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3 years ago

9

The snallest flowering plant is the flowering aquatic duckweed found in Australia. It is 0.0236 inch long and 0.0129 inch wide.

Write these dimensions as fractions in simplest form.

1 answer:

vaieri [72.5K]3 years ago

6 0

Answer:

A. t=66d

B. 66=d•t

C. d=66/t

D. d= 66t****

Step-by-step explanation:

the 66 ft/s is the speed, or the velocity.

since distance = time x velocity , or distance = time x rate

d = 66t

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For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple

almond37 [142]

Answer:

$\displaystyle \sin(A-B)=\frac{495}{1073}$

Step-by-step explanation:

We are given that:

$\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}$

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

$h = \sqrt{35^2 + 12^2} =37$

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

$a=\sqrt{29^2-20^2}=21$

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

$\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)$

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

$\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)$

Evaluate:

$\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}$

6 0

3 years ago

You mix soda water, fruit punch concentrate, and ginger ale in the ratio of 1 : 2 : 5 to make fruit punch. How many pints of eac

SIZIF [17.4K]

All you do is 1x+2x+5x=8x then you turn 4 s into pints. 1 gallon equals 4 pints 4*4=16 pints. 8x=16 x=2. Then you multiply everything by 2

1*2=2
2*2=4
2*5=10

2pints of soda water
4 pints of fruit punch
10 pints of ginger ale

3 0

3 years ago

Ben baked brownies in the brownie pan shown below. Each day, he is going to eat 303030 square centimeters of brownie from the pa

luda_lava [24]

Answer:

Option A. $30\ days$

Step-by-step explanation:

step 1

Find the area of the brownie pan

The area of the trapezoid is equal to

$A=\frac{1}{2}(30+42)(25)=900\ cm^{2}$

step 2

To calculate the number of days, divide the total area of the brownie pan by 30 square centimeters of brownie

so

$900/30=30\ days$

4 0

3 years ago

Read 2 more answers

Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 In which section of the graph does the actual solution

AlekseyPX

The answer to your question is 4

8 0

3 years ago

Read 2 more answers

Determine how many zeros, how many real or complex, and find the roots for f(x) = x3 − 5x2 − 25x + 125.

miskamm [114]

We can write this as:-

P(x) = + x^3 - 5x^2 - 25x + 125
There are 2 changes of real sign so by Descartes Rule of signs there are either 2 positive real roots or 0 positive roots.

P(-x) = - x^3 - 5x^2 + 25x + 125
There is just one change of sign so there is exactly 1 real negative root.

125 is a multiple of 5 so By rational root theorem 5 could be a positive root.

P(5) = 125 - 125 - 125 + 125 = 0 so one zero is 5
if we divide the polynomial by (x - 5) we get the quadratic
x^2 - 25
(x + 5)(x - 5) = 0

x = 5,-5

so the roots are 5 (multiplicity 2) and -5.
2 real positive zeroes and one real negative zero

7 0

3 years ago