Answer:
240 = 2 x 2 x 2 x 2 x 3 x 5 or 2^4x3x5
Step-by-step explanation:
240
/ \
2 120 (240 = 2 x 120)
/ \
2 60 (120 = 2 x 60)
/ \
2 30 (60 = 30 x 2)
/ \
2 15 (30 = 2 x 15)
/ \
3 5
Answer:
y = (3 / (x-7)) - 5
Step-by-step explanation:
The original equation has the asymptotes at x = 0 and y = 0.
We want to translate to the right by 7 units so that the asymptote is at x = 7 and downwards 5 units so that the asymptote is y = -5.
Now, in the first case, to move it to the right, you must subtract 7 from the independent variable (i.e. x)
And in the second case, to move a function down 5 units, subtract 5 units from the entire function.
Applying the above, the new function would be:
y = (3 / (x-7)) - 5
Answer:
k = 4
Step-by-step explanation:
if direct variation exists,
input * k = output
here, number of baskets = input and cost = output
3 * k = 12
5 * k = 20
6 * k = 24
8 * k = 32
15 * k = 60
does this always work for one k?
let's try it out
3 * k = 12
divide both sides by 3 to solve for k
k = 4
5 * k = 20
divide both sides by 5 to solve for k
k = 4
6 * k = 24
divide both sides by 6 to solve for k
k = 4
8 * k = 32
divide both sides by 8 to solve for k
k = 4
15 * k = 60
divide both sides by 15 to solve for k
k = 4
as k = 4 no matter what, there is a direct variation with k = 4
You have to find the angle of sunlight and the pole , which then cast a shadow
length of the pole is equal to 3.1m
creating a hypotenuse of 4.52m
the angle will be
[email protected] = opposite side / hypotenuse
= 1.46/4.52
= 0.32 that's 18.66 °
now for the building sin18.66° = opposite/hypotenuse
0.32 = 36.75/ hypotenuse
hypotenuse = 114.84 m
thus using Pythagoras theorem
114.84*114.84 = 36.75*36.75 + x^2
which comes around = 108.8 roughly 109 metres long
Answer:
cosB = 21/75, tanB = 72/21
Step-by-step explanation:
Here, we can use pythagoras to figure out all sides. 75^2-72^2 = 21^2. So, we have sides with lengths 21, 72, and 75. We are given that sinB = 72/75. The definition of sin is opposite of hypotenuse. So, the opposite of angle B is side CA and the hypotenuse is BA. This allows us to find that BC is the 21 length side. The cos of an angle is adjacent over hypotenuse. In this case, it is BC/BA which is 21/75. similarly, Tan is opposite over adjacent or 72/21. And we are done. Those are the values. TO remember these, use the acronym:
SOH CAH TOA. S refers to sin and OH refers to opposite over hypotenuse. Similarly C is cos, A is adjacent, and H is hypotenuse, and then T is tan, o is opposite and A is adjacent.
