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3 years ago

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[Related Rates]

1 answer:

Orlov [11]3 years ago

6 0

Below is the solution:

A(final)=16cm^2 ds/dT=6 da/dT=?

<span>A=(s)^2 A=16cm^2 , s=sqrt(A) , s=sqrt(16) , s=4cm </span>

<span>da/dT=2(s)(6cm/sec) , da/dT=12cm/sec(s) , da/dT=12cm/sec (4cm)
</span>
<span>Answer should be da/dT=48cm^2/sec
</span>
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Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day. At the same rates two Nissans, four Fords, and thr

Sindrei [870]

Answer:

The rental rate for the Fords is of $12 per day.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the cost of a Nissan.

y is the cost of a Ford.

z is the cost of a Chevrolet.

Three Nissans, two Fords, and four Chevrolets can be rented for $106 per day.

This means that:

$3x + 2y + 4z = 106$

Two Nissans, four Fords, and three Chevrolets cost $107 per day

This means that:

$2x + 4y + 3z = 107$

Four Nissans, three Fords, and two Chevrolets cost $102 per day.

This means that:

$4x + 3y + 2z = 102$

From the first equation:

$4z = 106 - 3x - 2y$

$2z = 53 - 1.5x - y$

$z = 26.5 - 0.75x - 0.5y$

Replacing into the third equation:

$4x + 3y + 53 - 1.5x - y = 102$

$2.5x + 2y = 49$

From the second equation:

$2x + 4y + 3z = 107$

$2x = 107 - 4y - 3z$

$x = 53.5 - 2y - 1.5z$

$x = 53.5 - 2y - 1.5(26.5 - 0.75x - 0.5y)$

$x - 1.125x = 53.5 - 2y - 39.75 + 0.75y$

$-0.125x = 13.75 - 1.25y$

$0.125x = 1.25y - 13.75$

$x = \frac{1.25y - 13.75}{0.125}$

$x = 10y - 110$

Find the rental rate for the Fords.

We have to find y, so:

$2.5x + 2y = 49$

$2.5(10y - 110) + 2y = 49$

$25y - 275 + 2y = 49$

$27y = 324$

$y = \frac{324}{27}$

$y = 12$

The rental rate for the Fords is of $12 per day.

3 0

3 years ago

Given points A (1, 2/3), B (x, -4/5), and C (-1/2, 4) determine the value of x such that all three points are collinear

AlladinOne [14]

Answer:

$x=\frac{83}{50}$

Step-by-step explanation:

we know that

If the three points are collinear

then

$m_A_B=m_A_C$

we have

A (1, 2/3), B (x, -4/5), and C (-1/2, 4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope AB

we have

$A(1,\frac{2}{3}),B(x,-\frac{4}{5})$

substitute in the formula

$m_A_B=\frac{-\frac{4}{5}-\frac{2}{3}}{x-1}$

$m_A_B=\frac{\frac{-12-10}{15}}{x-1}$

$m_A_B=-\frac{22}{15(x-1)}$

step 2

Find the slope AC

we have

$A(1,\frac{2}{3}),C(-\frac{1}{2},4)$

substitute in the formula

$m_A_C=\frac{4-\frac{2}{3}}{-\frac{1}{2}-1}$

$m_A_C=\frac{\frac{10}{3}}{-\frac{3}{2}}$

$m_A_C=-\frac{20}{9}$

step 3

Equate the slopes

$m_A_B=m_A_C$

$-\frac{22}{15(x-1)}=-\frac{20}{9}$

solve for x

$15(x-1)20=22(9)$

$300x-300=198$

$300x=198+300$

$300x=498$

$x=\frac{498}{300}$

simplify

$x=\frac{83}{50}$

8 0

3 years ago

If EH = 76, calculate DI.

Montano1993 [528]

Answer:

DI = 38

Step-by-step explanation:

Δ EHC and Δ DIC are similar and ratios of corresponding sides are equal, that is

$\frac{DI}{EH}$ = $\frac{DC}{EC}$ , substitute values

$\frac{DI}{76}$ = $\frac{1}{2}$ ( cross- multiply )

2DI = 76 ( divide both sides by 2 )

DI = 38

4 0

3 years ago

What is the root of this equation? <br>2x^2 - 4x + 9 = 0

faust18 [17]

Answer:

x = 1 + i sqrt(7/2) or x = 1 - i sqrt(7/2)

Step-by-step explanation:

Solve for x:

2 x^2 - 4 x + 9 = 0

Divide both sides by 2:

x^2 - 2 x + 9/2 = 0

Subtract 9/2 from both sides:

x^2 - 2 x = -9/2

Add 1 to both sides:

x^2 - 2 x + 1 = -7/2

Write the left hand side as a square:

(x - 1)^2 = -7/2

Take the square root of both sides:

x - 1 = i sqrt(7/2) or x - 1 = -i sqrt(7/2)

Add 1 to both sides:

x = 1 + i sqrt(7/2) or x - 1 = -i sqrt(7/2)

Add 1 to both sides:

Answer: x = 1 + i sqrt(7/2) or x = 1 - i sqrt(7/2)

4 0

3 years ago

I JUST NEED 4 PLS!!!!!!

Alchen [17]

Answer:

C

Step-by-step explanation:

When doing 4 divided by 2 you get 2. Looking at the sign it is saying 3 is greater than the number we solve for. Since we solved and got 2 we can double check and ask is 3 greater than 2? Yes it is so that would make the statement correct.

Hope this Helps :)

6 0

3 years ago