years ago
Please answer the question if you can (this is 8th Grade math)
Contact [7]

Answer:

D

Step-by-step explanation: The two angles are not equal. The alternate interior angles theorem states that if the alternate interior angles are equal when a pair of lines is cut by a transversal, the two lines are parallel. However, the two angles are not parallel, so the lines are not parallel.

6 0
3 years ago
Read 2 more answers
ANS ASAP... will mark him/her as BRAINLIEST The 1rst one!!
prisoha [69]

7x - 14 = 4x + 19

7x - 4x = 14 + 19

3x = 33

x = 11

6 0
3 years ago
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