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3 years ago

Solve the simultaneous equations x2 + y2 = 10 and x – 3y + 10 = 0.

Mathematics

1 answer:

ch4aika [34]3 years ago

3 0

Answer:

x = - 1, y = 3 or (-1 , 3)

Step-by-step explanation:

x – 3y + 10 = 0 x = 3y - 10 ... plug in

x² + y² = 10

(3y-10)² + y² = 10

10y² - 60y +90 = 0

y² - 6y + 9 = 0

(y - 3)² = 0

y = 3

x = - 1

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If a certain cannon is fired from a height of 8.8 meters above the ground, at a certain angle, the height of the cannonball ab

Dennis_Churaev [7]

Answer:

It would take approximately 6.50 second for the cannonball to strike the ground.

Step-by-step explanation:

Consider the provided function.

$h(t)=-4.9t^2+30.5t+8.8$

We need to find the time takes for the cannonball to strike the ground.

Substitute h(t) = 0 in above function.

$-4.9t^2+30.5t+8.8=0$

Multiply both sides by 10.

$-49t^2+305t+88=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are: $x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute a = -49, b = 305 and c=88

$t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}$

Ignore the negative value of t as time can't be a negative number.

Thus,

$t=\frac{305+\sqrt{110273}}{98}\approx6.50$

Hence, it would take approximately 6.50 second for the cannonball to strike the ground.

6 0

3 years ago

A city water tank holds 20 gallons of water. A technician empties 25% of the tank. How many more gallons of water must be remove

Alja [10]

Answer: 15 gallons

Step-by-step explanation:

There is 100% in any full thing. When the water tank was full, it had 20 gallons. After 25% of the water was removed, there is 75% left (100% - 25% = 75%). 75% can also equal 0.75. 20 × 0.75 = 15 gallons.

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3 years ago

what is the upward acceleration of a helicopter with a mass of 5,000kg if a force of 10,000 N acts on it in an upward direction

morpeh [17]

I think that would be: 2 m/s^2

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4 years ago

Quadrilateral A has side lengths 2, 3, 5, and 6. Quadrilateral B has side lengths 4, 5, 8,

Dahasolnce [82]

Answer:

No.

Step-by-step explanation:

2, 3, 5, 6

4, 5, 8, 10

If all of the sides are scaled, that must mean it is possible to maintain a ratio of each side.

2/4 = 0.5

3/5 = 0.6

5/8 = ?

6/10 = 0.6

No.

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4 years ago

Kyle uses a school gym to run a weekly yoga class. He must pay the school a fee for the use of the gym. Each person who comes pa

77julia77 [94]

Answer:

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3 years ago