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2 years ago

Part A

Mathematics

1 answer:

Deffense [45]2 years ago

5 0

Answer: Not safe

Step-by-step explanation:

Let the angle of elevation of the ramp be θ, then:

$\begin{aligned}&\sin \theta=\frac{1.5}{10}=0.15 \\&\theta=\sin ^{-1}(0.15) \approx 8.63^{\circ}\end{aligned}$

But the maximum angle for the ramp cannot exceed 7.1°. The calculated angle of elevation will make it difficult, if not impossible, for motorized wheelchairs to get up the ramp.

Therefore, the ramp at the local library is not safe for motorized wheelchairs

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How would I go about solving this problem???

schepotkina [342]

So.. if you take a peek at the picture below

the trunk is really just a half-cylinder on top of a square, with a depth of 2 meters

what's the volume? well, easy enough, take the volume of the cylinder, then half it
take the volume of the rectangular prism, and then add them both

$\bf \textit{volume of a cylinder}\\\\

\begin{array}{llll}
C=\pi r^2 h\\\\
\textit{half that}\\\\
\cfrac{\pi r^2 h}{2}
\end{array}\qquad 
\begin{cases}
r=radius\\
h=height\\
-------\\
r=\frac{1}{2}\\
h=2
\end{cases}\implies \cfrac{C}{2}=\cfrac{\pi \left( \frac{1}{2}\right)^2 2}{2}\\\\
-----------------------------\\\\
\textit{volume of a square}\\\\
V=lwh\qquad 
\begin{cases}
l=length\\
w=width\\
h=height
----------\\
l=1\\
w=1\\
h=2
\end{cases}\implies V=2$

now.. for the surface area... $\bf \textit{surface area of a cylinder}\\\\
\begin{array}{llll}
S=2\pi r(h+r)\\\\
\textit{half that}\\\\
\cfrac{2\pi r(h+r)}{2}
\end{array}\begin{cases}
r=radius\\
h=height\\
-------\\
r=\frac{1}{2}\\
h=2
\end{cases}$

now.. for the surface area of the prism... well

is really just 6 rectangles stacked up to each other at the edges

so... get the area of the lateral rectangles, and the one at the bottom, skip the rectangle atop, because is the one overlapping the cylinder, and is not outside, and thus is not surface area then

for the lateral ones, you have a front of 1x1, a back of 1x1 and a left of 1x2 and a right of 1x2, and then the one at the bottom, which is a 1x2

then add both surface areas, and that's the surface area of the trunk

5 0

3 years ago

HELP!!! BRAINLIEST ANSWER!!!!

vfiekz [6]

Answer:

x = 26, y = 9

Step-by-step explanation:

Add the bottom equations and set them equal to 180

8x -28 = 180

8x = 208 divide each by 8

x = 26

Find the bottom right, 3(26) - 11

78 - 11 = 67

The unlabeled top left box is also equal to 67 degrees.

So 2y + 5 = 23

2y = 18

y = 9

7 0

3 years ago

Read 2 more answers

ANSWER FOR BRAINLIEST:

AlekseyPX

Step-by-step explanation:

I think mode,range and median dpo ako sure

3 0

3 years ago

The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to in

oksano4ka [1.4K]

Answer:

Null hypothesis: $\mu \leq 8000$

Alternative hypothesis: $\mu > 8000$

$z=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2$

$p_v =P(Z>2)=0.0228$

Step-by-step explanation:

1) Data given and notation

$\bar X=8300$ represent the sample mean

$\sigma=1200$ represent the population standard deviation

$n=64$ sample size

$\mu_o =800$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 8000, the system of hypothesis are :

Null hypothesis: $\mu \leq 8000$

Alternative hypothesis: $\mu > 8000$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2$

4) P-value

Since is a one-side upper test the p value would given by:

$p_v =P(Z>2)=0.0228$

5) Conclusion

If we compare the p value and the significance level assumed, for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is significantly higher than $8000.

4 0

3 years ago

Write the equation for the parabola that has x− intercepts (−2,0) and (4,0) and y− intercept (0,4).

seropon [69]

Answer:

$y = -\frac{1}{2}(x^2-2x-8)$

Simplified it is $y=-\frac{1}{2}x^2+x+4$

Step-by-step explanation:

The x-intercepts of a parabola form the factors of the equation. Since the x -intercepts are (-2,0) and (4,0) then the factors are (x+2) and (x-4). Factors are pieces which multiply to make the equation.

$y=(x+2)(x-4)\\y=x^2+2x-4x-8\\y=x^2-2x-8$

This is the standard form of the parabola $ax^2+bx+c$ . Since the y-intercept of the parabola is (0,4) then a number must also be multiplied to it

$y=a(x^2-2x-8)$

We find a by plugging in x=0 and y=4.

$4=a(0^2-2(0)-8)\\4=a(0-0-8)\\4=a(-8)\\\frac{4}{-8} = a\\\frac{-1}{2} = a$

So the equation is $y = -\frac{1}{2}(x^2-2x-8)$ .

When simplified it is $y=-\frac{1}{2}x^2+x+4$

3 0

3 years ago