At which point on the curve y = √x is the tangent line parallel to the secant line joining two point on the curve whose x-coordinates are 1 and 4? a. (9/4. 3/2)
b. (0,0) c. (1/2, 1/√2)
d. (4,2) e None

(10x-3=15x-18)

X = -1

Hey there!

\(Answer:\boxed{x=-1}\)

\(Explanation:\)

10x - 3 = -5x - 18

10x - 3 + 5x = -5x - 18 + 5x      Add 5x to both sides

15 - 3 = -18

15x - 3 + 3 = -18 + 3    Add 3 to both sides

15x = -15

15x/15 = -15/15

x = -1

Hope this helps!

The volume of the cone isV = 42.41\(Cm^{3}\).

In order to calculate the volume of the solid, you use the following formula:

where

r: radius of the circular base of the cone = 3 cm

h: height from the circular base to the peak of the cone = 4.5 cm

You replace the values of r and h in the formula for the

volume V = \(\frac{1}{3}\) \(\pi\) \((3cm)^{2}\)4.5 =42.411  \(cm^{3}\) = 42.41 \(cm^{3}\)

Hence, the volume of the cone  is 42.41 \(Cm^{3}\)

Volume may be a  measure of occupied three-dimensional space. it's  often quantified numerically using SI derived units (such as the cubic meter and liter) or by various imperial units (such as the gallon, quart, cubic inch). The definition of length (cubed) is interrelated with volume.  the quantity  of a container is generally understood to be the capacity of the container; i.e.,  the quantity  of fluid (gas or liquid) that the container could hold,  instead of  the amount of space the container itself displaces.In  past , volume is measured using similar-shaped natural containers and  afterward , standardized containers. Some simple three-dimensional shapes can have its volume easily calculated using arithmetic formulas. Volumes of more complicated shapes  are often  calculated with integral calculus if a formula exists for the shape's boundary.

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Step-by-step explanation:

b²-4ac>0

(-2)²-4(1×3k)>0

4-12k>0

-12k>-4

k<⅓

Answer:

Step-by-step explanation:

b²-4ac>0

(-2)²-4(1×3k)>0

4-12k>0

-12k>-4

k<⅓

The equation 4x + 4y = 20 can be rewritten in slope-intercept form as y = -x + 5.

The equation 4x + 4y = 20 can be rewritten in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

To rewrite the equation in slope-intercept form, we need to isolate y on one side of the equation.

Step 1: Subtract 4x from both sides of the equation:
4x + 4y - 4x = 20 - 4x

This simplifies to:
4y = -4x + 20

Step 2: Divide both sides of the equation by 4 to solve for y:
4y/4 = (-4x + 20)/4

This simplifies to:
y = -x + 5

Now, the equation is in slope-intercept form, y = -x + 5. In this form, we can easily identify the slope, which is -1, and the y-intercept, which is 5.

The slope (-1) indicates that for every increase of 1 unit in the x-direction, the y-value decreases by 1 unit. The y-intercept (5) represents the point where the line intersects the y-axis when x is 0.

So, the equation 4x + 4y = 20 can be rewritten in slope-intercept form as y = -x + 5.

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The convolution of f(t) = e^(-5t) and g(t) = {2, 0, 0 ≤ t < 4; 0, t ≥ 4} is given by h(t) = {2e^(-5t), 0 ≤ t < 4; 2e^(-5(t-4)), t ≥ 4}.

The convolution of two functions f(t) and g(t) is defined as:

h(t) = ∫_0^t f(τ) g(t-τ) dτ

In this case, we have:

f(t) = e^(-5t)

g(t) = {2, 0, 0 ≤ t < 4; 0, t ≥ 4}

To find the convolution h(t), we need to split g(t) into two parts based on the value of t:

For 0 ≤ t < 4, we have g(t) = 2.

For t ≥ 4, we have g(t) = 0.

Therefore, we can write:

h(t) = ∫_0^t e^(-5τ) 2 dτ + ∫_4^t e^(-5τ) 0 dτ

Simplifying the second integral, we get:

h(t) = 2 ∫_0^t e^(-5τ) dτ

h(t) = 2 [-1/5 e^(-5τ)]_0^t

h(t) = 2 (-1/5 e^(-5t) + 1/5)

h(t) = 2e^(-5t) - 2/5, for 0 ≤ t < 4

For t ≥ 4, we have:

h(t) = ∫_0^4 e^(-5τ) g(t-τ) dτ + ∫_4^t e^(-5τ) g(t-τ) dτ

Since g(t-τ) is zero for t-τ < 0, we can simplify the first integral to:

∫_0^(t-4) e^(-5τ) 2 dτ

Using the same technique as before, we can evaluate this integral to get:

[-1/5 e^(-5τ)]_0^(t-4)

= -1/5 e^(-5(t-4)) + 1/5

For the second integral, we have g(t-τ) = 0, so it simplifies to 0.

Therefore, we have:

h(t) = -1/5 e^(-5(t-4)) + 1/5, for t ≥ 4

Combining the two expressions for h(t), we get:

h(t) = {2e^(-5t), 0 ≤ t < 4; 2e^(-5(t-4)), t ≥ 4}

Thus, the convolution of f(t) = e^(-5t) and g(t) = {2, 0, 0 ≤ t < 4; 0, t ≥ 4} is given by h(t) = {2e^(-5t), 0 ≤ t < 4; 2e^(-5(t-4)), t ≥ 4}.

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The convolution of f(t) = e^(-5t) and g(t) = {2, 0, 0 ≤ t < 4; 0, t ≥ 4} is given by h(t) = {2e^(-5t), 0 ≤ t < 4; 2e^(-5(t-4)), t ≥ 4}.

The convolution of two functions f(t) and g(t) is defined as:

h(t) = ∫_0^t f(τ) g(t-τ) dτ

In this case, we have:

f(t) = e^(-5t)

g(t) = {2, 0, 0 ≤ t < 4; 0, t ≥ 4}

To find the convolution h(t), we need to split g(t) into two parts based on the value of t:

For 0 ≤ t < 4, we have g(t) = 2.

For t ≥ 4, we have g(t) = 0.

Therefore, we can write:

h(t) = ∫_0^t e^(-5τ) 2 dτ + ∫_4^t e^(-5τ) 0 dτ

Simplifying the second integral, we get:

h(t) = 2 ∫_0^t e^(-5τ) dτ

h(t) = 2 [-1/5 e^(-5τ)]_0^t

h(t) = 2 (-1/5 e^(-5t) + 1/5)

h(t) = 2e^(-5t) - 2/5, for 0 ≤ t < 4

For t ≥ 4, we have:

h(t) = ∫_0^4 e^(-5τ) g(t-τ) dτ + ∫_4^t e^(-5τ) g(t-τ) dτ

Since g(t-τ) is zero for t-τ < 0, we can simplify the first integral to:

∫_0^(t-4) e^(-5τ) 2 dτ

Using the same technique as before, we can evaluate this integral to get:

[-1/5 e^(-5τ)]_0^(t-4)

= -1/5 e^(-5(t-4)) + 1/5

For the second integral, we have g(t-τ) = 0, so it simplifies to 0.

Therefore, we have:

h(t) = -1/5 e^(-5(t-4)) + 1/5, for t ≥ 4

Combining the two expressions for h(t), we get:

h(t) = {2e^(-5t), 0 ≤ t < 4; 2e^(-5(t-4)), t ≥ 4}

Thus, the convolution of f(t) = e^(-5t) and g(t) = {2, 0, 0 ≤ t < 4; 0, t ≥ 4} is given by h(t) = {2e^(-5t), 0 ≤ t < 4; 2e^(-5(t-4)), t ≥ 4}.

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Answer:

180°is the sum of the interior angles of an equilateral triangle

Answer:

B

Step-by-step explanation:

a²+b²=c²

3²+b²=5²

b²=5²-3²

b²=25-9=16 answer is 16

Answer:

we need the rest of the question

Answer:

what is the question

Step-by-step explanation:

And what are the answer choices

Answer:

1.6

Step-by-step explanation:

Answer:

(2,8), (-1,-7), (-2,-3), (-8,-7)

Step-by-step explanation:

It's this one because each input (x axis) has one and only one output (y axis) The others the input has more than one output making them wrong. Hope this helps

Answer:

D. 1x9x4

Step-by-step explanation:

V= l x w x h

There are 3,628,800 different arrangements of balls that could be pulled out of the bag. None of the answer choices given are correct, as they all suggest a number smaller than the actual number of arrangements

To calculate the number of different arrangements of balls that can be

pulled out of the bag, we need to use the formula for permutations.

Since there are 10 balls in the bag, we have 10 choices for the first ball, 9

choices for the second ball, 8 choices for the third ball, and so on.

Therefore, the total number of arrangements is:

10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

So, there are 3,628,800 different arrangements of balls that could be

pulled out of the bag.

None of the answer choices given are correct, as they all suggest a

number smaller than the actual number of arrangements.

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40 percentage of 75 is 30 and 2/5 of 75 is 30. So, Priya calculated in a correct way.

Given,

To find 40% of 75, Priya calculates 2/5 of 75

We have to find the value of 40% of 75.

Percentage;

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.

Now,

Lets find;

40% of 75

40/100 × 75 = 40/4 × 3 = 10 × 3 = 30

That is,

40% of 75 is 30.

Now,

2/5 of 75

2/5 × 75 = 2 × 15 = 30

That is,

2/5 of 75 is also 30

Therefore,

40 percentage of 75 is 30 and 2/5 of 75 is 30. So, Priya calculated in a correct way

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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As proportional relationship, the amount decreasing at a rate milligrams per hour can be written in expression P(t) = 500 + e⁻⁰²ˣ

In math, the relationships between two variables where their ratios are equivalent is known as proportional relationship.

Given that P(t) represent the amount of a certain drug, in milligrams, that is in the bloodstream at time t hours.

Here we have the rate at which the drug leaves the bloodstream proportional to the amount of the drug bloodstream.

The amount of the drug in the bloodstream can be modeled by dP/dt = kP, where k is a constant and t is time, in hours.

Here we need to find the expression.

Bloodstream = 500 milligrams

So, the expression for this proportional relationship is written as;

P(t) = 500 + e⁻⁰²ˣ

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Answer:

2/5 or 40%

Step-by-step explanation:

.40 is 40 hundredths or 40/100

40/100 can be reduced to 20/50 and reduced again to 10/25 and one more time to 2/5

Percentages are fractions out of 100 so 40/100 would be 40%.

Given that a circle with radius 20 has a corresponding angle of 305°.

To find the coordinates of a point on the circle, we use the formula:`(r cos (θ), r sin (θ))`Here, `r = 20` and `θ = 305°`.

Substituting the values of `r` and `θ` in the formula, we get:`(20 cos (305°), 20 sin (305°))`

Using the values of trigonometric ratios, we can write:cos(305°) = cos(360° - 305°) = cos(55°) ≈ -0.5736sin(305°) = sin(360° - 305°) = sin(55°) ≈ 0.8192

Hence, the coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`.

The coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`

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The angle of depression the plane should descend is 1.43 degrees.

A plane is flying at an altitude of 25,000 ft when it start it descent to the airport. The plane is a horizontal distance of 1000,000 ft from the airport.

Therefore, let's find the angle of depression.

Hence, this situation forms a right angle triangle.

Therefore,

tan ∅ = opposite / adjacent

where

Hence,

tan ∅ = 25000 / 1000000

∅ = tan⁻¹ 25 / 1000

∅ =  tan⁻¹  0.025

∅ = 1.43209618416

∅ = 1.43 degrees

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The ∆ABC is an isosceles triangle and have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides AB ≅ BC, then the triangle ∆ABC has two sides with similar length and base angles so;

angles m∠A and m∠C are the base angles are both equal to 51°

m∠B = 180° - (51 + 51)° {sum of interior angles of a triangle}

m∠B = 180° - 102°

m∠B = 78°

Therefore, the isosceles triangle ∆ABC have the base angles m∠A and m∠C equal to 51° and the angle m∠B is equal to 78°.

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The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

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Given:

A city's population has increased 40% in the last 5 years and is now 53,782 people.

To find:

The population 5 years ago.

Solution:

Let x be the population 5 years ago.

A city's population has increased 40% in the last 5 years.

So, present population is

\(x+x\times \dfrac{40}{100}=x+0.4x=1.4x\)

It is given that the present population is 53782.

\(1.4x=53782\)

\(x=\dfrac{53782}{1.4}\)

\(x=38415.7142857\)

\(x\approx 38416\)

Therefore, the population 5 years ago was about 38416.

To determine the position of the term in the sequence that first has a value greater than 1000, we need to solve the inequality 3n^2 > 1000. The position of the term is approximately 19.

We are given that the nth term of the sequence is given by 3n^2. We need to find the position (value of n) at which the term exceeds 1000.

To solve this, we set up the inequality:

3n^2 > 1000

Dividing both sides by 3, we have:

n^2 > 333.33

Taking the square root of both sides, we get:

n > √333.33

Approximating the square root of 333.33 to the nearest whole number, we find:

n > 18.24

Since n represents the position of the term in the sequence, it must be a positive whole number. Therefore, the smallest value of n that satisfies the inequality is 19.

Hence, the position of the term in the sequence that first has a value greater than 1000 is approximately 19.

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Draw the circle with the center at the intersection of the perpendicular bisectors and the radius equal to the distance found in step 4.

When constructing a circle circumscribed about a triangle, the following step is needed:

Identify the three vertices of the triangle.

Let's say the triangle has vertices A, B, and C.

Find the perpendicular bisectors of the triangle's sides.

For each side of the triangle, construct a line that is perpendicular to the side and passes through its midpoint.

Locate the point of intersection of the perpendicular bisectors.

The point where all three perpendicular bisectors intersect is the center of the circumscribed circle.

Measure the distance from the center to any of the triangle's vertices.

This distance is the radius of the circumscribed circle.

By following these steps, you can construct a circle that passes through all three vertices of the triangle. This circle is known as the circumscribed circle or circumcircle of the triangle. It is unique to each triangle and provides a useful geometric property that can be applied in various mathematical and geometric contexts.

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Answer:

Step-by-step explanation:

1.5  - 0.25 = 1.25 = 1 1/4

We can turn both fractions into decimals.

1/4 = 0.25

1 1/2 = 1.5

Subtract.

0.25 - 1.5 = -1.25

Turn back into a fraction.

-1.25 = -1 1/4

Best of Luck!

The particular solution of the given differential equation is : y(x) = -2cos(4x) - (1/2)sin(4x).

Given the differential equation is: I y" + 16 y =0 with initial values y(0) = -2, and y'(0) = -2.

We have to find the solution of the differential equation. We know that the standard form of a second-order homogeneous differential equation is:

y"+p(x)y'+q(x)y=0

The characteristic equation is obtained by substituting y=e^(mx) in the above equation. The characteristic equation is:

m²+p(x)m+q(x)=0

Comparing the above equation with

y" + 16 y = 0, we have,

p(x) = 0 and q(x) = 16

Therefore, the characteristic equation becomes:

m² + 16 = 0

m = ±4i

Hence, the general solution of the given differential equation is:

y(x) = c1cos(4x) + c2sin(4x). Now, let us apply the initial conditions:

y(0) = c1 = -2

Also, y'(x) = -4c1sin(4x) + 4c2cos(4x)Therefore,

y'(0) = 4= c2 = -2

c2 = -1/2

Therefore, the particular solution of the given differential equation is y(x) = -2cos(4x) - (1/2)sin(4x).

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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