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3 years ago

On which number line are −6 and its opposite shown?

Mathematics

1 answer:

lina2011 [118]3 years ago

3 0

Answer:

$-6\:and\:6$

Step-by-step explanation:

When talking about integers, opposites refer to the sign of the integers, meaning that the opposite of <em>negative</em> is <em>positive</em>, and vice versa.

I am joyous to assist you anytime.

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Marjorie is building a dog run that is 25'8" long and 8'8" wide. How much fencing will she need if the opening is 3'6" wide and

antiseptic1488 [7]

Answer:

782 in

Step-by-step explanation:

To find the length of fence, we have to find the perimeter first.

Given

Length = l = 25 feet 8 in

Width = w = 8 feet 8 in

Opening = o =3 feet 6 in

So,

we have to convert the lengths into same unit first

So,

l = (25*12)+8 = 308 in

w = ( 8*12) +8 = 104 in

O = (12*3) + 6 = 42 in

Perimeter = 2(l+w)

= 2(308+104)

=2(412)

=824

As the opening does not need fencing

Total fence = P - o

= 824 - 42

=782 in

65 feet 2 in ..

3 0

3 years ago

Solve the problem, calculate the line integral of f along h

Over [174]

The curve $\mathcal H$ is parameterized by

$\begin{cases}X(t)=R\cos t\\Y(t)=R\sin t\\Z(t)=Pt\end{cases}$

so in the line integral, we have

$\displaystyle\int_{\mathcal H}f(x,y,z)\,\mathrm ds=\int_{t=0}^{t=2\pi}f(X(t),Y(t),Z(t))\sqrt{\left(\frac{\mathrm dX}{\mathrm dt}\right)^2+\left(\frac{\mathrm dY}{\mathrm dt}\right)^2+\left(\frac{\mathrm dZ}{\mathrm dt}\right)^2}\,\mathrm dt$
$=\displaystyle\int_0^{2\pi}Y(t)^2\sqrt{(-R\sin t)^2+(R\cos t)^2+P^2}\,\mathrm dt$
$=\displaystyle\int_0^{2\pi}R^2\sin^2t\sqrt{R^2+P^2}\,\mathrm dt$
$=\displaystyle\frac{R^2\sqrt{R^2+P^2}}2\int_0^{2\pi}(1-\cos2t)\,\mathrm dt$
$=\pi R^2\sqrt{R^2+P^2}$

You are mistaken in thinking that the gradient theorem applies here. Recall that for a scalar function $f:\mathbb R^n\to\mathbb R$ , we have gradient $\nabla f:\mathbb R^n\to\mathbb R^n$ . The theorem itself then says that the line integral of $\nabla f(x,y,z)=\mathbf f(x,y,z)$ along a curve $C$ parameterized by $\mathbf r(t)$ , where $a\le t\le b$ , is given by

$\displaystyle\int_C\mathbf f(x,y,z)\,\mathrm d\mathbf r=f(\mathbf r(b))-f(\mathbf r(a))$

Specifically, in order for this theorem to even be considered in the first place, we would need to be integrating with respect to a vector field.

But this isn't the case: we're integrating $f(x,y,z)=y^2$ , a scalar function.

7 0

3 years ago

What's the equation of the line that passes through the points (4,4) and (0,-12)?

Law Incorporation [45]

Answer:

Step-by-step explanation:

You need to find the slope.

$m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m=\frac{-12-4 }{0-4 }\\m=\frac{-16}{-4}\\ m=4$

Since the slope is 4, the answer is B.

6 0

3 years ago

A recipe calls for 1/4 cup of brown sugar for every 2/3 cup of white sugar. How many cups of brown sugar is required for every c

sammy [17]

The right answer is Option B: 3/8

Step-by-step explanation:

Given,

1/4 cup of brown sugar is for 2/3 cup of white sugar.

Ratio of brown sugar to white sugar = $\frac{1}{4}:\frac{2}{3}$

Let,

x be the brown sugar required for 1 cup of white sugar.

Ratio of brown sugar to white sugar = x:1

Using proportion;

Ratio of brown sugar to white sugar :: Ratio of brown sugar to white sugar

$\frac{1}{4}:\frac{2}{3}::x:1$

Product of mean = Product of extreme

$\frac{2}{3}*x=\frac{1}{4}*1\\\frac{2}{3}x=\frac{1}{4}$

Multiplying both sides by 3/2

$\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}\\x=\frac{3}{8}$

3/8 cups of brown sugar is required for 1 cup of white sugar.

The right answer is Option B: 3/8

Keywords: ratio, proportion

Learn more about ratios at:

#LearnwithBrainly

3 0

3 years ago

10 students are competing in a dance competition. How many was can you award first, second, and third place?

weqwewe [10]

Given:

Total number of students = 10

To find:

How many was can you award first, second, and third place?

Solution:

Total number of students is 10. So, the total possible ways for the first award is 10.

We know that one student can hold only one place. So, after giving the first award, the number of remaining students is 9 and the total possible ways for the second award is 9.

Similarly, the total possible ways for the third award is 8.

Now, the total number of ways to award first, second, and third place is:

$10\times 9\times 8=720$

Therefore, the total number of ways to award first, second, and third place is 720.

4 0

3 years ago