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3 years ago

14

Maria solved the equation -5 n = -12. Her answer was n = 2. She is fairly confident about her answer, but wants to do a quick ch

eck of her solution using estimation. Which of the following shows a good check of her answer?

1 answer:

777dan777 [17]3 years ago

3 0

Plug in 2 to see if she is correct. Hope this helps!

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Please help on question 17 with step by step instructions <br> Thanks in advance xx

shutvik [7]

Let x = Initial Price

If we increase x by 5%, we are adding 0.05x

Therefore, the new price = x + 0.05x = 1.05x

If the ticket has increased by £2.30, £2.30 is 5% of the initial price, or 0.05x

0.05x = 2.30

x = 2.30/0.05

x = 46

Therefore, the price of the ticket before the increase was £46

You can also check this backwards by doing 46*0.05 = 2.30

6 0

3 years ago

How can I solve this?<br>Please use the simplest format

IgorLugansk [536]

Answer:

option D is true.

Step-by-step explanation:

The right-angled triangle is shown.

From the right-angled triangle,

The angle Ф = 60°

We know that the trigonometric ratio

tan Ф = opposite / adjacent

opposite = 4

adjacent = n

Thus,

tan 60 = 4 / n

√3 = 4/n

n = 4/√3

Thus,

n = 4/√3

= (4 × √3) / (√3 × √3)

= 4√3 / 3

Thus,

n = 4√3 / 3

Using Pythagorean theorem

m = √n²+4²

$m=\sqrt{\left(4\cdot \frac{\sqrt{3}}{3}\right)^2+4^2}$

$m=\sqrt{\frac{4^2}{3}+4^2}$

$m=\sqrt{\frac{64}{3}}$

$m=\frac{8}{\sqrt{3}}$

$m=\frac{8\sqrt{3}}{3}$

Thus,

$m=\frac{8\sqrt{3}}{3}$

n = 4√3 / 3

Therefore, option D is true.

3 0

3 years ago

Evaluate the surface integral. s x2 + y2 + z2 ds s is the part of the cylinder x2 + y2 = 4 that lies between the planes z = 0 an

Leya [2.2K]

Parameterize the lateral face $T_1$ of the cylinder by

$\mathbf r_1(u,v)=(x(u,v),y(u,v),z(u,v))=(2\cos u,2\sin u,v$

where $0\le u\le2\pi$ and $0\le v\le3$ , and parameterize the disks $T_2,T_3$ as

$\mathbf r_2(r,\theta)=(x(r,\theta),y(r,\theta),z(r,\theta))=(r\cos\theta,r\sin\theta,0)$
$\mathbf r_3(r,\theta)=(r\cos\theta,r\sin\theta,3)$

where $0\le r\le2$ and $0\le\theta\le2\pi$ .

The integral along the surface of the cylinder (with outward/positive orientation) is then

$\displaystyle\iint_S(x^2+y^2+z^2)\,\mathrm dS=\left\{\iint_{T_1}+\iint_{T_2}+\iint_{T_3}\right\}(x^2+y^2+z^2)\,\mathrm dS$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}((2\cos u)^2+(2\sin u)^2+v^2)\left\|{{\mathbf r}_1}_u\times{{\mathbf r}_2}_v\right\|\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+0^2)\left\|{{\mathbf r}_2}_r\times{{\mathbf r}_2}_\theta\right\|\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}((r\cos\theta)^2+(r\sin\theta)^2+3^2)\left\|{{\mathbf r}_3}_r\times{{\mathbf r}_3}_\theta\right\|\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle2\int_{u=0}^{u=2\pi}\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv\,\mathrm du+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r^3\,\mathrm d\theta\,\mathrm dr+\int_{r=0}^{r=2}\int_{\theta=0}^{\theta=2\pi}r(r^2+9)\,\mathrm d\theta\,\mathrm dr$
$=\displaystyle4\pi\int_{v=0}^{v=3}(v^2+4)\,\mathrm dv+2\pi\int_{r=0}^{r=2}r^3\,\mathrm dr+2\pi\int_{r=0}^{r=2}r(r^2+9)\,\mathrm dr$
$=136\pi$

7 0

4 years ago

garri49 [273]

Answer:

11-C

Step-by-step explanation:

Cause 11-C

equels the same amount as the one on the top of 11-C

6 0

3 years ago

Elimination/subtraction

denpristay [2]

Answer:

x = 0, y = 7

Step-by-step explanation:

Solving a system of equations using substitution requires one side to be equal to a variable present in the equation, in this case x or y. We should simplify the equation using elimination before substituting to reduce the chance of error.

In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. These equations arew already aligned for us.

3x - 10y=-70

-<u> 4x +9y = 63</u>

-x + y = 7

Now, for substitution, the equation must be set to a variable.

-x + y = 7

y = x + 7

Next, plug the equation in where applicable in another equation.

4x +9(x + 7) = 63

4x + 9x + 63 = 63

13x = 0

x = 0

The final step of substitution is to plug the known variable into an equation to find the other variable.

3(0) - 10y=-70

0 - 10y = -70

10y = 70

y = 7

I guarantee you this answer is correct, I worked it out using other methods and graphing prior to submitting this answer.

8 0

3 years ago

Read 2 more answers