a man 6 feet tall walks at a rate of 5 ft / sec away from a light that is 15 feet above the ground. when he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?

Answer:

x = 3

Step-by-step explanation:

4 + x = 7  Subtract 4 from both sides of the equation

4 - 4 - x = 7 - 4  Simplify

x = 3  X equals 3

Answer:

x = 3

Step-by-step explanation:

4 + x = 7

x + 4 - 4 = 7-4 = 3

x = 3

To solve for x, subtract 4 from both side of the equation.  This leaves x by itself on the left side of the equation.  Next subtract 4 from 7 to get the solution, x = 3.

The slope of the rapids is -0.067

Kannanaski Rapids drops  62 ft vertically

The horizontal distance of 920 ft.

tan θ is a commonly used trigonometric function along with other 5 functions. tan θ is also called as law of tangent. The tangent formula for a right-angled triangle can be defined as the ratio of the opposite side of a triangle to the adjacent side. It can also be represented as a ratio of the sine of the angle to the cosine of the angle.

Slope of Rapids= tanθ= [tex]\frac{y}{x}=\frac{-62}{920} \\[/tex]

=-0.067

Therefore, the slope of rapids is -0.067.

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The final solution is:

(1) Tu=<7, 1, 13>, Tv=<0, -1, 1> and n(u,v)=<14, -7, -7>.

(2) the area of S=Φ(D): Area(S) = 514.39

(3) ∬sf(x,y,z)ds = 190√(294) = 3257.82

What is the double integral?

A multiple integral is a definite integral of a function of several real variables, for instance, f or f.

1. Φ(u,v) gives the parametrization with its x, y, and z components. So, x=7u+4, y=u-v, and z=13u+v.

We can use this to get the tangent vectors by taking the respective partial derivatives.

Tu=<7, 1, 13> by taking the u derivatives of the components, and Tv=<0, -1, 1> by taking the v derivatives of the components.

2. Taking the cross product of Tu and Tv will give the normal vector n(u,v), which is <14, -7, -7>.

3. To find Area(S), you have to multiply the area of D by the magnitude of the normal vector from the previous step. D is the region defined by 0<=u<=5 and 0<=v<=6, so the area of D is 5*6=30.

Multiply this by the magnitude of the normal vector to find that Area(S)=30√(294)

Area(S) = 514.39

4. To integrate, we first must put the initial function in terms of the parameters we found in the first step.

Replace y with u-v and z with 13u+v. Next, multiply this integrand by the magnitude of the normal vector (√294) and apply the given bounds for u (0<=u<=5) and v (0<=v<=6).

From here the problem can be integrated like any other double integral, the final answer being 190√(294).

Hence, The final solution is:

(1) Tu=<7, 1, 13>, Tv=<0, -1, 1> and n(u,v)=<14, -7, -7>.

(2) the area of S=Φ(D): Area(S) = 514.39

(3) ∬sf(x,y,z)ds = 190√(294) = 3257.82

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Complete Question:

Show that Φ(u,v)=(7u+4,u−v,13u+v) parametrizes the plane 2x−y−z=8. Then: (a) Calculate Tu , Tv, and n(u,v). (b) Find the area of S=Φ(D), where D=(u,v):0≤u≤5,0≤v≤6. (c) Express f(x,y,z)=yz in terms of u and v and evaluate ∬sf(x,y,z)ds(a) Tu= , Tv= , n(u,v)=_______________(b) Area(S)=_______(c) ∬sf(x,y,z)ds=___________

Answer: x = 2 hours y= 7 hours = 9 hours a week, 80$ a week

Step-by-step explanation:

5$x2=10$   10$x7=70$ 70$ + 10$ = 80 $.

hopefully, maybe that helps for the first question.

Answer:

-6, 7

Step-by-step explanation:

Answer: B(-6,7)

Step-by-step explanation:

M(-5, 1)      A(-4,-5)       B(x,y)=?

[tex]\displaystyle\\M_x=\frac{x_A+x_B}{2} \\\\-5=\frac{-4+x_B}{2}\\\\[/tex]

Multiply both parts of the equation by 2:

[tex]-5(2)=-4+x_B\\\\-10=-4+x_B\\\\-10+4=-4+x_B+4\\\\-6=x_B\\\\Thus,\ x_B=-6[/tex]

[tex]\displaystyle\\\\\\1=\frac{-5+y_B}{2} \\\\[/tex]

Multiply both parts of the equation by 2:

[tex]1(2)=-5+y_B\\\\2=-5+y_B\\\\2+5=-5+y_B+5\\\\7=y_B\\\\Thus,\ y_B=7[/tex]

The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.

We have been given parametric equations x = t^2 − 3t, y = √t

We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

NWe know that the formula to find the area under the curve.

A = ∫[a to b] g(t)f'(t) dt

here, a = 0 and b = 3

so, A = ∫[0 to 3] √t (2t - 3) dt

A = ∫[0 to 3] (2t√t - 3√t) dt

A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt

A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]

A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0

A = 4/5 3^(5/2) - 2 3^(3/2)

A = 6√3 /5

A = 2.08

Therefore,  the area of the curve is 2.08 square units.

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Answer:

1

Step-by-step explanation:

because you can only cut it in a certain way that both pieces are the same measurements

Answer: They lose $250000 per year over the three years!

Step-by-step explanation:

First, find the total profit for the two following years

Take $625000 times 2 = $1250000

Next, find the total they made in 3 years

Take -$2000000 of the first year + $1250000 = - $750000

Now we find their average profit per year

Take -$750000 divided by 3 = -$250000

They lose $250000 per year over the three years

Answer:

3x²

= 3(10)²

= 3(100)

= 300

Step-by-step explanation:

Answer:

You buy the following from Walmart:

1 puzzle for $8, 1 TV for $350, 1 cutting board for $9, and 1 blender for $25

You have a 10% off coupon,  

What is the new Subtotal:

Sales tax is 5%: $

What is the total:

Step-by-step explanation:

To calculate how much Kaitlyn will have after four years with continuous compounding, we can use the following formula:

A = P * e^(r*t)

where A is the final amount, P is the initial principal (in this case, $3,000), r is the annual interest rate (4.08%), and t is the number of years (4). Plugging these values into the formula, we get:

A = $3,000 * e^(0.0408*4)

= $3,000 * e^0.1632

= $3,000 * 1.1759

= $3,527.77

Therefore, Kaitlyn will have $3,527.77 after four years with continuous compounding, which is close to [A] $3,532.18.

Answer:

Step-by-step explanation:

ok so standard form is

Ax+By=C

and its actually really simple

when you want to find the y-intercept

set x to 0

it will look something like

A(0)+By=C

By=C

y=C/B

It makes more sense with actual numbers

so

3x+2y=4

3(0)+2y=4

0+2y=4

2y=4

y=2

therefore the y intercept would be 2

for that equation

but you can do the same for x-intercept

just set y to 0

hope this helped :)

The cost of one day-Lilly is found to be $4 and the cost of one geranium is found to be $8. Therefore, Paul spent about $16 for day-Lilly and $56 for geranium. And Megan spent about $40 for day-Lilly and $88 for geranium.

Two or more algebraic equations that have a common variable and are solved simultaneously are referred to as simultaneous equations. We can find the answers to both unknowns if we have two separate equations with the same two unknowns in each. Here, we'll employ the addition-and-subtraction or elimination method.

Let's consider the cost of day-Lilly as x and the cost of geranium as y. The cost spent by Paul is written as 4x+7y=$72 and Megan is written as 10x+11y=$128.

Solving these two equations for x and  y,

[tex]\begin{aligned}40x+70y = \$720\\\underline{40x+44y=\$512}\\26y=\$208\\y=\$8 \end{aligned}[/tex]

Substitute the value of y in equation 4x+7y=$72 to get the value of x,

[tex]\begin{aligned}4x+7(8)&=\$72\\4x&=\$16\\x&=\$4\end{aligned}[/tex]

The answers are $4 and $8.

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The coordinate of the vertex B after the transformation of the given trapezoid is (-2, 2).

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

As per the given graph, the coordinate of vertex B is (-5, 4).

After the translation (x, y) → (x + 3, y - 2), the new coordinate can be obtained as,

(-5, 4) → (-5 + 3, 4 - 2)

⇒ (-2, 2)

Hence, the coordinate of B after the transformation is (-2, 2).

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Answer:

£22.33

Step-by-step explanation:

calculate the cost of an album and a single track using simultaneous equations.

let a represent an album and s a single track , then

3a + 4s = 18.13 → (1)

2a + 5s = 13.93 → (2)

multiplying (1) by - 2 and (2) by 3 and adding will eliminate a

- 6a - 8s = - 36.26 → (3)

6a + 15s = 41.79 → (4)

add (3) and (4) term by term to eliminate a

0 + 7s = 5.53

7s = 5.53 ( divide both sides by 7 )

s = 0.79

substitute s = 0.79 into either of the 2 equations and solve for a

substituting into (1)

3a + 4(0.79) = 18.13

3a + 3.16 = 18.13 ( subtract 3.16 from both sides )

3a = 14.97 ( divide both sides by 3 )

a = 4.99

that is album costs £4.99 and single track £0.79

then cost to Charlotte is

cost = (4 × £4.99) + (3 × £0.79) = £19.96 + £2.37 = £22.33

The cost of 4 albums and 3 single tracks is £22.33

Let the cost of 1 album = £x

and let the cost of 1 single track = £y

Now, the cost of 3 albums and 4 single tracks = £3*x + £4*y

and cost of 2 albums and 5 single tracks= £2*x + £5*y

Given that,

£3*x + £4*y = £18.13  -------->(1)

£2*x + £5*y = £13.93 -------->(2)

Multiply (1) equation by 2 and (2) equation by 3 then solve for x and y.

On applying the substitution method we have,

x = £4.99 and y = £0.79

Now, we have to calculate the value of 4 albums and 3 single tracks.

It can be written as 4*x +3*y

£4*4.99 + £3*0.79 = £22.33

So, the cost of 4 albums and 3 single tracks is £22.33

This question is based on a linear equation in two variables. Here, we used two equations based on two variables and then solved them with the help of the substitution method.

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Answer:

4 ( 2q + 5 )

Step-by-step explanation:

8q + 20

HCF is 4

= 4 ( 2q + 5 )

pls rate as brainliest

From the given options, option B is the only statement that is not true is ∠C ≅ ∠E.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

If Δ ABC is congruent to Δ DEF, then its corresponding parts must be congruent.

segment AB ≅ segment DE

segment BC ≅ segment EF

segment AC ≅ segment DF

∠A ≅ ∠D

∠B ≅ ∠E

∠C ≅ ∠F

Therefore, from the given options, option B is the only statement that is not true is ∠C ≅ ∠E.

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"Your question is incomplete, probably the complete question/missing part is:"

If triangle ABC is congruent to triangle DEF, which statement is not true?

A) Segment AB ≅ segment DE

B) ∠C ≅ ∠E

C) Segment BC ≅ segment EF

D) ∠A ≅ ∠D

The line of reflection and the image of after reflection graph is attached below  

What is line of reflection ?

The picture is consistent with the preimage when reflecting a figure in a line or a point. Every point on a figure is translated into an image by a reflection across a set line. The term "line of reflection" refers to the fixed line.

The line of reflection is a line across which an image will reflect. Every point in a figure is said to reflect the other figure if and only if it is equally spaced from every corresponding point in the other figure. The image that is reflected should be identical in size and shape but face the opposite way.

Graph the quadrilateral. By inspection, you can tell where the midpoint is. (see attachment 1)

Now, I'll draw a line through it. (see attachment 2)

To reflect across a line, think about the points traveling across the line the same number of spaces the point is from the line. For example, point A is three away from the line. So, A' will be 3 away from the other side. The coordinates will be at (-3,2). (see attachment 3).

Do the same for the other points, and you'll have your image.

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The relationship represented is linear. Where f(0) = 2 and f(n) = f(n-1)+4.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively. There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation.

Given,

Functions,

f(0) = 2

f(n) = f(n-1) + 4

Equating 0

f(0) = f(0-1) + 4

f(0) = 4

The relationship represented is linear. Where f(0) = 2 and f(n) = f(n-1)+4.

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Answer:

II) it has all sides of equal length

Answer:

6

Step-by-step explanation:

        6 is a factor of X , Y and Z.

    So, 6 will be a common factor of X + Y + Z.

An expression to represent the total penalty fees after 3 days late is given by T = 25d.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total penalty fees after 3 days late;

T = md + b

Where:

Therefore, the required linear function that represents the total penalty fees after 3 days late is given by this mathematical expression;

T = 25d

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According to the Kepler's third law, the squares of the period of a planet's orbit is proportional to the cube of the semimajor axis.

According to Kepler's third law,

     t2 = a3

Kepler's third law compares the orbital period and radius of orbit of a planet to those of other planets. This comparison between period and radius being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets. It provides an accurate description of the period and distance for a planet's orbits about the sun. The square of the period of a planet's orbit is proportional to the cube of its semimajor axis.  Kepler's Third Law depends on the total mass of the two bodies involved.

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Answer:

square and cube is the answers

Step-by-step explanation:

Answer:

No it is not possible, you would have to do 74.25 divided by 3

Step-by-step explanation:

3 divided by 74.25 = 0.0404040404

but

74.25 divided by 3 = 24.75

Answer:

5x^2 - 40x

Step-by-step explanation:

5x (x-8)

5x^2 - 40x

The probability that to total time to wash and condition a customer's hair will take longer more than 5 minutes is  0.63341

In this question we have been given that at supercuts, washing a customer's hair takes an average of 3. 5 minutes with a standard deviation

of 1. 2 minutes. Applying conditioner takes an average of 2. 1 minutes with a standard deviation of. 75 minutes.

μ1 = 3.5, μ2 = 2.1

σ1 = 1.2, σ2 = 0.75

The mean of the sum of the two random variables would be,

μ = μ1 + μ2

μ = 3.5 + 2.1

μ = 5.6

The Standard Deviation of the Sum of Two Independent Random Variables would be,

σ = √(σ1)² + (σ2)²

σ = √(1.2)² + (0.75)²

σ = 1.76

The probability that to total time to wash and condition a customer's hair will take longer more than 5 minutes.

i.e., P(x > 5)

First we find the z-score.

z = X - μ/σ

z = 5 - 5.6/1.76

z = -0.34091

P-value from Z-Table:

P(x<5) = 0.36659

So, P(x>5) = 1 - P(x<5)

                 = 0.63341

Therefore, the required probability is  0.63341

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Answer:

a = 120 cm2

Step-by-step explanation:

The prism has 5 sides:

2 triangles, base: 3 hight: 4, each

3 rectangles, 3x9, 5x9 and 4x9

Add the areas on each side to the total area:

[tex]a=(2)\frac{(3)(4)}{2} +(3)(9)+(5)(9)+(4)(9)=12+27+45+36[/tex]

[tex]a=120cm^{2}[/tex]

Hope this helps

Answer:

y=1/2x+1

Step-by-step explanation:

I think so I'm not an expert

Answer:

y = - [tex]\frac{1}{2}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 2 ) and (x₂, y₂ ) = (- 4, 1 )

m = [tex]\frac{1-(-2)}{-4-2}[/tex] = [tex]\frac{1+2}{-6}[/tex] = [tex]\frac{3}{-6}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 2 ) , then

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{2}[/tex] x - 1 ← equation of line

The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. This means that the surface area of the balloon is increasing at the rate of 8πr cm^2/sec.

The volume of a sphere is given by the formula 4/3πr^3, where r is the radius of the sphere. If the radius of the balloon is 6 cm, then the volume of the balloon is (4/3)π(6^3) = (4/3)π216 = 288π cm^3.

To find the rate at which the volume of the balloon is increasing, we need to take the derivative of the formula for the volume of a sphere with respect to time. This gives us (4/3)π(3r^2)(dr/dt).

Since the radius of the balloon is 6 cm and the surface area of the balloon is increasing at the rate of 8πr cm^2/sec, the rate at which the radius of the balloon is increasing is (8πr/4πr^2) = 2/r = 2/6 = 1/3 cm/sec.

Plugging this into the formula for the rate of change of the volume of the sphere, we get

Therefore, the volume of the balloon is increasing at a rate of 144π cm^3/sec when the radius of the balloon is 6 cm.

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Complete Question:

The surface area of a spherical balloon is increasing at the rate of 2 cm 2/sec. At what rate is the volume of the balloon is increasing when the radius of the balloon is 6 cm?

Answer:

y=3/4x-9/2

Step-by-step explanation:

y=mx+c

m=dy/dx

=-3/-4

=3/4

-3=(3/4*2)+c

-3=3/2+c

-9/2=c