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3 years ago

-5x + 9 = -3x + 1 solve the equation

Mathematics

1 answer:

Helen [10]3 years ago

3 0

Answer:

x=4

Step-by-step explanation:

Step 1: Add 3x to both sides.

−5x+9+3x=−3x+1+3x

−2x+9=1

Step 2: Subtract 9 from both sides.

−2x+9−9=1−9

−2x=−8

Step 3: Divide both sides by -2.

−2x/−2=−8/−2

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Use the discriminant to determine the nature of the roots of the following equation.

kvv77 [185]

Discussion

The discriminate is b^2 - 4*a*c

The general equation for a quadratic is ax^2 + bx + c

In this equation's case

a = 1

b= -5

c = - 3

Solve

(-5)^2 - 4*(1)*(-3)

25 - (-12)

25 + 12

Note

Since the discriminate is > 0, the roots are real and different. The roots do exist and there are 2 of them.

4 0

2 years ago

Evaluate

lora16 [44]

Answer:

Step-by-step explanation:

the top part with the variables filled in is 0 + (2x4) + (3x4x2) which is 32

the bottom part would be (3x0) + 4 which is 4

7 0

2 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1

charle [14.2K]

Answer- Length of the curve of intersection is 13.5191 sq.units

Solution-

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ $\frac{dx}{dt} = -\sin t$

$\frac{dy}{dt} = 2 \cos t$

$\frac{dz}{dt} = \sin t-2cos t$

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

∴ Arc length

$= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}$

$=\int_{0}^{2\pi}\sqrt{(-\sin t)^{2}+(2\cos t)^{2}+(\sin t-2\cos t)^{2}$

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$

Now evaluating the integral using calculator,

$=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t)$ $= 13.5191$

8 0

3 years ago

F(x) = -3(x - 1)2 + 3 How do you turn it into standard form

Zepler [3.9K]

Answer:

$\displaystyle \boxed{f(x) = 6x - 3x^2}$

Step-by-step explanation:

f(x) = −3(x² - 2x + 1) + 3

f(x) = −3x² + 6x - 3 + 3

f(x) = −3x² + 6x

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

7 0

3 years ago

Find the area of the shaded region .

Greeley [361]

Calculate area of the white region inside circle.

Area of the two white triangles in top left and bottom right:

$2 \cdot \frac{1}{2}(6)(6) = 36 ft^2$

Area of the two white quarter circles in the bottom left and top right:

$2 \cdot \frac{1}{4}\pi (6)^2 = 18\pi ft^2$

Total area of unshaded white region inside circle:

$(36 + 18\pi)ft^2$

Area of entire circle including the white and shaded regions

$\pi(6)^2 = 36\pi ft^2$

Area of shaded region is area of entire circle - area of unshaded white region

$36\pi - (36 + 18\pi) = (18\pi - 36) ft^2$

7 0

2 years ago