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3 years ago

There are two numbers that

Mathematics

2 answers:

maw [93]3 years ago

7 0

Answer:

Larger number is 20

Step-by-step explanation:

20 * -4 = -80

20 + (-4) = 16

Mumz [18]3 years ago

5 0

Answer

Step-by-step explanation:

-4*20=-80

-4+20=16

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Answer:

Step-by-step explanation: Not completely sure but i think the answer is 11

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4 years ago

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The hypotenuse of a right triangle measures 9 inches, and one of the acute angle measures 36 degrees. What is the area of the tr

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Find the length of the following curve. If you have a grapher, you may want to graph the curve to see what it looks like.

stepladder [879]

The length of the curve $y = \frac{1}{27}(9x^2 + 6)^\frac 32$ from x = 3 to x = 6 is 192 units

<h3>How to determine the length of the curve?</h3>

The curve is given as:

$y = \frac{1}{27}(9x^2 + 6)^\frac 32$ from x = 3 to x = 6

Start by differentiating the curve function

$y' = \frac 32 * \frac{1}{27}(9x^2 + 6)^\frac 12 * 18x$

Evaluate

$y' = x(9x^2 + 6)^\frac 12$

The length of the curve is calculated using:

$L =\int\limits^a_b {\sqrt{1 + y'^2}} \, dx$

This gives

$L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx$

Expand

$L =\int\limits^6_3 {\sqrt{1 + x^2(9x^2 + 6)}\ dx$

This gives

$L =\int\limits^6_3 {\sqrt{9x^4 + 6x^2 + 1}\ dx$

Express as a perfect square

$L =\int\limits^6_3 {\sqrt{(3x^2 + 1)^2}\ dx$

Evaluate the exponent

$L =\int\limits^6_3 {3x^2 + 1} \ dx$

Differentiate

$L = x^3 + x|\limits^6_3$

Expand

L = (6³ + 6) - (3³ + 3)

Evaluate

L = 192

Hence, the length of the curve is 192 units

Read more about curve lengths at:

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2 years ago

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Vaselesa [24]

Answer:

Step-by-step explanation:

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3 years ago

Solve this equation for x: 2x^2 + 12x - 7 = 0

zhannawk [14.2K]

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: $2x^2 + 12x - 7 = 0$

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

$2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7$

Step 2: Divide the equation all through by the coefficient of $x^2$ which is 2.

$x^2 + 6x=\frac{7}{2}$

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3= $3^2$

Therefore, we have:

$x^2 + 6x+3^2=\frac{7}{2}+3^2$

Step 4: Write the Left Hand side in the form $(x+k)^2$

$(x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\$

Step 5: Take the square root of both sides and solve for x

$x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355$

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3 years ago