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Diano4ka-milaya [45]
3 years ago
5

I need some help with this

Mathematics
1 answer:
Ivenika [448]3 years ago
6 0

Answer:

a) 6.1 feet

b) 12.6 feet

Step-by-step explanation:

Using trigonometric ratios we know that:

sin = \frac{opp}{hyp}\\cos = \frac{adj}{hyp}\\tan = \frac {opp}{adj}

AKA SohCahToa.

To find the height, we will use sine.

sin(26^o)= \frac{x}{14}\\14*sin(26^o)=\frac{x}{14}*14\\14sin(26^o)=x\\x=6.14

To find the length we will use cosine.

cos(26^o) = \frac{x}{14}\\14*cos(26^o)=\frac{x}{14}*14\\14cos(26^o)=x\\x=12.6

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This can be solved using a ratio. The ratio is: 13/20=x/60 this would then become 20x= 780  divide both sides by 20 and you get x=39. the answer is 39
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Glenn invested $22,000 at 7% interest compounded annually.   How much interest will Glenn earn in 3 years?
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I =125 r=6% t=1 what is p
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See question in screenshot below.
alexgriva [62]

The equation of the transformation of the exponential function <em>y</em> = 2ˣ in the form <em>y</em> = A·2ˣ + k, obtained from the simultaneous found using the points on the graph is <em>y</em> = (-2)·2ˣ + 3

<h3>What is an exponential equation?</h3>

An exponential equation is an equation that has exponents that consists of variables.

The given equation is <em>y</em> = 2ˣ

The equation for the transformation is; <em>y</em> = A·2ˣ + k

The points on the graphs are;

(0, 1), (1, -1) and (2, -5)

Plugging the <em>x </em>and <em>y</em>-values to find the value <em>A</em> and <em>k</em> gives  the following simultaneous equations;

When <em>x</em> = 0, <em>y</em> = 1, therefore;

1 = A·2⁰ + k = A + k

1 = A + k...(1)

When <em>x</em> = 1, <em>y</em> = -1, which gives;

-1 = A·2¹ + k

-1 = 2·A + k...(2)

Subtracting equation (1) from equation (2) gives;

-1 - 1 = 2·A - A + k - k

-2 = A

1 = A + k, therefore;

1 = -2 + k

k = 2 + 1 = 3

k = 3

Which gives;

y = -2·2ˣ + 3 = 3 - 2·2ˣ

Learn more about the solutions to simultaneous equations here:

brainly.com/question/26310043

#SPJ1

3 0
1 year ago
Miguelle is deciding which type of heating system to put in his house. An oil system costs $2700 to install and
stellarik [79]

Answer: (9, 10800)

Step-by-step explanation:

We will first let x be the number of years and y be the total cost.

In that case, let's plug in the values for each into the equation <em>y=mx+b, </em>where m is the slope and b is the y-intercept.

The y-intercept will be the <u>value we start with before any years pass</u>, so it will be the <u>installation cost</u>. The slope is <u>how fast the total cost will increase</u>. Since the <u>operation costs</u> have to be added on every year, it will be our slope.

With that in mind, let's create both of our equations:

  1. y = 900x + 2700 (Oil system)
  2. y = 200x + 9000 (Solar system)

Since y is solved for in the first equation, we can substitute it into the second equation:

900x + 2700 = 200x + 9000

700x + 2700 = 9000 <em>[Subtracting 200x from both sides]</em>

<em />700x = 6300 <em>[Subtracting 2700 from both sides]</em>

<em />x = 9 <em>[Dividing both sides by 700]</em>

<em />

We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:

y = 900(9) + 2700

y = 8100 + 2700 <em>[Multiplying]</em>

<em />y = 10800 <em>[Adding]</em>

Hence, the solution to this linear system is (9, 10800).

3 0
2 years ago
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