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2 years ago

Calculate P(-6,8) to the origin

Mathematics

1 answer:

Free_Kalibri [48]2 years ago

4 0

Answer:

The distance of the point P(-6, 8) from the origin is

OP2=(-6)2+82=36+64=100⇒OP=√100=10 units

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You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.

RUDIKE [14]

Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

$xy = 288 \\ \\ \\ \\ \Rightarrow y= \frac{288}{x}$

Substituting for y into the equation for the length of fencing needed, we have

$P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}$

For the amount of fencing to be minimum, then

$\frac{dP}{dx} =0 \\ \\ \Rightarrow1- \frac{576}{x^2} =0 \\ \\ \Rightarrow \frac{576}{x^2} =1 \\ \\ \Rightarrow x^2=576 \\ \\ \Rightarrow x=\sqrt{576}=24$

Now, recall that

$y= \frac{288}{x} = \frac{288}{24} =12$

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.

8 0

2 years ago

Sandy bought 3/4 yard of red ribbon and 2/3 yard of white ribbon to make some hair bows.Altogether,how many yards of ribbon did

Stolb23 [73]

Sandy bought 1 and 5/12 yards of ribbon

5 0

2 years ago

Read 2 more answers

The weight of a dog crate is 5.6 lbs. the crate and 3 puppies together weigh 36.35 lbs. estimate the weight of one puppy.

nata0808 [166]

36.35 - 5.6 = 30.75 ÷ 3 = 10.25

7 0

2 years ago

Suppose that y varies directly with x and y=5 when x=6. What is y when x=5? Be sure to simplify your answer.

Charra [1.4K]

Answer:

y = $\frac{25}{6}$

Step-by-step explanation:

Given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 5 when x = 6

k = $\frac{y}{x}$ = $\frac{5}{6}$

y = $\frac{5}{6}$ x ← equation of variation

When x = 5, then

y = $\frac{5}{6}$ × 5 = $\frac{25}{6}$

8 0

2 years ago

Help me please it’s due today

pentagon [3]

Answer:

1. B. $20

2.C. 19%

3. D. not here

Step-by-step explanation:

1. info we know

25+45+10+25+15+10 = 130

we need 20 more dollars

2. 25/130 x/100

cross multiply

2500/ 130x

divide

19 = x

3. same steps as last time

35/130 x/100

3500/130x

29%

5 0

2 years ago