Answer:
lateral area = 2320 m²
Step-by-step explanation:
The question wants us to calculate the lateral area of a square base pyramid. The square base pyramid has a side of 40 meters.The height is 21 meters.
Half of the square base is 40/2 = 20 meters . With the height it forms a right angle triangle. The hypotenuse side is the slant height of the pyramid.
Using Pythagoras's theorem
c² = a² + b²
c² = 20² + 21²
c² = 400 + 441
c² = 841
square root both sides
c = √841
c = 29 meters
The slant height of the pyramid is 29 meters.
The pyramid has four sided triangle. The lateral area is 4 multiply by the area of one triangle.
area of triangle = 1/2 × base × height
base = 40 meters
height = 29 meters
area = 1/2 × 40 × 29
area = 580
area of one triangle = 580 m²
Lateral area = 4(580)
lateral area = 2320 m²
Sec x is equal to 1/cosx, cot x is equal to cosx/sinx. cos x cancels, and you are left with 1/sinx. this is equal to cscx. Cosecant is : hypotenuse / opposite, so the answer is **D**
Answer: Major arc
Step-by-step explanation:
First, you have to find the equation of the perpendicular bisector of this given line.
to do that, you need the slope of the perpendicular line and one point.
Step 1: find the slope of the given line segment. We have the two end points (10, 15) and (-20, 5), so the slope is m=(15-5)/(10-(-20))=1/3
the slope of the perpendicular line is the negative reciprocal of the slope of the given line, m=-3/1=-3
step 2: find the middle point: x=(-20+10)/2=-5, y=(15+5)/2=10 (-5, 10)
so the equation of the perpendicular line in point-slope form is (y-10)=-3(x+5)
now plug in all the given coordinates to the equation to see which pair fits:
(-8, 19): 19-10=9, -3(-8+5)=9, so yes, (-8, 19) is on the perpendicular line.
try the other pairs, you will find that (1,-8) and (-5, 10) fit the equation too. (-5,10) happens to be the midpoint.
Answer:
Step-by-step explanation:
EXAMPLE #1:
What number is 75% of 4? (or Find 75% of 4.)
The PERCENT always goes over 100.
(It's a part of the whole 100%.)
4 appears with the word of:
It's the WHOLE and goes on the bottom.
A proportion showing one fraction with PART as the numerator and 4 as the denominator equal to another fraction with 75 as the numerator and 100 as the denominator.
We're trying to find the missing PART (on the top).
In a proportion the cross-products are equal: So 4 times 75 is equal to 100 times the PART.
The missing PART equals 4 times 75 divided by 100.
(Multiply the two opposite corners with numbers; then divide by the other number.)
4 times 75 = 100 times the part
300 = 100 times the part
300/100 = 100/100 times the part
3 = the part
A proportion showing the denominator, 4, times the diagonally opposite 75; divided by 100.
