GEOMETRY / TRIG<br> I really need help can anyone solve this <br> Find x:

d1i1m1o1n [39]

The answer you selected in that photo given, is correct. I can tell just by using common sense and by judging the other options second option (B) is looking the most clearest one to me.

8 0

2 years ago

A trough of water is 20 meters in length and its ends are in the shape of an isosceles triangle whose width is 7 meters and heig

Vaselesa [24]

Answer:

a) Depth changing rate of change is $0.24m/min$ , When the water is 6 meters deep

b) The width of the top of the water is changing at a rate of $0.17m/min$ , When the water is 6 meters deep

Step-by-step explanation:

As we can see in the attachment part II, there are similar triangles, so we have the following relation between them $\frac{3.5}{10} =\frac{a}{h}$ , then $a=0.35h$ .

a) As we have that volume is $V=\frac{1}{2} 2ahL=ahL$ , then $V=(0.35h^{2})L$ , so we can derivate it $\frac{dV}{dt}=2(0.35h)L\frac{dh}{dt}$ due to the chain rule, then we clean this expression for $\frac{dh}{dt}=\frac{1}{0.7hL}\frac{dV}{dt}$ and compute with the knowns $\frac{dh}{dt}=\frac{1}{0.7(6m)(20m)}2m^{3}/min=0.24m/min$ , is the depth changing rate of change when the water is 6 meters deep.

b) As the width of the top is $2a=0.7h$ , we can derivate it and obtain $\frac{da}{dt}=0.7\frac{dh}{dt} =0.7*0.24m/min=0.17m/min$ The width of the top of the water is changing, When the water is 6 meters deep at this rate

8 0

3 years ago

Rusty is 5.75 feet tall and casts a 7 foot shadow find the angle of elevation from the tip of the shadow to the top of Rusty’s h

11Alexandr11 [23.1K]

Answer:

Ф = 39.4 degrees

Step-by-step explanation:

The ratio 5.75 / 7 is the tangent of the angle of elevation. Using the inverse tangent function on a calculator returns Ф = 39.4 degrees.

5 0

3 years ago

Find the value of c that completes the square

PilotLPTM [1.2K]

Answer:

The value of c that completes the square $x^2+2x+c$ is 1

Step-by-step explanation:

We need to find the value of c that completes the square $x^2+2x+c$

The formula used will be: $a^2+2ab+b^2=(a+b)^2$

In the question given the value c can be found by breaking the middle term. we are given 2x while the general formula is 2ab for middle term so,

2(x)(1) = 2x

so, c= 1

Solving:

$x^2+2x+c\\=x^2+2(x)(1)+(1)^2-(1)^2\\=(x+1)^2-1$

So, the value of c that completes the square $x^2+2x+c$ is 1

6 0

3 years ago

Consider the following hypothesis test:

Gnom [1K]

Answer:

a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.

b. z=1.24. No, it can not be concluded that the population mean is greater than 50.

c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.

Step-by-step explanation:

We have a hypothesis test for the mean, with the hypothesis:

$H_0: \mu\leq50\\\\H_a:\mu> 50$

The sample size is n=55 and the population standard deviation is 6.

The significance level is 0.05.

We can calculate the standard error as:

$\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{55}}=0.809$

For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.

a. If the sample mean is M=52.5, the test statistic is:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{52.5-50}{0.809}=\dfrac{2.5}{0.809}=3.09$

The null hypothesis is rejected, as z>zc and falls in the rejection region.

b. If the sample mean is M=51, the test statistic is:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51-50}{0.809}=\dfrac{1}{0.809}=1.24$

The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.

c. If the sample mean is M=51.8, the test statistic is:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51.8-50}{0.809}=\dfrac{1.8}{0.809}=2.22$

The null hypothesis is rejected, as z>zc and falls in the rejection region.

8 0

4 years ago

GEOMETRY / TRIG I really need help can anyone solve this Find x: