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4 years ago

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A plant is already 45 centimeters tall, and will grow one centimeter every month. the plants height, H, (in centimeters), after

m months is given by the following:
H=45 + m
what is the plants height after 14 months

1 answer:

Lelu [443]4 years ago

5 0

Answer:

59

Step-by-step explanation:

45 +14 = 59

because there is 14 months in your equation. simply take the question and add 14.

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Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

D

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2> $\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}$ </h2>

Simplify:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}$

Evaluate:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}$

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

$\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}$

So, our answer is D.

7 0

3 years ago

A ship traveled for a total of 147 miles over the course of 8 hours. Heading south, the ship traveled at an average speed of 15

Cloud [144]

Alright

s=number of hours headd south
e=number of hours headed east

s+e=8

and
total is 147 miles
distance=speed times time
15s+24e=147

we got 2 equations

s+e=8
15s+24e=147
subsitution

s+e=8
minus e both sides
s=8-e
subsitut 8-e for s in other equaton

15s+24e=147
15(8-e)+24e=147
120-15e+24e=147
120+9e=147
minus 120 both sides
9e=27
divide both isdes by 9
e=3

sub back
s=8-e
s=8-3
s=5

it was headed south 5 miles

6 0

3 years ago

Which of the following questions represents a biased question? Do you plan to vote yes or no on Measure 2? Which do you prefer t

Naya [18.7K]

Last one is a biased question

8 0

3 years ago

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Solve the equation for y (y-3)^2=4y-12

Ket [755]

(y -3)^2 = 4y - 12

Expand.

(y-3)(y -3) = 4y - 12

y² - 6y + 9 = 4y - 12

y² - 6y -4y + 9 + 12 = 0

y² - 10y + 21 = 0

Factors are -7y and - 3y

y² - 10y + 21 = 0

y² - 3y - 7y + 21 = 0

y(y - 3) -7(y - 3) = 0

(y - 3)(y - 7) = 0

y-3 = 0 or y - 7 = 0

y = 0 + 3 or y = 0 + 7

y = 3 or 7

8 0

3 years ago

What is the value of sin(A)?

Rama09 [41]

Answer:

3/5

Step-by-step explanation:

6 0

3 years ago

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