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3 years ago

Complete the square to solve the equation below. x^2-10x-2=17

Mathematics

1 answer:

Naddika [18.5K]3 years ago

8 0

Answer:

Exact form : x = +_2 squareroot 11+5

Decimal form : x=11.63324958...,-1.63324958...

Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term. Solve for x by using the term to complete the square.

I hope this helps you out! :)

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Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0

STALIN [3.7K]

$\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0$

This ODE has characteristic equation

$r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)$

$=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0$

which has roots at $r=1,-1\pm i$ . Then the characteristic solution to the ODE is

$u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}$

$\implies\boxed{u(t)=C_1e^t+C_2e^{-t}\cos t+C_3e^{-t}\sin t}$

6 0

3 years ago

The statue of Liberty stands on a 150 ft. pedestal. From a point 250 ft. from the base of the

bekas [8.4K]

Answer:

148ft

Step-by-step explanation:

To solve this question, you'll have to imagine the statue makes a right angle triangle with the base since it has an angle of elevation from the base to the top of the torch.

Assuming the height from the pedestal to the top of the torch is y

The height of the statue is x

But we know the height of the pedestal = 150ft

The distance from the observer to the base of the pedestal = 250ft

And the angle of elevation = 50°

See attached document for better illustration.

Tanθ = opposite / adjacent

θ = 50°

Adjacent = 250

Opposite = y

Tan50 = t / 250

y = 50 × tan50

y = 50 × 1.1917

y = 297.925ft

The height of the statue from the base of the pedestal to the top of the torch is 297.925ft

The height of the statue = x

x = (height of the statue + height of the pedestal) - height of the pedestal

x = y - 150

x = 297.925 - 150

x = 147.925ft

Approximately 148ft

The height of the statue is 148ft

4 0

3 years ago

I need help on this. The portrait studio can buy photographs on canvas. The small canvas photograph print is $20 and the large c

Whitepunk [10]

<h3>Answer:</h3>

6 large prints
12 small prints

<h3>Step-by-step explanation:</h3>

<em>Numerical Reasoning</em>

Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...

... 2×$20 +45 = $85

To have revenue of at least $510, the studio must sell ...

... $510/$85 = 6

sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.

_____

<em>With an equation</em>

Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...

... 20·2x +45·x ≥ 510

... 85x ≥ 510

... x ≥ 510/85

... x ≥ 6

The studio needs to sell at least 6 large prints and 12 small prints.

8 0

3 years ago

Two make ice cream for a family reunion frank used 6 cups of cream 1/2 gallon of gallon of milk. How many pints of cream and mil

aleksley [76]

He used 7 pints all together because there at 2 cups in each pint and 4 pints in a half a gallon.

6 0

3 years ago

it takes 1/3 cup of sugar to make a milkshake you have 6 cups of sugar how many milk shakes can you make?

Gekata [30.6K]

Answer:

Step-by-step explanation:

1/3 * 18 = 6 or 6/(1/3) = 18 or 6 * 3 =18

6 0

3 years ago

Complete the square to solve the equation below. x^2-10x-2=17​

Complete the square to solve the equation below. x^2-10x-2=17