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3 years ago

10

From the top of a cliff, which is 120 meters above the water, tha angle of depression of a boat on the water is 18°. How far is

the boat from the bottom of the cliff?

1 answer:

harina [27]3 years ago

4 0

To find how far the boat is from the bottom of the cliff is you’ll use tan;

Tan18degrees=120/x

x=120/tan18degrees

x=369m

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What is the solution set of x2 + 5x + 1 = 0?

DerKrebs [107]

Answer:

$\huge\boxed{\left\{-\dfrac{5+\sqrt{21}}{2};\ \dfrac{-5+\sqrt{21}}{2}\right\}}$

Step-by-step explanation:

$x^2+5x+1=0\\\\\text{Use the quadratic formula:}\\\\\text{For}\ ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta < 0,\ \text{then the equation has no real solution}\\\text{if}\ \Delta=0,\ \text{then the equation has one real solution}\ x=\dfrac{-b}{2a}\\\text{if}\ \Delta>0,\ \text{then the equation has two real solution}\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}$

$\text{We have}\\\\a=1,\ b=5,\ c=1\\\\\Delta=5^2-4(1)(1)=25-4=21>0\\\\x=\dfrac{-5\pm\sqrt{21}}{2(1)}=\dfrac{-5\pm\sqrt{21}}{2}$

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3 years ago

Please find the area of tge triangle<br><br>help me please asap due tomorrow

Olin [163]

45

1. Area = 1/2 B(base) x H(height)

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2 years ago

Read 2 more answers

Let A = { x ∈ R : x 2 − 5 x + 4 ≤ 0 } , B = (3 , 5), and C = (3 , 4]. Show that A ∩ B = C . (Recall, you must show two separate

kolbaska11 [484]

Answer:

You can proceed as follows:

Step-by-step explanation:

First solve the quadratic inequality $x^{2}-5x+4\leq 0$ . To do that, factorize, then we have that $(x-4)(x-1)\leq 0$ . This implies that

$x-1\leq 0\, \text{and}\, x-4\geq 0$

or

$x-1 \geq 0\, \text{and}\, x-4\leq 0$

In the first case the solution is the empty set $\emptyset$ . In the second case the solution is the interval $1\leq x \leq 4$ . Now we have that

$A=[1,4]$

$B=(3,5)$

$C=(3,4]$ .

To show that $A\cap B\subseteq C$ consider $x\in A\cap B$ . Then $1\leq x \leq 4\, \text{and}\, 1$ , this implies that $3$ , then $x\in C$ . Now, to show that $C\subseteq A\cap B$ consider $x\in C$ , then $3$ , then $1\leq x \leq 4\, \text{and}\, 3$ , then $x\in [1,4] \, \text{and}\, x\in (3,5)$ , this implies that $x\in A\cap B$ .

Observe the image below.

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3 years ago

Apopulation grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.a) Write a function to model the

solong [7]

Answer:

a) $P(t) = 22000(1.071)^{t}$

b) The population increases 7.1% each year.

Step-by-step explanation:

The continuous population growth model is given by:

$P(t) = P_{0}(1+r)^{t}$

In which $P(t)$ is the population after t years, $P_{0}$ is the initial population and r is the growth rate.

In this problem, we have that:

A population grows from its initial levelof 22,000 at a continuous growth rcte of 7.1% per year.

This means that $P_{0} = 22000, r = 0.071$

a) Write a function to model the population increase.

$P(t) = 22000(1 + 0.071)~{t}$

$P(t) = 22000(1.071)^{t}$

b) By what percent does the populaiion increase each year?

$r = 0.071$

So the population increases 7.1% each year.

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3 years ago

A clothing store pays $89.47 for a dress. The store’s percent of markup is 50% and the tax is 7.6%. Find the selling price for t

Goryan [66]

Hi,
<span>SP=Selling Price
</span>CP of dress= $ 89.47
percent of mark up = 50%
SP without tax= 100+ mark up % /100 * CP
<span>SP without tax= 100+50/100 * 89.47
</span>SP without tax= 150/100 * 89.47
SP without tax= 1.5 * 89.47
<span>SP without tax= $ 134.205
</span>tot. SP(SP with tax)= 100 + tax %/100 * SP
<span>SP=100 + 7.6/100 * 134.205
</span>SP= 107.6/100 * 134.205
SP= 1.076 * 134.205
<span>SP= $144.40458
Hope this helps you.</span>

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3 years ago