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2 years ago

PLEASEEE HELLPPP!!!!!!!!

Mathematics

1 answer:

belka [17]2 years ago

5 0

Answer:

4.25 i think

Step-by-step explanation:

sorry i have not done these in a while it might be wrong

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Answer the following questions about the sphere whose equation is given by x2+y2+z2−8x+4y=−4. 1. Find the radius of the sphere.

Anna [14]

Answer:

we have (a,b,c)=(4,-2,0) and R=4 (radius)

Step-by-step explanation:

since

x²+y²+z²−8x+4y=−4

we have to complete the squares to finish with a equation of the form

(x-a)²+(y-b)²+(z-c)²=R²

that is the equation of a sphere of radius R and centre in (a,b,c)

thus

x²+y²+z²−8x+4y=−4

x²+y²+z²−8x+4y +4 = 0

x²+y²+z²−8x+4y +4 +16-16 =0

(x²−8x + 16) + (y² + 4y + 4 ) + (z²) -16 = 0

(x-4)² + (y+2)² + z² = 16

(x-4)² + (y-(-2))² + (z-0)² = 4²

thus we have a=4 , b= -2 , c= 0 and R=4

8 0

2 years ago

Terry buys an orange for 22p.

larisa86 [58]

£1=100p
100-22=78p
He gets 78p

5 0

2 years ago

a paddle boat can move at a speed of 6km/h in still water. the boat is paddeled 16km downstream in a river in the same time it t

kaheart [24]

$v-the\ speed\ of\ the\ river\\\\16:(6+v)=8:(6-v)\\\\\frac{16}{6+v}=\frac{8}{6-v}\\-------------\\multiply\ on\ the\ cross\\-------------\\8(6+v)=16(6-v)\\\\48+8v=96-16v\\\\8v+16v=96-48\\\\24v=48\ \ \ /:24\\\\v=2\ (km/h)\leftarrow Answer$

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2 years ago

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

2 years ago

Name the number that is three more than one-fifth of one-tenth of one-half of 5,000.

bearhunter [10]

Answer:

24 or 29 more numbers

Step-by-step explanation:

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2 years ago