Q. 1. Solve for x using determinants, x + y = 9, x - y + 3z = 2 and 4y - 32 - 5 = 0.​

Answer:

The velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].

Acceleration is constantly [tex]6\; {\rm m\cdot s^{-2}}[/tex] (and thus is never [tex]0[/tex].)

Step-by-step explanation:

The distance between the particle and the initial position is the displacement of this particle. Let [tex]x(t)[/tex] denote the displacement (in meters) of this particle at time [tex]t[/tex] (in seconds.) The question states that [tex]x(t) = 3\, t^{2} + t[/tex].

Differentiate displacement [tex]x(t)[/tex] with respect to time [tex]t[/tex] to find the velocity [tex]v(t)[/tex] (in [tex]{\rm m \cdot s^{-1}}[/tex]) of this particle:

[tex]\begin{aligned}v(t) &= \frac{d}{d t}\left[x(t)\right] \\ &= \frac{d}{d t}\left[3\, t^{2} + t\right] \\ &= 6\, t + 1 \end{aligned}[/tex].

Set velocity to [tex]25\; {\rm m\cdot s^{-1}}[/tex] and solve for time [tex]t[/tex] (in seconds):

[tex]v(t) = 25[/tex].

[tex]6\, t + 1 = 25[/tex].

[tex]t = 4[/tex].

Thus, the velocity of this particle is [tex]25\; {\rm m \cdot s^{-1}}[/tex] at [tex]t = 4\; {\rm s}[/tex].

Differentiate velocity [tex]v(t)[/tex] with respect to time [tex]t[/tex] to find the acceleration (in [tex]{\rm m\cdot s^{-2}}[/tex]) of this particle:

[tex]\begin{aligned}a(t) &= \frac{d}{d t}\left[v(t)\right] \\ &= \frac{d}{d t}\left[6\, t + 1\right] \\ &= 6\end{aligned}[/tex].

In other words, the acceleration of this particle is constantly equal to [tex]6\; {\rm m\cdot s^{-2}}[/tex]. Hence, the acceleration of this particle is never [tex]0[/tex].

Answer:

bottom one

Step-by-step explanation:

use (x , y)

the top one is -3,2

the bottom one is 2,-3

This graph represents function of y = 3(x−2)²-3.

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

The vertex form of parabola :

y=a(x−h)²+k

(h,k)is the vertex of the parabola, and

Substitute vertex(2,-3), into equation

y = a(x−2)²-3

Substitute a = 3 into equation

y = 3(x−2)²-3

Here is a graph of the y = 3(x−2)²-3

Learn more about parabola here:

brainly.com/question/4074088

#SPJ5

The volume of the chocolate is the amount of choclate used in the cherries

The amount of chocolate used is 17.24 cubic centimeters

Start by calculating the volume of the cherries using:

V = 4/3 π(D/2)^3

The diameter of the cherry is 2.8 cm.

So, we have:

V = 4/3π(2.8/2)^3

Evaluate

V = 11.49

Next, calculate the volume of the cherry and the chocolate.

V = 4/3π(0.5+2.8/2)^3

V = 28.73

Calculate the difference (d) between both volumes

d = 28.73 - 11.49

d = 17.24

Hence, the amount of chocolate used is 17.24 cubic centimeters

Read more about volumes at:

https://brainly.com/question/10171109

Answer:

38.5

Step-by-step explanation:

The equation says

S - 1.8x = 6.1, where x is the amount of years after 1998.

2016 is 18 years after 1998.

S - 1.8*18 = 6.1

S= 32.4 + 6.1

S= 38.5

Answer:

17pi/36 (PLATO answer)

Step-by-step explanation:

The little square on the angle means that the entire angle is 90 degrees

The larger angle is made up of two angles of measure 'x - 18' and 'x'

Let's put that into an equation form:

     (x - 18) + (x) = 90

        2x - 18 = 90

           2x = 108

            x  = 54

So x = 54

Hope that helps!

Step-by-step explanation:

the area of a rectangle is length × width.

in our case

37 × 18 = 666 ft²

so, we need 666 ft² of tiles.

Answer:

666 square feet

Step-by-step explanation:

To find the number of square feet of tile, we need to find the area:

A = L × W

A = 18 × 37

A = 666 ft²

Answer:

D.)25 children and 75 adults

Equation 1: a + c = 100

Equation 2: 3a + 2c = 275

Step-by-step explanation:

A team t-shirt costs $3 per adult and $2 per child.

Let the number of children be = c

Let the number of adults be = a

A team t-shirt costs $3 per adult that is 3a and $2 per child that is 2c, also given is that the total money collected is $275, so equation becomes:

On a certain day, the total number of adults (a) and children (c) who bought shirts was 100, equation becomes:

Now to know the number of children and adult, we can check by plugging in the values from options provided.

25 children and 75 adults  = 25(2)+75(3)=50+225 =275

Answer:

$636.17

Step-by-step explanation:

       First, we need to find the volume of the ball. Then, we will solve for the cost of it.

       Volume of a sphere and solving for the area:

V = [tex]\frac{4}{3}[/tex]πr³

V = [tex]\frac{4}{3}[/tex]π(7.5)³

V ≈ 1767.15 in³

       Now that we have the volume, next we need to find the cost. Since the lead costs $0.36 per in³, and our volume is in in³, we can multiply the volume by the cost.

1767.15 in³ * $0.36 = 636.174

       Money rounds to the hundredth place,

636.174 -> $636.17

          It will cost $636.17 to make one ball.

Answer:

Volume of a sphere = 4/3 Pi r³

if r = 7.5

= 4/3 pi 7.5³

= 4/3 pi 421.87

= 1687.5/3 pi

= 562.5 Pi

= 1767.15 in³

then

1767.15 x 0.36 = 636.17

if 1 in³ costs 0.36$

then 1767.15 in³ costs 636.17$

Answer:

g= 81

Step-by-step explanation:

Replace X with 15

g = 6x -9

g = 6(15) - 9

g = 90 - 9

g = 81

Step-by-step explanation:

g=6x-9

putting the value of x

g=6×15-9

g=81

Answer:

6

Step-by-step explanation:

to find the perimeter of a trapezoid you add all the sides together

therefore we do it backwards

24-3-6-9=6

Solution :-

We know that perimeter is the sum of all sides, and here we have been provided with perimeter and the length of three sides. Now, we can assume the length of other side as any variable, say x. And develop a linear equation, and solve it. Thus,

A/Q,

→ 3yd + 6yd + 9yd + x = 24yd

→ 18yd + x = 24yd

→ x = 24yd - 18yd

→ x = 6yd

Thus, the length of the fourth side is 6yd.

Hope that helps :)

Answer:

£252.58

Step-by-step explanation:

$346 × £0.73/$1 = £252.58

Please rate!! I hope this helps!!

Answer:

20π

Step-by-step explanation:

Area = πr^2

100π = πr^2

solve for r and r = 10

circumference of a circle is 2πr

therefore 2π×10=20π in

Step-by-step explanation:

63/37 = 1.702 = 1.7

#Ihopethishleps

Answer:

160 cm²

Step-by-step explanation:

Hello!

We can find the area of the blue shaded. region by finding the area of the rectangle, and subtracting the area of the triangle.

Area of rectangle:

Find the area of the rectangle

The units are cm so the area is 200 cm²

Area Triangle:

Find the area of the triangle

The units are cm so our area is 40 cm²

Area Shaded:

Now we can simply subtract the triangle area from the rectangle.

Answer:

1/10

when you do the LCM you get 70

divide each fraction by 70 and you will get the least to be a tenth

5 dozen = 300

so

1 dozen = 300 : 5 = 60

so

x 7 = rs 420

Answer:

Rs 420

Explanation:

Find the cost of each dozen pencils

Then multiply by 7

Final answer:

Answer:

$3.78

Step-by-step explanation:

30 dollars minus 7 dollars and 28 cents is twenty-two and seventy-two cents, then minus another eighteen and ninety-four cents, would end up at three dollars and seventy-eight cents.

Answer:

[tex]\boxed{\$3.78}[/tex]

Step-by-step explanation:

To find out how much money does Kaya have left, we need to subtract the total money spent from the total money brought to the mall.

In this problem, we can tell that Kaya brought $30 to the mall as stated in the question. Furthermore, the problem states that she spent $7.28 on food, and $18.94 on a necklace. This means that the sum of 7.28 and 18.94 is the money spent by Kaya.

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[tex]\$30 - (\$7.28 + \$18.94) = \text{Money remained}[/tex]

➡ [tex]\$30 - (\$26.22) = \text{Money remained}[/tex]

➡ [tex]\$30 - \$26.22 = \text{Money remained}[/tex]

➡ [tex]\bold{\underline{\$3.78} = Money \ remained}}[/tex]

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Answer:

B and E

Step-by-step explanation:

E is 3/4 8 times (this is just simple multiplication) and B is 3/4 8 times just shorter. Simplified if you will.

Answer:

40

Step-by-step explanation:

you have to multiply x by 4 to get y when x=4 and y=16. so if x=10, then you have to multiply what x is (10) by 4 because there is a common ratio.

hope this helps!! please give brainliest!!!!!!

Answer:

The graph would not be as able to see the form and/or function so hope this helps

Answer:

I believe he sells each bar for .75 cents

Answer:

47.6 euros

Step-by-step explanation:

68 x .70 = 47.6

.70 = 70%

70% of 68

of means multiply

You turn the percent into a decimal and multiply

Answer:

15 students in each bus.

Step-by-step explanation:

Subtract 10 from 100 and you get 90 then divide 90 by 6 and that gives you how many students in each bus

[tex]\dfrac{x^2+7x+12}{x^2-x-12}\\\\=\dfrac{x^2 +3x+4x +12}{x^2 -4x+3x-12}\\\\=\dfrac{x(x+3)+4(x+3)}{x(x-4)+3(x-4)}\\\\=\dfrac{(x+4)(x+3)}{(x-4)(x+3)}\\\\=\dfrac{x+4}{x-4}\\\\\text{Restrictions:}~ x\neq 4 ,~ x\neq -3[/tex]

Answer:

the answer is 3040 and does