given the following function, what is the instantaneous rate of change at X=2?y=1/3x^3+2x^2-4x+1

Answer:

x=6

Step-by-step explanation:

BD is bisecting of <B

x/3=8/4    the theorem of  the bisecting

4*x=3*8

4x=24

x=24/4

x=6

Answer:

Step-by-step explanation:

20 * ((2*20)-6)

20*34

680

Step-by-step explanation:

We can write

X=-2,-1,0,1,2

And the equation is y=3x+4-------(1)

First we should be put all the value in equation (1)

y=2,1,4,7,10

And the answer will

(x, y) ={ (-2,2),(-1,1),(0,4),(1,7),(2,8)}

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

Answer:

\( \\ \)

Step-by-step explanation:

Using formula:

\( \: \: \: \: \: \: \: \: \: \: {\underline{\boxed {\pmb{ \sf{Volume \: of \: cylinder = \pi r^2h}}}}} \: \pink\star \)

\( \\ \)

Where,

\( \\ \)

Substituting the required values in the above formula :

\( \\ \)

\( \dashrightarrow \sf \: \: Volume = 3.14 \times {(15)}^{2} \times 17 \\ \\ \)

\(\dashrightarrow \sf \: \: Volume = 3.14 \times 225 \times 17 \\ \\ \)

\(\dashrightarrow \sf \: \: Volume = 706.5 \times 17 \\ \\ \)

\(\dashrightarrow~~{\boxed {\pink{\pmb{\sf {Volume = 12016.5 \: {cm}^{3}}}}}} \\ \\ \)

Hence,

Answer :

⠀

Explanation :

We know,

\({ \longrightarrow \qquad{\boldsymbol {\pmb{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}}\)

Where,

⠀

Substituting the values in the formula :

\({ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times ({15})^{2} \times 17 \: }}}}\)

⠀

\({ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \: \times 225 \times 17}}}}\)

⠀

\({ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times 3825 }}}}\)

⠀

\({ \longrightarrow \qquad{ \pmb{ \sf{ Volume_{(cylinder)} = 12010.5 }}}}\)

⠀

Therefore,

The three positive numbers whose sum is 27 will be 14, 1, and 12.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

Suppose the three positive numbers are x, y and z.

If the summation of numbers is 27.

⇒ x + y + z = 27 --- (1)

⇒ z = 27 - x - y

Suppose the square sum of the number be S.

∴ S = x² + y² + z²

⇒ S = x²+ y² + (27 - x - y)² --- (2)

We will optimize the function, partially differentiating it with respect to x and y, and setting dS/dx = 0 to get the minimum value of S.

2x + 2(27- x - y)(-1) = 0

2x - 54 + 2x + 2y = 0

4x + 2y - 54 = 0

y = 27 - 2x --- (3)

Differentiate partially with respect to y as

2y + 2(27 - x - y)(-1) = 0

2y - 54 + 2x + 2y = 0

4y + 2x - 54 = 0

x = 54 - 2y --- (4)

Substitute the value of y = 27 - 2x in the equation (4),

x = 12 - 2(27 - 2x)

x = 12 - 54 + 4x

4x - x = 54 - 12

3x = 42

⇒ x = 14

By substituting x = 14 in equation (3)

y =2(14) - 27

y = 28 - 27

⇒ y = 1

Substitute the values of x and y in equation (1),

14 + (1) + z = 27

z = -14+27-1

z= 12

Thus, the three positive numbers whose sum is 27 will be 14, 1, and 12.

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\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ J(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{10}~,~\stackrel{y_2}{-5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 10 +2}{2}~~~ ,~~~ \cfrac{ -5 +1}{2} \right) \implies \left(\cfrac{ 12 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies (6~~,~-2)\)

The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable  sum range of .05 fluid ounces or less.

The simulation did not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces, indicating that the variability of the juice dispensed was within the acceptable sum of range

The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable range of .05 fluid ounces or less.

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Answer:

no

Step-by-step explanation:

because Kira ordered 5 pieces of crab while Marcy has ordered 6 pieces of crab

The two triangles are congruent since they have equal angles and equal sides.

Congruent triangles are two triangles that have exactly the same size and shape.

In other words we can say that they have the same angles and the same side lengths.

So when two triangles are congruent, all of their corresponding parts including the angles and sides are equal.

For the given triangles

The missing value of angle C = 180 - (18 + 110) = 52⁰

The missing value of angle F = 180 - (18 + 52) = 110⁰

So it is obvious that the two triangles are congruent since they have equal angles and equal sides.

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Answer:

x1 = -7+3t

x2 = (11-7t)/2

Step-by-step explanation:

Given the system of equations

x1 − 3x3 = −7 ...,...... 1

3x1 + x2 − 2x3 = −5 ....... 2

2x1 + 2x2 + x3 = −3 ....... 3

Setting x3 = t.

Substitute x3 = t into equation 1 to get x1 in terms of t.

x1 − 3x3 = −7

x1-3(t) = -7

x1-3t = -7

Add 3t to both sides;

x1-3t+3t = -7+3t

x1 = -7+3t

To get x2, substitute x1 = -7+3t and x3 = t into equation 3

2x1 + 2x2 + x3 = −3

2(-7+3t)+2x2+t = -3

Open the parenthesis

-14+6t+2x2+t = -3

Collect like terms

2x2+6t+t = -3+14

2x2+7t = 11

Subtract 7t from both sides

2x2+7t-7t = 11-7t

2x2= 11-7t

Divide both sides by 2

2x2/2 = (11-7t)/2

x2 = (11-7t)/2

Hence the solution to the system if equation (x1, x2, x3) = (-7+3t, (11-7t)/2, t)

Answer:

4 (3.2 exactly but you can't go to the store and say I want to buy 3.2 gallons of paint. They will look at you funny, So in this case you will by 4)

Step-by-step explanation:

2640/825 = 3.2 gallons

Answer:

Step-by-step explanation:

1 gallon = 825 square feet

x gallons = 2640 square feet

1/x = 825/2640        Cross multiply

825 x = 2640          Divide by 825

x = 2640/825

x = 3.2 gallons.

The 0.2 has to be rounded up (usually you would round down. That's because you have to get another gallon to paint the small area that is not covered.

So the rounded answer is 4 gallons.

y-(-9) = -6(x-(-4)), y = -6x-33

The exponential function obtained from the table is represented by the formula y is 650(1.045)x.

A function with the exponential shape is:

y = abˣ

where an is y's initial value, b are multipliers, and y and x are variables.

The bacterial population at x hours should be represented by y.

With 650 bacteria cells at the beginning, the group.

a = 650

4.5% is the growth rate.

b = 100% + 4.5% = 104.5% = 1.045

The exponential function obtained from the table is represented by the formula y = 650(1.045)x.

The exponential function obtained from the table is represented by the formula y is 650(1.045)x.

Thirty hours later:

y = 650(1.045)³⁰ = 2434.

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Price plus tax = Total amount - Shipping charge

Price plus tax = $95.68 - $5.25

Price plus tax = $90.43

Let, x is the price excluding tax :

\(x+\dfrac{5x}{100}=90.43\\\\105x=9043\\\\x=\$86.12\)

Also, she used $5 off promo code.

So, Original price = $86.12 + $5

Original price = $91.12 .

Hence, this is the required solution.

Answer:

$91.12

Step-by-step explanation:

Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

The center of the hanger represents an equal sign, since both sides of the hanger are equal.

Given different coloured triangles and shapes, we can assign a variable to each of them.

Let one green triangle be equal to \(a\).

Let one blue square be equal to \(b\)

Let one red circle be equal to \(c\).

Let one yellow pentagon be equal to \(d\).

On the left side of the hanger/equation, there are 3 green triangles. This means that one of our terms in our equation will be \(3a\).

Under the triangles on the left side is 1 blue square. This means that the next term could be \(1b\), or just \(b\).

Next is 2 red circles ⇒ \(2c\)

And finally are 3 yellow pentagons ⇒ \(3d\)

To sum up the left side as an expression, we can write all the terms we have just written as a sum:

\(3a+b+2c+3d\)

Now, after doing the same procedure for the right side of the hanger, we get:

\(2a+3b+c+2d\)

For now, we only have two expressions representing the two sides of the hanger:

Left: \(3a+b+2c+3d\)

Right: \(2a+3b+c+2d\)

To turn these into an equation, we must have an equal sign.

Remember that both sides of the hanger are equal. Knowing this, we can state the following:

Left side = Right side

\(3a+b+2c+3d = 2a+3b+c+2d\)

\(3a+b+2c+3d = 2a+3b+c+2d\)

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.

We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.

Marian earns $4,100.00 per month

Suppose Marian wants  to save for  x months,  then the maximum amount that she can spend on the house is:

4100  *   x    +  21390

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

Hope this helps!

Answer:

\(x^{\frac{2}{3} }\)

Step-by-step explanation:

⇒ \(x^({\frac{4+2}{3}) } ^{\frac{1}{3} }\)

⇒ \((x^{\frac{6}{3} })\)

⇒ \((x^{2} )\frac{1}{3}\)

⇒ \(x^{\frac{2}{3} }\)

Answer:

b. -3

Step-by-step explanation:

30 - 3 = 27

27 - 3 = 24

24 - 3 = 21....

The Value of x is 2/3.

The value of x, we need to determine the mean of the given values and set it equal to the expression for the mean.

The mean (average) is calculated by adding up all the values and dividing by the number of values. In this case, we have five values: x, x+3, x-5, 2x, and 3x.

Mean = (x + x+3 + x-5 + 2x + 3x) / 5

Next, we simplify the expression:

Mean = (5x - 2 + 3x) / 5

Mean = (8x - 2) / 5

We are given that the mean is also equal to x:

Mean = x

Setting these two expressions equal to each other, we have:

(x) = (8x - 2) / 5

To solve for x, we can cross-multiply:

5x = 8x - 2

Bringing all the x terms to one side of the equation and the constant terms to the other side:

5x - 8x = -2

-3x = -2

Dividing both sides by -3:

x = -2 / -3

Simplifying, we get:

x = 2/3

Therefore, the value of x is 2/3.

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Answer:

1/7

Step-by-step explanation:

You have to multiply across the top then the bottom.

Answer:

5

Step-by-step explanation:

We have x-2 = 5

x-2 = 5 we separate parenthesis.

x(-2) = 5(+2)

x = 7

We can check this as what the x-2 is saying is  7-2 = 5

Answer:

Since it is an equilateral triangle,

Perimeter = 3s = 3 x side

=> 15 = 3 X (x - 2)

=> 15 = 3(x - 2)

=> 15 = 3x - 6

=> 3x = 15 + 6

=> 3x = 21

=> x = 21/3

=> x = 7

When x = 7,

=> Side = 7 - 2 = 5 inches

Since, it is an equilateral triangle all sides are of 5 inches each.

The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?

The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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The domain and the range of the function are

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a piecewise function

When combined gives an absolute function

The rule of a function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is greater than the constant term

In this case, it is 0

So, the range is y > 0

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Question

The graph represents the piecewise function:

f(x) =

What is the domain and range of the function

Answer:

16716p

Step-by-step explanation:

28 x 150 x ( 5 x 8 ) - 30

Answer:

d

Step-by-step explanation:

The segment inside the triangle bisects the angle and divides the opposite sides into segments that are proportional to the other two sides, that is

\(\frac{x}{17}\) = \(\frac{37.5}{52.5-37.5}\) = \(\frac{37.5}{15}\) ( cross- multiply )

15x = 637.5 ( divide both sides by 15 )

x = 42.5 → d