If
f(x) = 6x2 − x3,
find f '(1) and use it to find an equation of the tangent line to the curve
y = 6x2 − x3
at the point (1, 5).

Answer:

The last one

Step-by-step explanation:

Answer:

D, Divide both sides by -4.6

Step-by-step explanation:

You want to get the x and the regular integers on separate sides of the equals sign, so you divide the -4.6 to get the x on its own side of the equals sign. That's the first step to solving the equation.

Answer:B

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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Answer: Option 1

Step-by-step explanation:

The domain is the set of x values that make the radicand non-negative. Since the radicand is a perfect square, it will always be non-negative for any real value of x.

The solution of the integral of 8 cos(x)+ √3 = 5√3 is  8π√3.

The given function is 8 cos(x)+ √3 = 5√3

The function can be simplified as follows;

8 cos(x) + √3 = 5√3

collect similar terms together;

8 cos(x) + √3 - 5√3 = 0

8 cos(x)  - 4√3 = 0

integral of  8 cos(x)  - 4√3  = 8 sin(x) - 4√3x

the value of the integral over (0, 2π)

= 8 sin(0) - 4√3(0) -  (8 sin(2π) - 4√3(2π))

= 0 + 8π√3

= 8π√3

Thus, the solution of the integral of 8 cos(x)+ √3 = 5√3 is  8π√3.

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Answer:

\(\text{\textit{x}} \ \ = \ \ \displaystyle\frac{\pi}{6} \ \ \ \text{or} \ \ \ \displaystyle\frac{11\pi}{6}\)

Step-by-step explanation:

Given the trigonometric equation

                               \(8 \ \cos{\left(\textit{x}\right)} \ + \ \sqrt{3} \ = \ 5\sqrt{3}\),

hence solving for \(\textit{x}\) yields

                                  \(8 \ \cos{\left(\textit{x}\right)}\ = \ 5\sqrt{3} \ - \ \sqrt{3} \\ \\ \\ \-\hspace{8px} \cos{\left(x\right)} \ = \ \displaystyle\frac{4\sqrt{3}}{8} \\ \\ \\ \-\hspace{8px} \cos{\left(x\right)} \ = \ \displaystyle\frac{\sqrt{3}}{2} \\ \\ \\ \-\hspace{29px} \textit{x} \ \ \ = \ {\cos}^{-1}\left(\displaystyle\frac{\sqrt{3}}{2}}}\right) \\ \\ \\ \-\hspace{29px} \textit{x} \ \ \ = \ \displaystyle\frac{\pi}{6}\).

Since cosine is positive in both quadrant I and quadrant IV, thus

                                     \(\textit{x} \ \ = \ \ 2\pi \ - \ \displaystyle\frac{\pi}{6} \ \ = \ \ \displaystyle\frac{11\pi}{6}\).

Therefore the solutions are

                                               \(\textit{x} \ \ = \ \ \displaystyle{\frac{\pi}{6}} \ \ \text{or} \ \ \displaystyle{\frac{11\pi}{6}}\).

The value of function which cross the y-axis at point (0, 7) will be;

⇒ y = x + 7

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point which cross the function = (0, 7)

Now,

Since, The point which cross the function = (0, 7)

Hence, The point must be satisfy the function.

By option (1);

⇒ y = x + 7

Put (x, y) = (0, 7)

⇒ 7 = 0 + 7

⇒ 7 = 7

Thus, The correct function which passes through the point (0, 7) is,

⇒ y = x + 7

Option (i) is true.

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Answer:

green

Step-by-step explanation:

11a^3−4a^2−14a−7

Answer:

11a³-4a²-14a-7

(The light blue/green one)

Step-by-step explanation:

We'll need to combine like terms (terms with the same variables and exponents)

(4a³-8a-4a²)+(7a³-7-6a)

add/subtract

we'll keep -4a² and -7 as is as there aren't any other terms like them

11a³-14a-4a²-7

put into standard form:

11a²-4a²-14a-7

(The light blue/Green one)

Hope this helps!

The above equation's midpoint is represented by the expression Midpoint = (3.5,2,2) (1.5,-4.8). ( 2.5,-1.3 )

Midpoint =( 2.5,-1.3 )

The formula for determining the midpoint is

\($\left(x_m, y_m\right)=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$\)

\($\left(x_m, y_m\right)=$\)the midpoint's coordinates

\($\left(x_1, y_1\right)=$\) the first point's coordinates

\($\left(x_2, y_2\right)=$\) the second point's coordinates

Divide the distance between the two endpoints by 2, then multiply it by 3. The middle of that line is at these distances from each end. As an alternative, multiply the sum of the two endpoints' x coordinates by 2. For the y coordinates, repeat the process. the location on a line when the distances to both ends are equal. a period of time midway between the start and finish of an event.

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Answer:

16 units

Step-by-step explanation:

diameter is double the radius

hope it helps!!!

Answer:

16

Step-by-step explanation:

radius = diameter / 2

diameter= radius x 2

              =8x 2

               = 16

hope it helps you:)

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We can notice that this is a quadrilateral with two pairs of equal sides, with that we will see that:

m∠D = 98°

In the image we can see a quadrilateral ABCD, on that image we can see that:

AB = CD

AD = BC

You can notice that because of the "arrows" on the sides.

From that, we can conclude that the measures of the angles meet the conditions:

m∠A = m∠C

m∠D = m∠B

On the image we also can see that:

m∠B = 98°

And the measure of angle B is equal to the measure of angle D, then we can conclude that the measure of angle D is also 98°, so:

m∠D = 98°

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You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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Equation x = 1 represents the vertical line passing through (1 ,-9).

" Equation of a line is defined as an algebraic expression which is represented by linear equation in two variables with highest degree 1. Minimum two coordinates required to draw a line."

According to the question,

Coordinates in the plane represented by (x, y)

We have

Line passing through the point  = (1 ,-9)

x = 1 for different values of y represents a line perpendicular to x-axis.

Therefore,

Vertical line passing through (1, -9) is equals x = 1.

Hence, Option(B) is the correct answer.

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The value of the expression on evaluation is 96π / 5.

Here we have to find the value of the expression.

∫∫∫x² dV

E is indeed the solid that exists inside the cylinder x² + y² = 4 above the surface z =0.

E's precession through into xy-plane is x² + y² ≤4 where r≤2 with Ф[0, 2π].

∫∫∫ x² dV = ∫\(\int\limits^2\pi _0 {} \, \int\limits^2_0{} \, \int\limits^3r_0\) r² cos² Фrd dФ

             = \(\int\limits^2\pi _0 {} \, \int\limits^2_0 \int\limits^3r_z=0 {} \,\)r³ cos²Ф dz dr dФ

            = \(\int\limits^2\pi _0 {} \, \int\limits^2_0 {} \,\) 3\(r^{4}\)cos²Ф dr dФ

           = 3 \(\int\limits^2\pi _0 {} \,\) 1/2 \(2^{5}\)/ 5 ( 1 + cos² Ф )dr dФ

           = 48 / 5 [( Ф + 1/2 sin 2Ф)\(]^{2\pi } _{0}\)

            = 96π / 5

Therefore the value of the expression is 96π/5.

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The 500 sample size and 95% confidence level will both tend to increase the width of the confidence interval.

In this question, we have been given  the combinations of sample size and confidence level.

We need to select a combinations of sample size and confidence level that will give the widest interval.

We know that the confidence level is typically set in the range of 99% to 80%. The 95% confidence interval will be wider than the 90% interval and which will be wider than the 80% interval.

As we know increasing the confidence will increase the margin of error which results in a wider interval.

But increasing the sample size decreases the width of confidence intervals, as it decreases the standard error.

This means, for the widest interval we need to select a high confidence interval and small sample size.

Therefore, the sample size = 500 and the confidence interval = 95% will give the widest interval.

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3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

The nearest foot is 19

The missing value for the quadratic function is given as follows:

y = -3.

As a function of it's roots x* and x**, the quadratic function is defined as follows:

y = a(x - x*)(x - x**)

In which a is the leading coefficient.

The roots of the function are the values of x when y = 0, hence:

x* = -4, x** = -2.

Thus:

y = a(x + 4)(x + 2)

y = a(x² + 6x + 8).

When x = 0, y = -8, hence the leading coefficient a of the function is given as follows:

8a = -8

a = -1.

Hence:

y = -x² - 6x - 8;

The missing value is the value of y when x = -1, hence:

y = -(-1)² - 6(-1) - 8

y = -3.

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The horizontal shift is to the right.

The exact period is 8/7.

In a trigonometric function, written of the form

y = A csc (Bx - C)

the parameters are interpreted as follows

A is the amplitude

B is period / 2π

C is the horizontal shift

comparing with the equation y = 2 csc (7π/4x - 21π/2). we have that

horizontal shift = -21π/2 since it is positive it is to the right

The exact period is

Period = 2π / (7π/4)

= 8/7

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The resulting value of the the expression 6769 x 925 by first rounding each number so that it has only 1 nonzero digit is 63,000

Round off

Round off refers a number is made simpler by keeping its value intact but closer to the next number. And it is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

Given,

Here we need to estimate  6769 x 925 by first rounding each number so that it has only 1 nonzero digit.

Here we have to take individual terms to round off then we get,

By rounding 6799 so that it has only one non-zero digit is rounding it to nearest thousand.

6769 rounds to nearest thousand as 7000 as hundreds digit 7 > 5.

Similarly, by rounding 925 so that it has only one non-zero digit is rounding it to nearest hundred.

925 rounds to nearest hundred as 900 as tens digit 2 < 5.

Now, the estimated value after rounding each number so that it has only one non-zero digit is

=> 7000 x 900

=> 63000.

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The required graph of the function y=x²+4x+3 for the interval -3 ≤ x ≤ 3.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The given function,
y=x²+4x+3

Since we have given the interval for the value of the x, as -3 to 3
By putting value in the above expression we get y,
put x = -3
y = (-3)² + 4(-3) + 3
y = 9 - 12 + 3
y = 0

Similarly, other values are shown through the map.

Thus, the required graph of the function y=x²+4x+3 for the interval -3 ≤ x ≤ 3.

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Answer: 23.76 sq yds

Step-by-step explanation:

0.5*9.9*4.7=23.76

Area of triangle: 0.5*b*h

THE ANSWER IS IN THE PHOTO

Answer:

Step-by-step explanation:

x(x+3) + 2(x+3) + x(x-2) - 3(x-2) - 2x2 - 2x =0

x2 + 3x + 2x + 6 + x2 - 2x - 3x + 6 - 2x2 - 2x = 0

x2 + x2- 2x2 +  3x + 2x - 2x - 3x - 2x + 6 + 6 = 0

2x2 - 2x2 - 2x + 12 =0

-2x = -12

X = -12/-2

X = 6

here, x2 is x squared.

Answer:

Elgas is 35.

Step-by-step explanation:

Let's set up an equation.

Alvin is 7 years younger than Elgas.

A = E - 7

The sum of their ages is 63.

A + E = 63

Let's use substitution.

Plug in the first equation of A into the second equation.

A + E = 63

(E - 7) + E = 63

Combine like terms.

2E - 7 = 63

Add 7 to both sides.

2E = 70

Divide both sides by 2.

E = 35

Elgas is 35.

Hope this helps!

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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20% of the participants are girls and got a medal, and 33% of the girls got a medal.

First, we know that 40% of the participants were boys, so the other 60% were girls.

We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:

P = (0.4)*(0.5) = 0.2

So, 20% of the participants are boys and got a medal.

We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.

Then if the percentage of girls that got a medal is x (in decimal form), we must have that:

Q = (0.6)*(x) = 0.2

      x = 0.2/0.6 = 0.33

x = 0.33

This means that 33% of the girls got a medal.

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Answer:

  a) 30 kangaroos in 2030

  b) decreasing 8% per year

  c) large t results in fractional kangaroos: P(100) ≈ 1/55 kangaroo

Step-by-step explanation:

We assume your equation is supposed to be ...

  P(t) = 76(0.92^t)

__

a) P(10) = 76(0.92^10) = 76(0.4344) = 30.01 ≈ 30

In the year 2030, the population of kangaroos in the province is modeled to be 30.

__

b) The population is decreasing. The base 0.92 of the exponent t is the cause. The population is changing by 0.92 -1 = -0.08 = -8% each year.

The population is decreasing by 8% each year.

__

c) The model loses its value once the population drops below 1/2 kangaroo. For large values of t, it predicts only fractional kangaroos, hence is not realistic.

  P(100) = 75(0.92^100) = 76(0.0002392)

  P(100) ≈ 0.0182, about 1/55th of a kangaroo

Step-by-step explanation:

Refer to pic..............