Find the gradient of the line

3y + 2x = 1

how to guys

The equation of the tangent line to the curve is:

[tex]y - 4 = 0.0024(x - 2)[/tex]

Which has a slope of 0.0024.

The tangent line of a curve [tex]f(x)[/tex] at a point [tex](x_0,y_0)[/tex] is given by:

[tex]y - y_0 = f^{\prime}(x_0)(x - x_0)[/tex]

In this problem, the curve is:

[tex]f(x) = e^{-4x}\sin{6x}[/tex]

The derivative is:

[tex]f^{\prime}(x) = -4e^{-4x}\sin{6x} + 6e^{-4x}\cos{6x}[/tex]

Point P(2,4), thus [tex]x_0 = 2, y_0 = 4[/tex].

The slope is:

[tex]f^{\prime}(2) = -4e^{-4(2)}\sin{6(2)} + 6e^{-4(2)}\cos{6(2)} = 0.0024[/tex]

Then, the equation of the line is:

[tex]y - y_0 = f^{\prime}(x_0)(x - x_0)[/tex]

[tex]y - 4 = 0.0024(x - 2)[/tex]

A similar problem is given at https://brainly.com/question/22426360

The equation that can be used to represent this situation is 8x + 10y = 1600

Let x represent the number of student tickets sold and y represents the number of adult tickets sold.

Since students ticket cost $8 and adult tickets cost $10, and the total ticket sold was $1600, hence this can be represented by the equation:

8x + 10y = 1600

Therefore the graph of the above equation is attached

Find out more at: https://brainly.com/question/24947711

Answer:?

Step-by-step explanation:

?

Answer:

here.

3/4x−4−5/8x=−3

or, 3/4x−5/8x=−3+4

or, 3/4x−5/8x=1

or, 3*2/2*(4x)-5/8x=1

or,6/8x-5/8x=1

or,(6-5)/8x=1

or,1/8x=1

or,1=8x

or,x=1/8

Answer:

[tex]0+2-4=-2[/tex]

Step-by-step explanation:

We start at 0 and move 2 to the right to get to 2. Then, we move 4 to the left to get to -2.

So, our equation is [tex]0+2-4=-2[/tex], the 0 being our starting point, the +2 coming from moving to the right 2, the -4 coming from moving to the right 4, and the -2 being our end point.

Using the inverse function, it is found that the equation is:

[tex]P(t) = \frac{e^{0.1t}}{50} + 20[/tex]

It's initial value is 20.

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

We want to find the inverse of:

[tex]y = P^{-1}(t) = 10\ln{50t - 1000}[/tex]

To do this, we exchange y and t, and isolate y.

Then:

[tex]10\ln{50y - 1000} = t[/tex]

[tex]\ln{50y - 1000} = \frac{t}{10}[/tex]

[tex]e^{\ln{50y - 1000}} = e^{0.1t}[/tex]

[tex]50y - 1000 = e^{0.1t}[/tex]

[tex]50y = e^{0.1t} + 1000[/tex]

[tex]y = \frac{e^{0.1t} + 1000}{50}[/tex]

[tex]y = \frac{e^{0.1t}}{50} + \frac{1000}{50}[/tex]

[tex]P(t) = \frac{e^{0.1t}}{50} + 20[/tex]

It's initial value is:

[tex]P(0) = \frac{e^{0.1(0)}}{50} + 20 = 0.02 + 20 = 20.02[/tex]

Rounding, 20.

A similar problem is given at https://brainly.com/question/23950969

Answer:

P = 1/50e^0.1t + 20

Step-by-step explanation:

Answer:

2 prime factors

Answer: 2 prime factors

Step-by-step explanation:  A semiprime is a number n that has just 2 prime factors p and q so n = p × q. It is therefore "almost" a prime (which has only one prime factor, itself!) or a semiprime.

Answer:

w=-1

Step-by-step explanation:

Algebra.

Answer:

Step-by-step explanation:

Answer:

A number multiplied by a variable.

Step-by-step explanation:

For example, 4 is a coefficient.

[tex]4x[/tex]

Answer:

0.12 chose strawberry as their favorite

The two properties newton used to rewrite the expression are;

- Associative Property; Because it involves change of grouping of numbers in the expression.

- Distributive Property; Because it involves distribution of a number outside a bracket to numbers inside that same bracket.

- Associative Property

- Commutative Property

- Distributive Property

Let us define each of them;

1) Associative Property; This property in algebra is one that means that no

matter how we group the numbers, we will still get the same result. e.g.

x + (y + z) = (x + y) + z.

2) Commutative Property; This property means that we can change the

order of operation and still get the same answer. For example;

p × q × r = p × r × q

3) Distributive Property; This property means that multiplying the sum of

two or more which are in a bracket by a number outside the will be equal to

the answer gotten when we multiply each number in the bracket

individually by the number outside and then adding their respective

products together. For example; p(q + r) = (p * q) + (p * r)

Newton has the expression; (4 × 23) × 25

Since it is multiplication, he can use any of the three properties above but let us use the associative and distributive properties as they are most suited to this expression.

(4 × 23) × 25 = 4 × (23 × 25)

(4 × 23) × 25 = (25 × 4) + (25 × 23)

Read more at; https://brainly.com/question/20724601

Answer:

1 hour

Step-by-step explanation:

1/2 hour:1/2 pool

1/2x2 hour:1/2x2 pool

1 hour: 1pool

Answer:

Yes

Step-by-step explanation:

7:14=1:2

3:6=1:2

Answer:

[tex]\sf\longmapsto \: 6.666[/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: \: \frac{15}{2.25} [/tex]

Or it can be written as 15÷2.25

Thus,the answer will be in decimal.

[tex]\sf\longmapsto \: 6.666[/tex]

Answer:

8/t + t^2 = 18

Step-by-step explanation:

8/t + t^2

t = 4

8/4 + 4^2

2 + 16 = 18

8/t + t^2 = 18

Answer: 3/4 are eqivelent to 6/8

Step-by-step explanation:

Answer:

600 hives

Step-by-step explanation:

If 30 is 5% of the total number of hives Joshua has, then 5%x20=100%

So, 30x20=100%

      30x20=600

hope it helped :)

Answer:

B this is the smallest number

Answer:0.8004

Step-by-step explanation:

Answer:

just count the zero A is the answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

8x-5x+3+9=3x+12

combine like terms

Answer: point o.

Step-by-step explanation:

Answer:

3.0 seconds

Step-by-step explanation:

i took the test.

The time it takes the rock to reach 50 feet on its way down is 13.2 seconds and option B is the correct answer.

We have,

We are given the equation for the height of the rock as it travels upward and then downward:

h = -1672 + 63.2t - 4.9t²

We want to find the time it takes for the rock to reach a height of 50 feet on its way down.

This means we need to solve for t when h = 50:

50 = -1672 + 63.2t - 4.9t²

Rearrange the equation to isolate the quadratic term:

4.9t² - 63.2t + (1672 + 50) = 0

4.9t² - 63.2t + 1722 = 0

For an equation of the form "ax² + bx + c = 0", the solutions for "x" are given by:

x = (-b ± √(b² - 4ac)) / 2a

In your equation, the coefficients are:

a = 4.9

b = -63.2

c = 1722

Plugging these values into the quadratic formula:

t = (-(-63.2) ± √((-63.2)² - 4 * 4.9 * 1722)) / (2 * 4.9)

Now, let's calculate the discriminant (the value inside the square root):

Discriminant = (-63.2)² - 4 * 4.9 * 1722 ≈ 39884.96 - 33529.6 ≈ 6355.36

Since the discriminant is positive, there are two distinct real solutions for "t".

Now, plug the discriminant back into the quadratic formula and solve for "t":

t = (63.2 ± √6355.36) / 9.8

Now, calculate the square root of the discriminant:

√6355.36 ≈ 79.58

Now, plug in the values for "t":

t₁ = (63.2 + 79.58) / 9.8 ≈ 13.02

t₂ = (63.2 - 79.58) / 9.8 ≈ -1.69

So, the solutions for the equation 4.9t² - 63.2t + 1722 = 0 are approximately:

t₁ ≈ 14.61

t₂ ≈ -1.69 (rejected)

Thus,

The time it takes the rock to reach 50 feet on its way down is B. 13.2 seconds.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ3

Answer:

$ 1,193.80

Step-by-step explanation:

Balance + deposits =

725.35+472.25+175.35+194.50+317.85 = $ 1,885.30

$1,885.30 - withdrawals =

1885.30 - 150.30-237.60-45.75-257.85 = $ 1,193.80

The sunglasses were originally priced at $ 21.

Given that Lori brought sunglasses and flip-flops at a half-off sale, to determine, if she spent a total of $ 21 on the two items, what was the original price of the sunglasses (taking into account that they both cost the same) will be you must perform the following calculation:

Thus, the total price of both goods is $ 42, which, divided in half, results in $ 21 (42/2).

Therefore, the sunglasses were originally priced at $ 21.

Learn more in https://brainly.com/question/731526

Answer:

parallel : y = -3x + 3

perpendicular : y = 1/3x + 3

Step-by-step explanation:

rewrite 3x + y - 3 = 0

y = -3x + 3

parallel has the same slope

so

parallel : y = -3x + 3

perpendicular is negative reciprocal of the slope

so

-3x becomes 1/3x

so

perpendicular : y = 1/3x + 3

Answer:

[tex]y = - \frac{4}{5} x + \frac{6}{5} [/tex]

Step-by-step explanation:

First subtract 4x on both sides in order to get -5y alone. Now you have -5y = 4x + 6 (since neither 6 nor 4x are like terms). Now divide -5 on both sides in order to get rid of it, so we can get y by its self. Now you have y = -4/5 x + 6/5

Hope this makes sense. Also please tell me if I'm wrong and I'll be happy to look at it again for ya :)

The uniform width of the frame is 16.61 inches.

Since a rectangular canvas picture measures 12 inches by 28 inches, and the canvas is mounted inside a frame of uniform width, increasing the total area covered by both canvas and frame to 612 square inches, to find the uniform width of the frame you must perform the following calculation:

Therefore, the uniform width of the frame is 16.61 inches.

Learn more in https://brainly.com/question/15218328