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professor190 [17]

3 years ago

11

A person in a certain family eats 724.4 lbs of fruit and vegetables in a year. What is the average consumtion in one day ( use 1

year =365 days

1 answer:

butalik [34]3 years ago

4 0

<span>1.98465753425 lbs of produce per day
</span><span>0.08269406392 lbs of produce per day
</span>Hope this helps!

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What is the exact value of sin(theta + beta)?

NISA [10]

Answer: $\frac{-3\sqrt{13}+4\sqrt{3}}{20}$

This is the single fraction of -3*sqrt(13)+4*sqrt(3) up top all over 20.

sqrt = square root

=======================================================

Explanation:

Angle theta is between pi and 3pi/2. This places the angle in quadrant Q3 where both cosine and sine are negative

Use the pythagorean trig identity to get the following:

$\sin^2 \theta + \cos^2 \theta = 1\\\\\sin^2 \theta + \left(-\frac{\sqrt{3}}{4}\right)^2 = 1\\\\\sin^2 \theta + \frac{3}{16} = 1\\\\\sin^2 \theta = 1 - \frac{3}{16}\\\\\sin^2 \theta = \frac{16}{16} - \frac{3}{16}\\\\\sin^2 \theta = \frac{16-3}{16}\\\\\sin^2 \theta = \frac{13}{16}\\\\\sin \theta = -\sqrt{\frac{13}{16}} \ \text{ ... sine is negative in Q3}\\\\\sin \theta = -\frac{\sqrt{13}}{\sqrt{16}}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\$

Angle beta is in Q1 where sine and cosine are positive.

Draw a right triangle with legs 3 and 4. The hypotenuse is 5 through the pythagorean theorem. In other words, we have a 3-4-5 right triangle.

Since $\tan \beta = \frac{3}{4}$ , this means $\sin \beta = \frac{3}{5} \ \text{ and } \ \cos \beta = \frac{4}{5}$

Use these ideas:

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

In this case we have: opposite = 3, adjacent = 4, hypotenuse = 5.

-------------------------------------

To recap:

$\cos \theta = -\frac{\sqrt{3}}{4}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\\cos \beta = \frac{3}{5}\\\\\sin \beta = \frac{4}{5}\\\\$

They lead to this

$\sin\left(\theta + \beta\right) = \sin \theta * \cos \beta - \cos \theta * \sin \beta\\\\\sin\left(\theta + \beta\right) = -\frac{\sqrt{13}}{4} * \frac{3}{5} - \left(-\frac{\sqrt{3}}{4}\right) * \frac{4}{5}\\\\\sin\left(\theta + \beta\right) = -\frac{3\sqrt{13}}{20}+\frac{4\sqrt{3}}{20}\\\\\sin\left(\theta + \beta\right) = \frac{-3\sqrt{13}+4\sqrt{3}}{20}\\\\$

6 0

3 years ago

german

The volume is given by

$V=\pi hr^2$

Since the height is 3 times the radius of the base, we can substitute $h=3r$ :

$V=\pi (3r)r^2=3\pi r^3$

And we know that the volume is $24\pi$ (I'm actually assuming that there's a typo in the question, otherwise the options wouldn't match):

$24\pi=3\pi r^3 \iff r^3=8 \iff r=2$

The height is 3 times the radius, so it is

$h=2\cdot 3 = 6$

7 0

3 years ago

2 to the 3rd power divided by 2 to the 6th power

marissa [1.9K]

1/8 is the answer you’re welcome

5 0

3 years ago

BRAINLIEST!!! +10 POINTS!!! REAL ANSWERS ONLY PLEASE!!!

IRINA_888 [86]

Answer:

plus ten points huh i only see five

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

wyatt opend a savings account 4 years ago. the account earns 4%interest compounded quarterly if the current balance is $1,000.00

Doss [256]

Answer:

He deposited initially $852.82

Step-by-step explanation:

The rule of the compound interest is $A=P(1+\frac{r}{n})^{nt}$ , where

A is the new amount

P is the initial amount

r is the rate in decimal

n is the period of the time

t is the time

∵ Wyatt opened a savings account 4 years ago

∴ t = 4

∵ The account earns 4% interest compounded quarterly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 4 ⇒ compounded quarterly

∵ The current balance is $1,000.00

∴ A = 1,000

→ Substitute these values in the rule above to find P

∵ 1,000 = $P(1+\frac{0.04}{4})^{4(4)}$

∴ 1,000 = $P(1+0.01)^{16}$

∴ 1,000 = $P(1.01)^{16}$

→ Divide both sides by $(1.01)^{16}$

∴ 852.8212622 = P

→ Round it to the nearest cent (2d.p)

∴ P = 852.82

∴ He deposited initially $852.82

4 0

3 years ago