pls help i need help asap

The depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

To find the rate at which the depth of the water is changing, we can use related rates.

Given:
Height of the cone (h) = 8 meters
Base radius (r) = 26 meters
Rate of filling (dV/dt) = 12 m³/s
Radius of the top of the water (x) = 10 meters

First, we establish the relationship between the height and radius of the cone using similar triangles. The ratio of the height to the radius is constant, so we have h/r = 8/26.

Next, we differentiate both sides of the equation with respect to time (t) to find dh/dt in terms of dx/dt. This gives us (dh/dt)/(dr/dt) = 0.3077.

We can then substitute the given values into the equation: (dh/dt)/(dx/dt) = 0.3077. Rearranging the equation, we find that dx/dt = (dh/dt) / 0.3077.

To find the value of dh/dt, we can substitute the given rate of filling, dV/dt = 12 m³/s, into the equation. Solving for dh/dt, we get dh/dt = 3.693 m/s.

Finally, we substitute the values of dh/dt and 0.3077 into the equation to find dx/dt. This gives us dx/dt ≈ 0.39 m/s.

Therefore, the depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

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The number of different groups of team captains that could be made is 1771 groups

We are given that;

Number of baseball team players; n = 23 players

Number of players chosen randomly; r = 3 players

Now, to know how many different groups of team captains could be made, we will make use of the combination formula which is;

nCr = n!/(r!(n - r)!)

Thus;

23C3 = 23!/(3!(23 - 3)!) = 1771

Thus, we conclude that the number of different groups of team captains that could be made is 1771 groups

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Answer:

x=-3

Step-by-step explanation:

5x+3=2x-6

-2x (both sides)

3x+3=-6

-3 (both sides)

3x=-9

divided by 3 (both sides)

answer is x=-3

Answer:

x= -3

Step-by-step explanation:

Answer:

x = √89

Step-by-step explanation:

The question shows a diagram of a right-angled triangle. The lengths of two of the shorter sides are given, while the length of the longest side, called the hypotenuse of the triangle, needs to be calculated.

To do this, we have to use the Pythagorean Theorem:

\(\boxed{a^2 + b^2 = c^2}\)

where:

a, b ⇒ lengths of the two smaller sides of the triangle

c ⇒ length of the hypotenuse

The given lengths of the two smaller sides of the triangle are 5 and 8 units. Therefore, using the above formula, we can calculate the length of the hypotenuse, x:

5² + 8² = x²

⇒ 25 + 64 = x²

⇒ 89 = x²

⇒ x = √89

Therefore, the third option is correct.

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Find the slope of the parallel line

(7, 2) and is parallel to y= -2x+1?

When two lines are parallel, they have the same slope.  

                ⇒  if the slope of the given line is = - 2      

                     then the slope of the parallel line (m) = - 2

Determine the equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:  

                              ⇒  y - 2  =  - 2 (x - 7)                                  

We can therefore write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:  

                     since   y - 2  = - 2 (x - 7)  

Answer:

$15

Step-by-step explanation:

Answer

Use division, how many times will 14 go into 210?

210÷14=15

$15

Or you can also multiply 15x14=210

Answer:

0.75

Step-by-step explanation:

green\(=20-3-2-5=10\)

yellow or green \(=5+10=15\)

P(yellow or green )\(=\frac{15}{20} =\frac{3}{4} =0.75\)

Answer:

C

Step-by-step explanation:

It is the only answer where the negative signs do not even out on both sides of the equation.

Answer:

m=3n

Step-by-step explanation:

3 movies per month. So 3 n per m.

Answer:

n=3m

Step-by-step explanation:

n is number of movies

3 is the 3 movies per month

m is each month

so it's n=3m

ok

Result = 4 7/16

The range for the given scenario is  {540, 553.5, 567, 580.5, 594, 607.5} and this is continuous.

A function is defined as follows:

f(x) = y

Where x is the input variable and y is the output variable

Then the set of output values for the set of input values is said to be the range of the function.

The given function is P(t) = 13.50t

Where t is the input variable. The variable 't' represents the working hours.

The given interval for t is 40 - 45 hours weekly.

Then the output values for the given interval of input values are:

for t = {40, 41, 42, 43, 44, 45};

P(40) = 13.50(40) = 540

P(41) = 13.50(41) = 553.5

P(42) = 13.50(42) = 567

P(43) = 13.50(43) = 580.5

P(44) = 13.50(44) = 594

P(45) = 13.50(45) = 607.5

Then the range for the given scenario is {540, 553.5, 567, 580.5, 594, 607.5}.

Since the difference between each value is the same i.e.,

553.5 - 540 = 13.5 or 567 - 553.5 = 13.5 and so on.

So, this scenario is continuous.

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Answer:

Slope: 1

__________

y-intercept: (0,0)

Step-by-step explanation:

Answer:

Starting from the one on the left.

Upper left:

145 degrees

Down left:

35 degrees

Down right:

145 degrees.

-------------

Now for the right image.

Upper left:

153 degrees

Down left:

27 degrees

Down right:

153 degrees

Step-by-step explanation:

Apply the same steps for the second image as for the first.

One thing to keep in mind is that a flat line (horizontal or vertical), as an angle of 180 degrees.

And another useful reminder is that opposed angles have the same degree.

Starting from the one on the left.

Upper left:

180 - 35 = 145 degree

Down left:

since it is opposed to the upper right angle which is 35 degrees this one is also equal to 35 degrees.

Down right:

since it is opposed to the upper left angle which is 145 degrees this one is also equal to 145 degrees.

You can always double check by making sure one flat side (left or right or up or down), is equal to 180 degrees.

example: on the right image, for the down part, I wrote as answers 27 degrees (for down left because it is opposed to upper right) and 153 degrees (for down right because it is opposed to upper left) => 153 + 27 = 180 degrees

Answer:

20

Step-by-step explanation:

The slope formula is y= mx+b

m= slope

x= x (the variable)

b= y-intercept

in this case, 20 would be m in the formula.

remember slope is rise/run. (Rise up, then go left or right)

hope this helps :)

Answer:

Yes

Step-by-step explanation:

Let the numbers be p q r such that p>q>r

So p + q + r = 3q

2q = p+ r

And q< p but q> c,

So by Solving this would give

q= (p+ r)/2

so q is the mean of p & r.

Since the only other number that fits is q,

Then q is the mean of the numbers p,q,r

As so q is also the median of this set

Thus proving that the mean is the same as the median.

Answer:

Girls to Total:  24/32 or 3/4

Step-by-step explanation:

Girls: 24

All Students: 8+24 = 32

Girls to Total:  24/32 or 3/4

(a) Mrs Jeya gave 30 stickers to Group B on Tuesday. (b) Mrs Jeya bought a total of 126 stickers.

(a) Let's first calculate the number of stickers Mrs Jeya had remaining after giving 1/4 of the stickers to Group A. If she had 72 stickers remaining, it means that 3/4 of the original number of stickers is equal to 72. We can set up the equation:

(3/4) * x = 72

To solve for x, we multiply both sides of the equation by 4/3:

x = (72 * 4) / 3 = 96

So Mrs Jeya initially had 96 stickers.

Now, on Tuesday, she gave 5/12 of the remaining stickers to Group B. We know that the remaining number of stickers after giving to Group A was 72. Let's calculate the number of stickers she gave to Group B:

(5/12) * 72 = 30

Therefore, Mrs Jeya gave 30 stickers to Group B on Tuesday.

(b) To determine how many stickers Mrs Jeya bought, we need to add up the stickers she gave to Group A, the stickers she gave to Group B, and the remaining stickers.

Stickers given to Group A: 1/4 * 96 = 24

Stickers given to Group B: 30

Remaining stickers: 72

Total stickers = Stickers given to Group A + Stickers given to Group B + Remaining stickers

              = 24 + 30 + 72

              = 126

Therefore, Mrs Jeya bought a total of 126 stickers.

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Answer:

d. plants take in water for photosynthesis

Step-by-step explanation:

an adaptation would be a way the plant has adapted in response to a specific environment

all plants take in water for photosynthesis, so it's not an adaptation to a habitat since plants in all habitats do that

The cost equation is used to estimate total costs associated with a given level of activity or output, where f is the fixed cost and v is the variable cost per unit of activity. The variable cost component (vx) changes in proportion to the level of activity or output (x), whereas the fixed cost component (f) remains constant regardless of the level of activity.

In the cost equation tc = f + vx, x is best described as the level of activity or the quantity of the input variable. The cost equation is a mathematical representation of the relationship between the total cost of production and the level of activity or the quantity of the input variable. The variable x represents the number of units produced or the amount of resources used in the production process, which can be measured in terms of labor hours, machine hours, or any other relevant unit of measure. The variable v represents the variable cost per unit of activity, and f represents the fixed cost of production.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Winner is paid :

Monthly pay while on tour = $5000

Pay per CD sold =. $2

A) Equation which relates total earning in terms of number of months 'm' while on tour and the number 'n' of CD's sold.

(Monthly pay * number of months) + (pay per CD * number of CD's)

Earning = 5000m + 2n

B) How much will the winner earn after the first month if 500 CDs are sold?

m = 1, n = 500

5000(1) + 2(500) = $6000

C) Suppose after the third month on tour the new recording artist has earned a total of $74 000. How many GDs were sold?

m = 3

74000 = 5000(3) + 2n

74000 = 15000 + 2n

74000 - 15000 = 2n

59000 = 2n

n = 59000 / 2

n = 29500 CD's

D) In Canada, a record album or CD achieves gold status once it seLls 50 000 units. How much will the artist make if the CD goes gold after 6 months of touring?

n = Gold = 50000 ; m = 6

5000(6) + 2(50000)

30000 + 100000 = 130,000

Answer:

\(\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}\)

Step-by-step explanation:

We can use either the Power Rule or the Quotient Rule to find the derivative of 3/x².

Rewrite \(\displaystyle \frac{3}{x^2}\) as \(\displaystyle 3\cdot \frac{1}{x^2}\) which is equivalent to \(3\cdot x^-^2\).

Now we can apply the power rule to 3x⁻². Subtract 1 from the exponent and multiply the coefficient by -2.

This can be rewritten as \(\displaystyle -\frac{6}{x^3}\).

Substituting 3 for f(x) and x² for g(x), we get:

Simplify.

Using exponent rules, we can rewrite this as:

This can be rewritten as \(\displaystyle -\frac{6}{x^3}\), which is the same as what we got using the product rule.

Answer:

\(\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}\).

Step-by-step explanation:

Let \(f(x)\) and \(g(x)\) denote two functions of \(x\). Assume that \(g(x) \ne 0\). The quotient rule states that:

\(\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}\).

In this question:

Find \({f}^{\prime}(x)\) and \({g}^{\prime}(x)\).

Notice that the value of \(f(x)\) is constantly \(3\) regardless of the value of \(x\). By the constant rule, \({f}^{\prime}(x) = 0\).

For \({g}^{\prime}(x)\), consider the power rule:

if \(m\) represents a rational number (such as \(2\),) then by the power rule, \(\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}\).

Apply this rule to find \({g}^{\prime}(x)\).

\(\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}\).

Substitute \(f(x) = 3\), \({f}^{\prime}(x) = 0\), \(g(x) = x^{2}\), and \({g}^{\prime}(x) = 2\, x\) into the quotient rule expression to find \(\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right]\):

\(\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}\).

Therefore, \(\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}\).

The equation that can be used to find x, the number of spotlights the committee rented is x * C = 800

To solve a first-degree equation, we must find the value of the unknown (which we will call x) and, for this to be possible, just isolate the value of x in equality, that is, x must be alone in one of the members of the equation.

Since the committee spends $800 on spotlights, we can set up the equation:

\(x * C = 800\)

In this equation, x is the number of spotlights rented and C is  the cost per spotlight.

This equation allows us to find the value of x, the number of spotlights rented, by substituting the appropriate value for C.

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Answer:

Answer is 104

Step-by-step explanation:

The selling price of the coat is $104.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Original price = $200

Selling price.

= 52% of $200

= 52/100 x 200

= $104

Thus,

$104 is the selling price of the coat.

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Answer:

The correct option is;

C. 3.25 + 5.50·S ≤ 30

Step-by-step explanation:

The given parameters are;

The cost of the chocolate milk ordered = $3.25

The unit quantity of pancake sales = Stack

The number of pancakes in a stack = 4

The amount a stack of four pancakes is sold = $5.50

The number of pancakes Benjamin wants to buy = As many as he can

The number of stacks of pancakes Benjamin buys = S

The cost of the pancakes Benjamin buys = $5.5 × S

The cost of the number of pancakes Benjamin buys

The maximum amount Benjamin wants his bill to amount to = $30

Therefore we have;

The cost of chocolate milk ordered + The cost of pancakes Benjamin buys  ≤ $30

Which gives;

$3.25 + $5.50 × S  ≤ $30

Therefore, the correct option is 3.25 + 5.50·S ≤ 30.

Answer: 3

Step-by-step explanation:

When you subtract 25 from 22 you get 3 and when you subtract 3 from 25 you 22.

Answer:

12×8/2=48

10×10=100

2(48)+3(100)

96+300= 396ft²

Answer:

33.6cm

Step-by-step explanation:

I'm assuming the length is 3x as there are quite a few typos

perimeter = 2 x length + 2 x width

84 = 2 x 3x + 2 x 12x

84 = 6x + 24x

84 = 30x

84/30 = 2.8

x = 2.8

12x = 2.8 x 12 = 33.6 cm

False. Consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices.

The highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices.The definition of a minimum spanning tree states that it is a subset of edges of a graph that connect all of the vertices without forming any cycles, and with the minimum total weight. If a graph contains an edge with the highest weight, it may still be included in the MST if it is the only connection between two vertices. To illustrate this, consider a graph with 4 vertices, where there is an edge of weight 8 between the two farthest vertices, and an edge of weight 10 between the two closest vertices. In this case, the highest weight edge (10) would be included in the MST, as it is the only connection between the two closest vertices, and thus the minimum total weight is achieved.

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