Answer:
54.3deg
Step-by-step explanation:
sin(angle) = 65/80
angle = 54.34deg
The area of △XYZ according to the figure is 363ft²
<h3>Area of triangles</h3>
The formula for calculating the area of a triangle is expressed as:
A = 0.5bh
- b is the base
- h is the height
<h3>Calculate area of each triangles</h3>
For the triangle △NMO
Area of △NMO = 0.5bh
147 = 0.5b(14/12)
147 = 7b/12
7b = 12 * 147
b = 252
b = 252ft
b = 3024in
Get the base of △XYZ
14/3024 = 22/XZ
XZ = 4,752in
Area of △XYZ = 0.5 (4,752)(22)
Area of △XYZ= 52,272in²
Area of △XYZ = 363ft²
Hence the area of △XYZ is 363ft²
Learn more on area of triangles here: brainly.com/question/17335144
Answer:
7.840136054421769
Step-by-step explanation:
Answer:
The shadow is decreasing at the rate of 3.55 inch/min
Step-by-step explanation:
The height of the building = 60ft
The shadow of the building on the level ground is 25ft long
Ѳ is increasing at the rate of 0.24°/min
Using SOHCAHTOA,
Tan Ѳ = opposite/ adjacent
= height of the building / length of the shadow
Tan Ѳ = h/x
X= h/tan Ѳ
Recall that tan Ѳ = sin Ѳ/cos Ѳ
X= h/x (sin Ѳ/cos Ѳ)
Differentiate with respect to t
dx/dt = (-h/sin²Ѳ)dѲ/dt
When x= 25ft
tanѲ = h/x
= 60/25
Ѳ= tan^-1(60/25)
= 67.38°
dѲ/dt= 0.24°/min
Convert the height in ft to inches
1 ft = 12 inches
Therefore, 60ft = 60*12
= 720 inches
Convert degree/min to radian/min
1°= 0.0175radian
Therefore, 0.24° = 0.24 * 0.0175
= 0.0042 radian/min
Recall that
dx/dt = (-h/sin²Ѳ)dѲ/dt
= (-720/sin²(67.38))*0.0042
= (-720/0.8521)*0.0042
-3.55 inch/min
Therefore, the rate at which the length of the shadow of the building decreases is 3.55 inches/min
Answer:
C
Step-by-step explanation:
Firstly, we set up the null and alternative hypothesis as follows;
The null hypothesis is;
H0: μ ≥ 12
The alternative hypothesis is;
Ha : μ < 12
Next step is to calculate the test statistic z
Mathematically;
z = (x - μ )/ σ /√n
= (11.58 - 12) /1.93/√(80
Test statistic z = -1.92
Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel
P(z < -1.92) = 0.0274
P-value = 0.0274
alpha = 0.05
From the above, we can see that
P-value < alpha
And because of this, we are going to reject the null hypothesis and therefore accept the alternative.
We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."
