The radius of a circle is 7 cm.find its area to the nearest 10th

Answer: 15.85km

Step-by-step explanation:

The car starts at the point (0,0)

Let's define east as the positive x-axis and north as the positive y-axis.

first, the car travels 10km southeast, so the angle is -45° from the east.

Then the new position of the car is:

(10km*cos(-45°), 10km*sin(-45°)) = (7.07km, -7.07km)

Now, from this point the car travels 15km with an angle of 60° (counting from the east)

So the new position is:

(7.07km + 15km*cos(60°), -7.07km + 15km*sin(60°)) = (14.57km  , 5.91km)

The magnitude of a vector (x, y) is √(x^2 + y^2)

So the magnitude of the vector (14.57km  , 5.91km) is:

√((14.57km)^2 + (5.91km)^2) = 15.85km

The magnitude of the car's resultant vector is 15.72.

Given that,

A car travels 10km southeast,

And then 15 km in a direction 60 degrees north of east.

We have to find,

The magnitude of the car's resultant vector.

According to the question,

To resultant direction calculate by using the sum of vectors following all the steps given below.

A car travels 10 km southeast,

And then 15 km in a direction 60 degrees north of east.

The first vector has module is 10 and angle is 315°,

In the south direction, the angle is  270° and east is 360°,

So the angle in southeast,

[tex]\rm = \dfrac{270+360}{2}\\\\= \dfrac{630}{2}\\\\= 315 \ degree[/tex]

The second vector has module 15 and angle = 40°

Decompose both vectors in their horizontal and vertical component:

The horizontal component of the first vector is,

[tex]\rm = 10 \times cos(315) = 10 \times 0.70= 7.07[/tex]

The vertical component of the first vector is,

[tex]= \rm 10 \times sin(315) = -7.07[/tex]

The horizontal component of the second vector is,

[tex]\rm = 15 \times cos(60) = 15 \times 0.5= 7.5[/tex]

The vertical component of the second vector is,

[tex]\rm = 15 \times sin(40) = 15 \times 0.86= 12.99[/tex]

The sum of the horizontal component of the resultant vector is,

[tex]= 7.07+7.5=14.57[/tex]

And the sum of the vertical component of the resultant vector is,

[tex]= -7.07+12.99=5.91[/tex]

The magnitude of the vector (14.57km, 5.91km) is:

Therefore,

The magnitude of the car's resultant vector is,

[tex]\rm Resulatant = \sqrt{(14.57)^2+ (5.91)^2}\\\\ Resulatant = \sqrt{212.28+ 34.92} \\\ \\ Resulatant = \sqrt{247.20}\\\\ Resulatant = 15.72[/tex]

Hence, The required magnitude of the car's resultant vector is 15.72.

For more details refer to the link given below.

https://brainly.com/question/16541081

Answer:

90 km/hr

Step-by-step explanation:

If x is the speed of the slower car, and x+20 is the speed of the faster car, then:

5x + 5(x+20) = 1000

x + x + 20 = 200

2x + 20 = 200

x + 10 = 100

x = 90

Answer:

x = 18

Step-by-step explanation:

5(x - 8) = 50

Divide both sides by 5.

x - 8 = 10

Add 8 to both sides.

x = 18

Answer:

x=18

Step-by-step explanation:

5(x − 8) = 50.

5x-40=50

+40              +40

5x/5=90/5

x=18

Answer:

x²+(y-5)²=25

Step-by-step explanation:

To convert polar into rectagular

[tex]->r=\sqrt{x^2+y^2} =>r^2=x^2+y^2\\[/tex]

also, y=rsin θ => sin θ=y/r

r= 10sinθ

r=[tex]\frac{10y}{r}[/tex] => r²=10y

therefore, x²+y²-10y=0

By completing the squares on y²-10y gives

x²+(y-5)²=25

which is the equation of the circle.

This is the Cartesian equation of a circle with center  ( 0, 5)    

and radius,  r=5  

Answer:

C. y=1/2 x + 5

Step-by-step explanation:

In the attached file

Answer:

A is correct, when two lines have 1 intersection (1 solution).

Step-by-step explanation:

B Two lines are parallel => No intersection (no solution).

C Two lines are coincident => Many intersection (many solutions).

Hope this helps!

:)

Step-by-step explanation:

As these two lines are not parallel so going to intersect at one point so having one solution

Answer:

(p+e)/(r-n) =  x

Step-by-step explanation:

p + nx=rx-e

Add e to each side

p +e+ nx=rx-e+e

p +e+ nx=rx

Subtract nx from each side

p +e+ nx - nx=rx-nx

p+e = rx -nx

Factor out x

p+e = x(r-n)

Divide each side by (r-n)

(p+e)/(r-n) =  x(r-n)/(r-n)

(p+e)/(r-n) =  x

Answer:

a. 135 is correct

Step-by-step explanation:

We have the following information:

dogs lover: 150

cats lover: 120

as the null hypothesis:

H, there are equal number of dogs lover and cats lover, so the expected frequency in each cell will be equal and that is:

f = (150 + 120) / 2

f = 270/2 = 135

so option a. 135 is correct

Answer:3000m and 3km

Step-by-step explanation:

To convert from cm to m,divide by 100 and from m to km,divide by 1000

Answer:

  2.2×10⁹

Step-by-step explanation:

The distributive property is useful here. Recognize that 10⁹ is a common factor:

  (5.4×10⁹) - (3.2×10⁹) = (5.4 -3.2)×10⁹ = 2.2×10⁹

Answer: 2.2×10⁹

Step-by-step explanation:

Answer:

theres no picture.

Step-by-step explanation:

Answer:

C) -0.89 i think

Step-by-step explanation:

Answer:

[tex]\dfrac{3(y-5)}{2}[/tex]

Step-by-step explanation:

[tex]\dfrac{2y^2-6y-20}{4y+12}\div \dfrac{y^2+5y+6}{3y^2+18y+27}=\\\\\dfrac{2(y-5)(y+2)}{4(y+3)}\cdot \dfrac{3(y+3)^2}{(y+3)(y+2)}=\\\\\dfrac{6(y-5)(y+2)(y+3)(y+3)}{4(y+2)(y+3)(y+3)}=\\\\\dfrac{3(y-5)}{2}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

A

Answer:

D.

Step-by-step explanation:

A statistical question can answered by collecting data and having various answers. The other options refer to a specific person/thing and give only one piece of data while the last option refers to many teachers and many pieces of data.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

If the pattern continues, so that each term is separated by a distance of 3, then the sequence is given by the recursive rule

[tex]\begin{cases}a_1=1\\a_n=a_{n-1}+3&\text{for }n>1\end{cases}[/tex]

From this definition, we can write [tex]a_n[/tex] in terms of [tex]a_1[/tex]:

[tex]a_2=a_1+3[/tex]

[tex]a_3=a_2+3=(a_1+3)+3=a_1+2\cdot3[/tex]

[tex]a_4=a_3+3=(a_1+2\cdot3)+3=a_1+3\cdot3[/tex]

[tex]a_5=a_4+3=(a_1+3\cdot3)+3=a_1+4\cdot3[/tex]

and so on, up to

[tex]a_n=a_1+(n-1)\cdot3[/tex]

(notice how the subscript on a and coefficient on 3 add up to n)

or

[tex]a_n=1+3(n-1)=3n-2[/tex]

Answer:

n=1/2 of n x 8 divided by 4 -2

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Given that the formula of surface area of rectangular prism is S.A = 2(length×width) + 2(length×height) + 2(width×height). Then substitute the values into the formula :

Let length = 5,

Let width = 3,

Let height = 2,

[tex]s.a = 2(5 \times 3) + 2(5 \times 2) + 2(3 \times 2)[/tex]

[tex]s.a = 2(15) + 2(10) + 2(6)[/tex]

[tex]s.a = 15 + 15 + 10 + 10 + 6 + 6[/tex]

Answer:

The answer is D

Step-by-step explanation:

Answer:

total cost = $22.4 + $1.12 = $23.52

Step-by-step explanation:

Mr McNeil bought 2 magazines for $7.45 and 1 book for $14.95 . The sales tax is 6% . The total cost of Mr McNeil can be calculated as follows.

He bought 2 magazines for $7.45  .This means the sum of the prize of the 2 magazine he bought is $7.45 and the prize for the single book he bought is $14.95.  The total cost of the items he bought excluding the sales tax is the sum of the whole items he bought.

total cost excluding sales tax = $7.45 + 14.95 = $22.4

The sales tax is 5% which can be calculated as follows

5/100 × 22.4 = 112/100 = $1.12

The total cost of Mr McNeil purchase including his sales tax is

total cost = $22.4 + $1.12 = $23.52

Answer:

vaulue is 4

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

Brother's age =24

Om's age =19

Step-by-step explanation:

Let bro's age be x

Let om's age be x-5

x+x-5=43

2 x -5=43

2 x = 43+5

2 x = 48

x = 24

Answer:

It is 4

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

xsin∅

Step-by-step explanation:

If the ladder is x foot long, and it can safely make a maximum angle ∅  with the floor, then, the maximum height it can reach will be xsin∅

Answer:

Following the 4 to 1 ratio ladder rule

Step-by-step explanation:

set the base 1 foot out from the wall for every 4 feet it reaches up.

Answer:

8.4897959183673

Step-by-step explanation:

Answer:

3199

Step-by-step explanation:

3387 – 45 – 46 – 48 – 49 = 3199

Answer:

It is 48

Step-by-step explanation:

trust me I did the test.

Answer:

If there are 800 trees and 1/4 of them die to this disease.

Step-by-step explanation:

800=400x2=800/2=400 so 100/400 die so 200/800 die so in 4 years time the whole population will die.

Answer:

P(t)=800(3/4)^t

Step-by-step explanation:

Answer:

For the first case converting ml to L we got:

[tex] 200mL *\frac{1L}{1000 mL}= 0.2 L[/tex]

And we see that 0.2 L is lower than 2 L so then:

[tex] 200 mL < 2L[/tex]

And in the other way if we convert L to mL we got:

[tex] 2L *\frac{1000mL}{1L} = 2000 mL[/tex]

And we see that [/tex] 200mL < 2000 mL[/tex]

So then the answer would be <

Step-by-step explanation:

For this case we can solve this problem converting ml to L or converting L to ml.

For the first case converting ml to L we got:

[tex] 200mL *\frac{1L}{1000 mL}= 0.2 L[/tex]

And we see that 0.2 L is lower than 2 L so then:

[tex] 200 mL < 2L[/tex]

And in the other way if we convert L to mL we got:

[tex] 2L *\frac{1000mL}{1L} = 2000 mL[/tex]

And we see that [/tex] 200mL < 2000 mL[/tex]

So then the answer would be <

Answer:

14

Step-by-step explanation:

i uses a calculator and kept adding up

Answer:

The correct answer is C

Step-by-step explanation:

X+U= [-1,  -1] on the top and [0, -23/4] on the bottom

Therefore A-(X+U) gives you [5/3, 7] on the top and [4, 5] on the bottom

Hope this helps! :)

Answer:

Danke Shun!!!!!

Step-by-step explanation:

Oh mein Gott, danke für die kostenlosen Punkte, Kumpel !!

Please consider the attached file.

We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.

We will use Pythagoras theorem to solve for KJ as:

[tex]KJ^2=KM^2+MJ^2[/tex]

[tex]KJ^2=6^2+3^2[/tex]

[tex]KJ^2=36+9[/tex]

[tex]KJ^2=45[/tex]

Now we will take positive square root on both sides:

[tex]\sqrt{KJ^2}=\sqrt{45}[/tex]

[tex]KJ=\sqrt{9\cdot 5}[/tex]

[tex]KJ=3\sqrt{5}[/tex]

Therefore, the length of line segment KJ is [tex]3\sqrt{5}[/tex] and option D is the correct choice.

Answer:

Step-by-step explanation:

what is the length of line segment kJ