Find the measure of z.

The formula for the volume of a rectangular prism is V = lwh. Which is the equivalent equation solved for h?

wel

Answer:

V /(lw) = h

Step-by-step explanation:

V = lwh

Divide each side by lw

V/ ( lw) = lwh/(lw)

V /(lw) = h

4 0

3 years ago

In this problem, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order de x'' + x = 0. find a solut

nordsb [41]

If you are already given the general solution, finding the particular solution means to impose some conditions in order to fix the coefficients of the general solution.

The first thing we need to impose is that the function must output -1 when the input is zero. So, if we plug zero as input we have

$x(t) = c_1 \cos(t) + c_2 \sin(t) \implies x(0) = c_1 \cos(0) + c_2 \sin(0) = c_1$

But we want $x(0)=-1$ , which implies $x(0)=c_1=-1$

So, we fixed the first coefficient. To fix the second one, we can use the second piece of information (and of course the already-found value for $c_1$ ).

We want the first derivative to output 3 when the input is zero. So, first of all, let's compute the first derivative, and evaluate it in zero:

$x(t) = -\cos(t) + c_2 \sin(t) \implies x'(t) = \sin(t) + c_2\cos(t)$

$x'(0) = \sin(0) + c_2\cos(0) = c_2$

And as before, since $x'(0)=c_2$ and we want $x'(0)=3$ , we deduce $c_2=3$ .

So, once we fix both coefficients, the general solution becomes

$x(t) = c_1 \cos(t) + c_2 \sin(t) \mapsto -\cos(t)+3\sin(t)$

3 0

3 years ago

In △MNK MN = NK, m∠N = 110º, MK = 5. Find MN.

alexgriva [62]

Answer:

MN = 3.03 ≈ 3

Step-by-step explanation:

Given: In ΔMNK MN = NK , m∠N = 110° and MK = 5.

To find: MN = ?

Sol: In ΔMNK,

∠M + ∠N + ∠K = 180° (sum of angles of a triangle)

2∠M = 180° - 110° ( ∠M =∠K since MN = MK)

∠M = 70°/2 = 35°

∴ ∠M = ∠K = 35°

Now, Using Sine Rule for finding sides,

$\frac{m}{sinM} = \frac{n}{sinN} = \frac{k}{SinK}$

$\frac{k}{sinK} = \frac{n}{sinN}$

$\frac{5}{sin 110^{\circ}} = \frac{k}{sin 35^{\circ}}$

$k = \frac{5 sin 35^{\circ}}{sin 110^{\circ}}$

Now ∵ sin 35° = 0.57 and sin 110° = 0.94 approx.

By substituting these values in above expression,

$k = \frac{5 \times 0.57}{0.94}$

k = $\frac{2.85}{0.94}$

k = 3.03

Therefore, MN = 3 approx.

8 0

3 years ago

A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students state

Lorico [155]

Answer:

$a=502 +1.28*81=605.68$

So the value of height that separates the bottom 90% of data from the top 10% is 605.68.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(502,81)$

Where $\mu=502$ and $\sigma=81$

We want to find a value a, such that we satisfy this condition:

$P(X>a)=0.1$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

$P(X$