A ball, thrown vertically upwards, from the ground, has its height h (in meters) expressed as a function of time t (in seconds), elapsed after the launch, by the law h(t) = 20t - 5t2. According to this information, determine the height at which the ball is 3 seconds after the throw and the maximum height reached by the ball.

Answer:

Step-by-step explanation:

Distribute 7 to the first number

7 * -3/4 = -21/4

-21/4 = 5  -1/4

Distribute 7 to the second number

7 * -3

= -21

Put the numbers together

They separated the parenthesis.

So it is still 7 * -3/4

and

7*-3.

Hope this helps,

Kavitha

Answer: the value of the integral is in the range:

0.006  ≤  int ≤  0.008

Step-by-step explanation:

First, we have the function

5*tan(3x), and the range in this case is: pi/12 ≤ x ≤ pi/9

Then, the first step is find the maximum and minimum of f(x) in this range.

We know that between 0 and pi/2, tan(x) is a growing function, then

then the limits are

5*tan(3*pi/9) = 5*tan(pi/3) = M=  0.091

5*tan(3*pi/12) = 5*tan(pi/4) =m = 0.069

Then the value of the integral is between:

0.069*(3.14/9 - 3.14/12) ≤  int ≤  0.091*(3.14/9 - 3.14/12)

0.006  ≤  int ≤  0.008

Answer:

h=3V/πr²

Step-by-step explanation:

Answer:

3V / (pi r^2) =  h

Step-by-step explanation:

V= pi r squared h/3

Multiply each side by 3

3V = pi r^2 h /3  * 3

3V = pi r^2 h

Divide each side by pi r^2

3V / (pi r^2) = pi r^2 h /( pi r^2)

3V / (pi r^2) =  h

Answer:

2:8 is the ratio to an equal ratio

Answer:

3:2

Step-by-step explanation:

Ewen has 48 white tiles and 16 blue tiles

The cost of each white tile was £2

The cost of each blue tile was £4

Therefore the total cost of 48 white tiles is

= 48×2

= £96

The total cost of 16 blue tiles is

= 16×4

= £64

The ratio of the total cost of the white tiles and blue tile can be calculated by dividing the cost of both tiles by their greatest common factor

The greatest common factor of £96 and £64 is 32

96/32 = 3

64/32= 2

Ratio= 3:2

Hence the ratio of the total cost of the white tiles to the blue tiles is 3:2

Answer:

To find the circumference

diameter x 3.14 = circumference

We can undo the multiplication and divide to get the diameter

37.68 /3.14 = 12

diameter / 2= radius

12 / 2 = 6

the radius is 6

radius x radius x pi = area

6 x 6 x 3.14 = 113.04

113.04 is the answer

Hope this helps

Step-by-step explanation:

Answer:

113.04 square inches.

Step-by-step explanation:

The formula to find the circumference is 2πr. The formula for the area is πr^2. We are trying to find r in order to solve the problem.

It says use 3.14 for π. The circumference is 37.68 inches.

2πr = 37.68

2 * 3.14r = 37.68

3.14r = 18.84

r = 6

Now that we know the radius of the circle, we can find the area!

πr^2 = 3.14 * (6^2) = 3.14 * 36 = 113.04.

Hope this helps!

Answer:

              [tex]\underline{x\in\left\{-6\,,\ 1\right\}}[/tex]

Step-by-step explanation:

[tex]x^2+5x-6=0\\\\a=1\,,\ \ b=5\,,\ \ c=-6\\\\x_1=\dfrac{-5-\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5-\sqrt{25+24}}2=\dfrac{-5-\sqrt{49}}2=\dfrac{-5-7}2=-6\\\\x_2=\dfrac{-5+\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5+7}2=1[/tex]

Answer:

Step-by-step explanation: Answer is B-6,1

Answer:

A ; -4

Step-by-step explanation:

3a = 12b then a = 4b (dividing by 3)

we put 4b in the equation instead of a:

(-4b / b) = -4

.. ..

Answer:

A. -4

Step-by-step explanation:

3a/b = 12

Let b = 2

3a/2 = 12

3a = 24

a = 8

( - a/b)

( - 8/2)

( - 4)

Answer:

P(XX) = 69/190

Step-by-step explanation:

Given:

20 balls, 10R, 3B, 7W.

Two taken without replacement.

Find probability of two identical colours.

P(XX)

Solution:

We use the multiplication rule for the probability of each of the 2 draws

P(RR) = 10/20*9/19 = 90/380

P(BB) = 3/20*2/19 = 6/380

P(WW) = 7/20*6/19 = 42/380

Probability of drawing two identical coloured balls

P(XX) = (90+6+42)/380 = 138/380 = 69/190

Answer:

it could be angle DGF or CGA (they are both supplementary to angle CGD)

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

From the blue graph of f(x) we can see that the function value is -6 when x = 6.  Similarly, g(5) = -5.

Then:  4*f(6) - 6*g(5) becomes:

           4*(-6) - 6*(-5), or

              -24 +  30  = 6

The value of ⋅f(6)−6⋅g(5)= 6

An operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).

Given:

From the blue graph we can see that

f(x)= -6 when x = 6.

Similarly, g(5) = -5.

thus,

4*f(6) - 6*g(5)

=3 4*(-6) - 6*(-5)

=-24 +  30

= 6

Learn more about this concept here:

https://brainly.com/question/20379727

#SPJ2

Answer:

4. -1/2 and 2

5. N and R

Step-by-step explanation:

Well if you want me too do 5 I’ll do 4 too.

So for #4 it’s actually pretty simple we just have to seperate y that’s it.

So first we have to get y by itself by subtracting 3x to the other side so the equation looks like this now [tex]6y=-3x+12[/tex].

Now we have to take away the 6 and to do that we divide it to all the numbers and variables. Which gets us [tex]y=-1/2x+2[/tex].

So m and b are -1/2 and 2.

So we have to graph y = -1/2x + 2 so look at the image below.

So looking at the image we can see it passes through the points N and R.

Answer:

The line passes through points N and R.

Step-by-step explanation:

I graphed the equation on the graph below.

Answer:  [tex]\bold{b)\quad \dfrac{\pi}{2}+n\pi,\ \dfrac{\pi}{4}+2n\pi}[/tex]

Step-by-step explanation:

cos x tan x - cos x = 0

cos x (tan x - 1) = 0

cos x = 0          tan x - 1 = 0

[tex]x=\dfrac{\pi}{2},\ \dfrac{3\pi}{2}[/tex]         tan x = 1

                         [tex]x=\dfrac{\pi}{4},\ \dfrac{5\pi}{4}[/tex]

Thanks! I hope my answer would be easy to understand.

Answer:

85.33333

Step-by-step explanation:

You would simply substitute 4 whenever there is an x.

f(4) = (1/3) * 4^4

= (1/3) * 16 * 16

= (1/3) * 256

= 256/3

= 85.3333333333333333333333333333333333333

which is about 85.3333, or 85 and 1/3, or 256/3.

Hope this helps!

Answer:Y=9

Step-by-step explanation:

Answer:

Y=9

Step-by-step explanation:

Took the test and got 100%.

Answer:

40m³

Step-by-step explanation:

[tex]\sqrt[3]{5}[/tex] = 1.709975947

1.709975947 × 2 = 3.419951893

3.419951893³ = 40

Answer:

volume of the box multiply scale factor

=5 × 2

=10m

Answer:

An inequality is a relation which makes a non equal comparison between two of more numbers or other mathematic equations. > I'd greater than < is less than = equal to. ≥ is greater than or equal ≤ less than or equal to. = equal to ≠ not equal

Step-by-step explanation:

Inequality- is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Answer:

En una semana, 1344 kilos

En un mes, 5760 kilos

Step-by-step explanation:

Tambo tiene 12 vacas y cada vaca produce un promedio de 16 litros por día.

Por lo tanto, en un día, las 12 vacas podrían producir:

12 * 16 = 192 litros

En una semana, las 12 vacas podrían producir:

192 * 7 = 1344 litros = 1344 kilos

En un mes, las 12 vacas podrían producir:

192 * 30 = 5760 litros = 5760 kilos

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

-200, 0 and -5

Step-by-step explanation:

Area can never be zero or negative.

Answer:

125°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 8 (octagon), thus

sum = 180° × 6 = 1080°

let x represent one of the equal angles, then

3x + 705 = 1080 ( subtract 705 from both sides )

3x = 375 ( divide both sides by 3 )

x = 125

Thus the size of one equal angle = 125°

Answer:

-3

Step-by-step explanation:

Given the function f(x) = -(-x)

we want to evaluate f(-3)

What we do simply here is substitute the value of -3 for x in the equation

That would be ;

f(-3) = -(-(-3)) = -(3) = -3

Answer:

VA/VB = 8

Step-by-step explanation:

You have a sphere A with diameter 12, that is, radius 6, which can be written as follow:

[tex]V_A=\frac{4}{3}\pi r_A^3=\frac{4}{3}\pi (6)^3=288\pi[/tex]             (1)

The sphere A is dilated by a scale factor of one half to sphere B. Then, you have:

[tex]V_B=\frac{4}{3}\pi r_B^3=\frac{4}{3}\pi (\frac{6}{2})^3=36\pi[/tex]       (2)

From the results of equation (2) and (1) you can calculate the ratio VA/VB:

[tex]\frac{V_A}{V_B}=\frac{288\pi}{36\pi}=8[/tex]

The ratio of the volumes of both sphere A and B is 8

Answer:

8:1

Step-by-step explanation:

hope this helps

Answer:

I guess that we want to create 4 digit numbers that are divisible by 5, only using the odd numbers in the image.

We know that a number is divisible by 5 only if the last digit (the units digit) is a zero or a five, in the image we only have a five, so our 4-digit numbers need to end with a five, so we have a digit fixed in five and the other 3 digits can be other numbers.

We have two different approaches to this:

First, if each odd number can be used only once, we already used the five, so we can use the other 4 numbers.

Then, for the first digit, we have 4 options.

for the second digit, we have 3 options (because we already used one)

for the third digit, we have 2 options (because we already used 2)

then the number of combinations is equal to the product of the number of options for each selection:

C = 4*3*2 = 24 combinations.

The second approach is If the numbers in the image can be repeated (for example, 5555 or 3435 are allowed)

we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third, we also have 5 options, then, with the same reasoning as above, we have:

C = 5*5*5 = 25*5 = 125 combinations.

Answer:

D

Step-by-step explanation:

10 dimes = 1.00

3 nickels =15 cent

Answer:

B. 5 nickles and 9 dimes

Step-by-step explanation:

For this problem, the answer needs to both be equivalent to $1.15 and have a total of 14 nickels and dimes.

B is the only answer choice that has a total of 14 nickels and dimes and is equivalent to $1.15:

9 nickels+5 dimes=total of 14 coins while 5 nickels (25 cents) and 9 dimes (90 cents) is equivalent to $1.15.

Answer:

the solution to the system of nonlinear equations is C. (0,3)

Answer:

c. x - 2/3

Step-by-step explanation:

The given equation is f(x) = [tex]3x^4 - 5x^3 - 71 x^2 + 157x + 60[/tex]

To test if the given equations are factors of the polynomial, check if the remainder is equal to zero if substituted into the equation.

For x - 3, x = 3

Substituting x = 3 into the given polynomial:

[tex]f(3) = 3(3)^4 - 5(3)^3 - 71 (3)^2 + 157(3) + 60\\f(3) = 0[/tex]

x - 3 is a factor

For x - 4, x = 4

Substituting x = 4 into the given polynomial:

[tex]f(4) = 3(4)^4 - 5(4)^3 - 71 (4)^2 + 157(4) + 60\\f(4) = 0[/tex]

x - 4 is a factor

For x - 2/3, x = 2/3

Substituting x = 2/3 into the given polynomial:

[tex]f(2/3) = 3(2/3)^4 - 5(2/3)^3 - 71 (2/3)^2 + 157(2/3) + 60\\f(2/3) = 132.22[/tex]

x - 2/3 is  not a factor

For x + 1/3, x = -1/3

Substituting x = -1/3 into the given polynomial:

[tex]f(-1/3) = 3(-1/3)^4 - 5(-1/3)^3 - 71 (-1/3)^2 + 157(-1/3) + 60\\f(-1/3) = 0[/tex]

x + 1/3 is  a factor

Answer:

(a) 0.2824

(b) 0.0002441

Step-by-step explanation:

Assuming that the population is large enough to behave as a binomial distribution (between whites and non-whites), the probability of 12 out of 12 juros being white is:

[tex]P(w=12) = p(w)^{12}[/tex]

Where p(w) is the proportion of the population that is white:

(a) for p = 0.90

[tex]P(w=12) = 0.90^{12}\\P(w=12) =0.2824[/tex]

The probability is 0.2824.

(b) for p = 0.50

[tex]P(w=12) = 0.50^{12}\\P(w=12) =0.0002441[/tex]

The probability is 0.0002441.

Hey there! :)

Answer:

x = -6.

Step-by-step explanation:

Given:

[tex]\sqrt[3]{5x-4} = \sqrt[3]{7x + 8}[/tex]

Cube both sides:

5x - 4 = 7x + 8

Subtract 5x from both sides:

-4 = 2x + 8

Subtract 8 from both sides:

-12 = 2x

x = -6.