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4 years ago

The quadratic equation 2x^2 + bx + 18 = 0 has a double root. Find all possible values of b.

1 answer:

4 0

When a quadratic equation ax^2+bx+c has a double root, the discriminant,
D=b^2-4ac=0
Here
a=2,
b=b,
c=18
and
D=b^2-4ac=b^2-4*2*18=0
solve for b
b^2-144=0
=> b= &pm; sqrt(144)= &pm; 12

So in order that the given equation has double roots, the possible values of b are &pm; 12.

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serious [3.7K]

Answer:

Center: (4,8)

Radius: 2.5

Equation: $(x-4)^2+(y-8)^2=6.25$

Step-by-step explanation:

It was given that; the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).

Note that the longest chord is the diameter;

The midpoint of the ends of the diameter gives us the center;

Use the midpoint formula;

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )$

The center is at; $(\frac{4+4)}{2} ,\frac{5.5+10.5}{2}=(4,8)$

To find the radius, use the distance formula to find the distance from the center to one of the endpoints.

The distance formula is;

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$r=\sqrt{(4-4)^2+(10.5-8)^2}$

$r=\sqrt{0^2+(2.5)^2}$

$r=\sqrt{0^2+(2.5)^2}=2.5$

The equation of the circle in standard form is given by;

$(x-h)^2+(y-k)^2=r^2$

We substitute the center and the radius into the formula to get;

$(x-4)^2+(y-8)^2=2.5^2$

$(x-4)^2+(y-8)^2=6.25$

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3 years ago

A cylinder has a height of 10 inches and a radius of 17 inches. What is its volume? Use ≈ 3.14 and round your answer to the ne

Gelneren [198K]

Steps:

Radius= 17in

Height= 10in

Formula: V=πr2h

Shape: Right cylinder

Solved for volume

H= Height

R= Radius

Description:

We know that R is 17 inches, and H is 10 inches. Since we are finding the volume we use the formula V=πr2h to calculate. After calculating your answer will come as V≈9079.2in³. You also said to round your answer to the nearest hundredth. After rounding your answer to th enearest hundredth your answer will come as 9,079.20.

Answer: V≈9079.2in³

Round to the nearest hundredth = 9,079.20

Please mark brainliest

<em><u>Hope this helps.</u></em>

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4 years ago

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seraphim [82]

Answer:

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A motorist traveled 311 miles on 12 gallons of gas. To the nearest tenth, how many miles can the motorist travel on one gallon o

allsm [11]

The motorist can travel 25.92 miles on one gallon of gas

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Answer:

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