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nadezda [96]
3 years ago
9

A farmer decides to take up breeding cows. He decides he will buy 7 more cows each year.

Mathematics
1 answer:
Xelga [282]3 years ago
7 0

Answer:

200 cows

Step-by-step explanation:

7n+x=340 where n equals the number of years and x is the starting amount. Since he has been buying cows for 20 years, we plug 20 in for n. This would give you 140+x=340. After subtracting 140 from both sides you come to the conclusion that x=200.

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A N S W E R Q U I C K P L E A S E
chubhunter [2.5K]

Answer:

1. A

2. D

3. D

Step-by-step explanation:

The standard form of a parabola is

y=\frac{1}{4p}(x-h)^2+k            ..... (1)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

1. The directrix of a parabola is y=−8 . The focus of the parabola is (−2,−6) .

k-p=-8                   ...(a)

(h,k+p)=(-2,-6)

k+p=-6            .... (b)

h=-2

On solving (a) and (b),  we get k=-7 and p=1.

Put h=-2, k=-7 and p=1 in equation (1).

y=\frac{1}{4(1)}(x-(-2))^2+(-7)

y=\frac{1}{4}(x+2)^2-7

Therefore option A is correct.

2 The directrix of a parabola is the line y=5 . The focus of the parabola is (2,1) .

k-p=5                   ...(c)

(h,k+p)=(2,1)

k+p=1            .... (d)

h=2

On solving (c) and (d),  we get k=3 and p=-2.

Put h=2, k=3 and p=-2 in equation (1).

y=\frac{1}{4(-2)}(x-(2))^2+(3)

y=-\frac{1}{8}(x-2)^2+3

Therefore option D is correct.

3. The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3 .

k-p=-3                   ...(e)

(h,k+p)=(0,-2)

k+p=-2            .... (f)

h=0

On solving (e) and (f),  we get k=-2.5 and p=0.5.

Put h=0, k=-2.5 and p=0.5 in equation (1).

y=\frac{1}{4(0.5)}(x-(0))^2+(-2.5)

y=\frac{1}{2}(x)^2-2.5

y=\frac{1}{2}(x)^2-\frac{5}{2}

Therefore option D is correct.

5 0
3 years ago
Jane drove 355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles?
Vlad [161]
I think it is 14 if my calculations are correct.

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6 0
3 years ago
John is building a fence for his dog. He knows that he wants to make the width 3 feet longer than twice the length. Find the are
BaLLatris [955]
View screenshot below

7 0
3 years ago
Example 2
PIT_PIT [208]

Answer: (a) 314.2cm², (b) 157.1cm², (c) 78.55cm² (e) 6.77

Step-by-step explanation: (a)  Area of the circle with radius of 10 cm = πr²

                                                                          = 3.142 × 10 × 10

                                                                          = 3.142 × 100

                                                                          = 314.2cm²

The formula                                                       = πr²

(b)  Area of the half of a circle known as semicircle

                                                                         = πr²/2

                                                                         = 3.142 ×10 × 10/2

                                                                         = 3.142 × 50

                                                                         = 157.1cm²

The formula                                                      = πr²/2

(c)  A quarter of a circle is called quadrant

                                                            = πr²/4

                                                            = 3.142 × 10 × 10/4

                                                            = 314.2/4

                                                            = 78.55cm²

The formula is written thus = πr²/4, which implies that the circle is divided into 4 unit

(d) The conjecture about how to determine the area of the sector is

Formula of a sector = ∅/360(πr²)

<u>Information</u>

The arc  cant be 60°, therefore information incomplete.

(e) Area of the sector with the angle AOB of 60° = 24.

To find the radius of the angle, make v the subject of the formula from the formula.

Sector area = πr²∅/360°

equate formula to 24.

Therefore πr²∅/360° = 24

Multiply through by360° to make it a linear expression

It now becomes πr²∅ =24× 360°

                                                     r² = 24  x 360/π × ∅°

                                                     r² = 24 × 360° /3.142 × 60°

                                                     r² = 3,640/188.52

                                                     r² = 45.8

To find r , we take the square root of both side by applying laws of indicies

                                    Therefore r = √45 .8

                                                      r = 6.77

(f)   General formula = ∅°/360° × (πr²)

angle substended at centre by the arc = x°

assuming the radius of the circle = ycm, Therefore,  area of the sector = { ∅°/360° × πy² }

                                                     

                                                   

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