Calculate the volume of the figure.

Step-by-step explanation:

At t = 20 min, V = 45,000 L.

At t = 70 min, V = 0 L.

a) The rate is the slope:

m = ΔV/Δt

m = (0 L − 45,000 L) / (70 min − 20 min)

m = -900 L/min

b) Using the slope to find V when t = 0 min:

m = ΔV/Δt

-900 L/min = (V − 0 L) / (0 min − 70 min)

V = 63,000 L

c) Use slope-intercept form to find the equation.

V = -900t + 63,000

d) At t = 62 min:

V = -900(62) + 63,000

V = 7200

Answer:

a. -900 L/min

b. Vo = 63,000 Liters

c. V ( t ) = 63,000 - 900*t

d. 7,200 Liters

Step-by-step explanation:

Solution:-

We have a swimming pool which is drained at a constant linear rate. Certain readings were taken for the volume of water remaining in the pool ( V ) at different instances time ( t ) as follows.

                t = 20 mins ,   V = 45,000 Liters

                t = 70 mins , V = 0 Liters

To determine the rate ( m ) at which water drains from the pool. We can use the linear rate formulation as follows:

                             [tex]m = \frac{V_2 - V_1}{t_2 - t_1} \\\\m = \frac{0 - 45000}{70 - 20} \\\\m = \frac{-45,000}{50} = - 900 \frac{L}{min}[/tex]

We can form a linear relationship between the volume ( V ) remaining in the swimming pool at time ( t ), using slope-intercept form of linear equation as follows:

                              [tex]V = m*t + V_o[/tex]

Where,

                  m: the rate at which water drains

                  Vo: the initial volume in the pool at time t = 0.

We can use either of the data point given to determine the initial amount of volume ( Vo ) in the pool.

                           [tex]0 = -900*( 70 ) + V_o\\\\V_o = 63,000 L[/tex]

We can now completely express the relationship between the amount of volume ( V ) remaining in the pool at time ( t ) as follows:

                             [tex]V ( t ) = 63,000 - 900*t[/tex]

We can use the above relation to determine the amount of volume left after t = 62 minutes as follows:

                           [tex]V ( 62 ) = 63,000 - 900*(62 )\\\\V ( 62 ) = 63,000 - 55,800\\\\V ( 62 ) = 7,200 L[/tex]

Answer:

A

Step-by-step explanation:

Answer:

4x^3+8x^2

Step-by-step explanation:

Multiply each term:

4x^3+8x^2

PLZ MARK ME BRAINLIEST

Answer:

The share price increased by $40

Step-by-step explanation:

In the first year: (t = 1)

=> V = [tex]2.95 +2log10(10(1)+1)[/tex]

=> [tex]V = 2.95 + 2 (10+1)\\V = 2.95+2(11)[/tex]

=> [tex]V = 2.95+22[/tex]

=> V = $ 24.95

In the 3rd Year: (t = 3)

=> [tex]V = 2.95 + 2log10(10(3)+1)[/tex]

=> [tex]V = 2.95+ 2(30+1)[/tex]

=> [tex]V = 2.95+2(31)[/tex]

=> V = 2.95 + 62

=> V = $64.95

The Share Price increased by:

=> $64.95-$24.95

=> $40

The share price increased by $40

Answer:

Step-by-step explanation:

a) Since these are production vehicles, we don't expect their top speed to be more than about 70 m/s, so the distance functions probably lose their validity after t = 25. Of course, t < 0 has no meaning in this case, so the suitable domain is about ...

  0 ≤ t ≤ 25

Note that the domain for the second car would be 3 ≤ t ≤ 25.

__

b) The graph of this system shows the cars will both have driven the same distance after 16.348 seconds.

__

c) At that time, the cars will have driven 310.0 meters.

_____

Non-graphical solution

If you like, you can solve the equation for t:

  d1 = d2

  1.16t^2 = 1.74(t -3)^2

  0 = 0.58t^2 -10.44t +15.66

  t = (10.44 +√(10.44^2 -4(0.58)(15.66)))/(2(0.58)) = (10.44+8.524)/1.16

  t = 16.348 . . . . time in seconds the cars are at the same distance

That distance is found using either equation for distance:

  1.16t^2 = 1.16(16.348^2) = 310.036 . . . meters

Answer:

The distance from AD to BC is 7

Step-by-step explanation:

The information given are;

The type of inscribed quadrilateral ABCD = Isosceles trapezoid

The radius of the circle = 5

Segment AD of ABCD = 6

The median of the trapezoid ABCD = 7

Given the trapezoid theorem, the median is equal to half the length of the two bases added together, we have;

(AD + BC)/2 = 7

Which gives;

(6 + BC)/2 = 7

BC = 7×2 - 6 = 8

Therefore the distance from AD to BC is given by the distance from BC to the median line added to the distance from AD to the median line given as follows;

The distance from BC to the median = √(Radius² - (BC/2)²) = √(5² - (8/2)²) = 3

The distance from BC to the median = 3

The distance from AD to the median = √(Radius² - (AD/2)²) = √(5² - (6/2)²) = 4

Which gives;

The distance from AD to BC = 3 + 4 = 7

Answer:

duty = 64

Total cost is 224

Step-by-step explanation:

First find the cost of the 5 sets

5 * 32 = 160

Then find the duty

160 * 40%

160 * .4 =    64

Add this to the cost of the sets

160+64 =224

Answer:

The larger canister has 8 times the volume and 4 times the volume of the smaller one.

Step-by-step explanation:

The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.

The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.

The canisters are in the shape of a cylinder.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

The surface area of a cylinder is given as:

A = 2πr(r + h)

SMALLER CANISTER

Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres

Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres

LARGER CANISTER

Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres

Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres

By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.

Answer:

Yeah, what they said above.

Step-by-step explanation:

Answer:

A

i

Step-by-step explanation:

Hope it helps

Answer:

[tex]\displaystyle x = \frac{\pi}{3} +k\, \pi[/tex] or [tex]\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi[/tex], where [tex]k[/tex] is an integer.

There are three such angles between [tex]0[/tex] and [tex]2\pi[/tex]: [tex]\displaystyle \frac{\pi}{3}[/tex], [tex]\displaystyle \frac{2\, \pi}{3}[/tex], and [tex]\displaystyle \frac{4\,\pi}{3}[/tex].

Step-by-step explanation:

By the double angle identity of sines:

[tex]\sin(2\, x) = 2\, \sin x \cdot \cos x[/tex].

Rewrite the original equation with this identity:

[tex]2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0[/tex].

Note, that [tex]2\, (2\, \sin x \cdot \cos x)[/tex] and [tex](-2\, \sin x)[/tex] share the common factor [tex](2\, \sin x)[/tex]. On the other hand, [tex]2\sqrt{3}\, \cos x[/tex] and [tex](-\sqrt{3})[/tex] share the common factor [tex]\sqrt[3}[/tex]. Combine these terms pairwise using the two common factors:

[tex](2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0[/tex].

Note the new common factor [tex](2\, \cos x - 1)[/tex]. Therefore:

[tex]\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0[/tex].

This equation holds as long as either [tex]\left(2\, \sin x + \sqrt{3}\right)[/tex] or [tex](2\, \cos x - 1)[/tex] is zero. Let [tex]k[/tex] be an integer. Accordingly:

Any [tex]x[/tex] that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

Answer:

Step-by-step explanation:

There is only one intercepting point, it means one solution.

Answer:

answer pic below :)

Step-by-step explanation:

Answer:

Four unique planes

Step-by-step explanation:

Given that the points are non co-planar, triangular planes can be formed by the joining of three points

The points will therefore appear to be at the corners of a triangular pyramid or tetrahedron such that together the four points will form a three dimensional figure bounded by triangular planes

The number of triangular planes that can therefore be formed is given by the combination of four objects taking three at a time as follows;

₄C₃ = 4!/(3!×(4-3)! = 4

Which gives four possible unique planes.

Answer:

36°

Step-by-step explanation:

<U + < V + <W = 180° (sum of angles in a triangle)

<W = 54°

The tangent is always perpendicular to the radius drawn to the point of tangency...

therefore,

<U = 90°

90° + <V + 54° = 180°

144° + <V = 180°

<V = 180° - 144°

<V = 36°

Answer:

V=36

Step-by-step explanation:

tangent makes rigt angle with radius angle U=90

W+V+U=180

V=180-90-54

V=36

Answer:

(a) D(t) = 250t -500 miles

(b) Controller has 2 hours, but including time for pilots to divert course or altitude.

Step-by-step explanation:

Given:

two planes at same altitude heading in a collision course.

Plane A at 400 miles from collision point at 200 mph

Plane B at 300 miles from collision point at 150 mph.

Theoretical collision happens in

t = 400/200 = 300/150 = 2 hours

Distance ya of plane A from collision point as a function of time in hours

ya(t) = 400 -200t

Distance yb of plane B from collision point as a function of time in hours

yb(t) = 300-150t

(a) Distance between two planes,

Since the two planes are on courses perpendicular to each other, will need using pythagorean theorem

D(t) = sqrt(ya(t)^2+yb(t)^2)

= sqrt((400-200t)^2+(300-150t)^2)

= 250(t-2)

D(t) = 250t -500 miles

b. time available

Time until D(t) = 0

solve D(t) = 0

D(t) = 0

250(t-2) = 0

t = 2  (two hours)

Answer:

a) -500 mph

b) 1/2 h

Step-by-step explanation:

a)[tex]\frac{ (150(-300))+(200(-400))}{\sqrt{150x^{2} +200^{2} } }[/tex]

b) [tex]\frac{\sqrt{150^{2}+200^{2} } }{500}[/tex]

Answer:

<3 = 112 degrees

<4 = 68 degrees

Step-by-step explanation:

<3 = 112 degrees (Alternate angles are congruent)

And,

<4+<3 = 180 (Angles on a straight line add up to 180)

=> <4 + 112 = 180

=> <4 = 180-112

=> <4 = 68 degrees

Answer:

Step-by-step explanation:

Angles at a point add up to 360°

To find x add up all the angles and equate them to 360°

That's

168 + 123 + x = 360

291 + x = 360

x = 360 - 291

x = 69°

Hope this helps you

Answer:

x = 69

Step-by-step explanation:

The sum of a circle is 360 degrees

x+ 168+123 = 360

Combine like terms

x +291 = 360

Subtract 291 from each side

x+291-291 = 360-291

x =69

Answer:

Step-by-step explanation:

Since there are two lines on the graph, we will find the equation of both lines. The standard form of equation of a line is y = mx+c where;

m is the slope of the line = y₂-y₁/x₂-x₁

c is the intercept (the point where the line cuts the y axis)

For the blue line;

It can be seen that the coordinate of the lines are (1,4) and (0, -1)

m = -1-4/0-1

m = -5/-1

m = 5

For this line, it can be seen that the line cuts the y-axis at -1, hence the intercept of the line is -1

The equation of the blue line will be y = 5x+(-1)

y = 5x-1

For the red line;

It can be seen that the coordinate of the lines are (0,5) and (5, 0)

m = 0-5/5-0

m = -5/5

m = -1

For this line, it can be seen that the line cuts the y-axis at 5, hence the intercept of the line is 5

The equation of the red line will be y = -x+5

Hence, the system of equations that has the solution shown in the graph are y = 5x-1 and  y = -x+5

Answer:

  B(-6, 0)

Step-by-step explanation:

You want to find B such that ...

  (B -A) = (3/4)(C -A) . . . . the required distance relation

  4(B -A) = 3(C -A) . . . . . . multiply by 4

  4B = 3C +A . . . . . . . . . . add 4A, simplify

Now, we can solve for B and substitute the given coordinates:

  B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)

The coordinates of point B are (-6, 0).

Answer:

the answer your looking for is (-3,-3)

Step-by-step explanation:

Answer:

1.

a) exact form: -1 /14 or decimal form: -0.0714285

b) exact form: -23/120 or decimal form: -0.1916

2.

a) 89

b)98

c) 5.7

d) 4.8

3.

i) 2*2*2*2*2*2*3*3*3

ii) 3*3*3*5*5*5

iii) 2*2*2*2*2*2*2*2*2*2*2*2

iv) 2*2*2*2*2*2*5*5*5

9.

i) x = -9

ii) x + 1/7

I hope this helps get you started :)

Answer:

y=2x-5

Step-by-step explanation:

y=mx+c

mx=slope

In this case, the slope is already given to you which means the m=2.

y=2x+c.

The coordinates are (14, 23) and when you put -5 into c, the line goes through the coordinates (14, 23).

Hope this helps!

Answer:

U to V: 5/2

V to U: 2/5

Step-by-step explanation:

Simplify the ratio of the corresponding sides.

20 in to 8 in

25 in to 10 in

30 in to 12 in

Answer:

This means volume of the larger canister is 8 times more than volume of the smaller canister.

This means surface area of the larger canister is 4 times greater than volume of the smaller canister.

Step-by-step explanation:

Smaller canister

Diameter=9cm

Radius=diameter/2

=9/2=4.5cm

Height=12cm

Larger canister (double of the smaller canister)

Radius=4.5*2=9cm

Height=12*2=24cm

Volume=πr^2h

Surface area=2πrh + 2πr^2

Volume of smaller canister=πr^2h

=3.14*(4.5)^2*12

=3.14*20.25*12

=763.02

Surface area of the smaller canister=2πrh + 2πr^2

=2*3.14*4.5*12 + 2*3*14*(4.5)^2

=339.12 + 127.17

=466.29

Volume of larger canister=πr^2h

=3.14*(9)^2*24

=3.14*81*24

=6104.16

Surface area of larger canister=2πrh + 2πr^2

=2*3*14*9*24 + 2*3.14*(9)^2

=1356.48 + 508.68

=1865.16

Compare smaller and larger volume of the canister:

Volume if larger/volume of smaller

=6104.16/763.02

=8

This means volume of the larger canister is 8 times more than volume of the smaller canister

Compare surface area of larger and smaller canister:

Surface area of larger canister/surface area of smaller canister=1865.16/466.29

=4

This means surface area of the larger canister is 4 times greater than volume of the smaller canister

Answer:

Yeah, what she said above.

Step-by-step explanation:

Answer: The number of possibilities = 380

Step-by-step explanation:

Given, There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen.

Since, captain and alternate captain comes in order.

Number of ways to choose r things out of n things (when order matters) :

[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]

Number of ways to choose 2 players ( for  captain and alternate captain ) from 20 players :

[tex]^{20}P_2=\dfrac{20!}{18!}=20\times19=380[/tex]

Hence, the number of possibilities = 380

Answer:

so if it is asking about the exact percentage then the answer is B but if it is the percentage in all the answer is D.

Step-by-step explanation:  My reasoning behind is that 70 percent of the neighborhood wants a playground if it is 40 to 17

Percentage Hill point residence want playground is about 70% .

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

According to the question

Hill point residence want playground =  0.40

Total who want playground = 0.58

now,

Percentage Hill point residence want playground over total

[tex]\frac{0.40}{0.58} *100[/tex]

= 68.96%

≈ 70%

Hence, Percentage Hill point residence want playground is about 70% .

To know more about Percentage here:

https://brainly.com/question/16797504

#SPJ2

Answer:

7.1 inches

Step-by-step explanation:

perimeter you go round from apointof your choice so

add 2+2=4

then apply 1/4πd for the round part

d=4 and it's quarter a circle then add them together

Answer:

7.1 inches

Step-by-step explanation:

To find the perimeter of the circle you would need to follow the formula: 2piR. Since r=2, 2*2=4. So 4 multiplied by pi (3.14 or 22/7). Since this is a quarter of a circle you would divide the answer 12.56 by four which equals 3.14. Now just add the extra two 2s left on the flat sides of the figure which ends up with your answer of 7.14 OR 7.1.

Hope this helps!! <3

Answer: I think it's 2

Step-by-step explanation: i am not dat good at math

Answer:

33m 40cm.

Step-by-step explanation:

One side of the shed measures 8 meters and 35 centimetres, which is 800 + 35 = 835 centimetres.

Since the shed is a square, all side lengths are 835 centimetres long. So, the perimeter is 835 * 4 = 3,340 centimetres. That means that the perimeter is 33 meters and 40 centimetres.

Hope this helps!

Part A

Answer:  33.2 degrees F

Explanation: Adding on a negative is the same as subtracting. So 72.3 + (-39.1) = 72.3 - 39.1 = 33.2

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

Part B

Answer: 70 +  2   +  0.3    + (-30) + (-9) + (   -0.1   )

Explanation:

Think of 72 as 70+2. Furthermore, think of 72.3 as 70+2+0.3; we just break the number up into its corresponding digits (adding zeros when needed). The 7 is in the tens place, the 2 is in the units or ones place, and the 3 is in the tenths place.

Similarly, we have 39.1 break down into 30+9+0.1, in which all three terms are made negative to represent -39.1

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

Part C

Answer:   70 + (-30) + 2 + (-9) + 0.3 + ( -0.1  )  

Explanation: Arrange the tens place value items to be next to each other. Same goes for the units place value, and also the tenths place value.

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

Part D

Answer:  [70 + (-30)] +  [ 2 + (-9) ] + [ 0.3 + ( -0.1  ) ]

Explanation: Take the result of part C and surround each pair of terms in square brackets to show how the terms pair up.

Answer:

18

Step-by-step explanation:

Answer:

18.

Step-by-step explanation:

[4 + (3 - 1)] * 3

= (4 + 2) * 3

= 6 * 3

= 18

Hope this helps!