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2 years ago

A pole casts a 6-foot shadow. If the distance from the top of the pole to the tip of the shadow is

Mathematics

1 answer:

KATRIN_1 [288]2 years ago

3 0

Answer:

8feet high

Step-by-step explanation:

To get the height of the pole, we will use the pythagoras theorem. Let H be the height

H² = 10² -6²

H² = 100 - 36

H² = 64

H = √64

H = 8feet

Hence the pole is 8feet high

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stealth61 [152]

$\large\underline{\sf{Solution-}}$

We have to evaluate the given expression.

$\rm = \sqrt{ \dfrac{1 - \sin(x) }{1 + \sin(x) } }$

If we multiple both numerator and denominator by 1 - sin(x), then the value remains same. Let's do that.

$\rm = \sqrt{ \dfrac{[1 - \sin(x)][1 - \sin(x) ]}{[1 + \sin(x)][1 - \sin(x) ]} }$

$\rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{1- \sin^{2} (x) } }$

We know that:

$\rm \longmapsto { \sin}^{2}(x) + \cos^{2}(x) = 1$

$\rm \longmapsto \cos^{2}(x) = 1 - { \sin}^{2}(x)$

Therefore, the expression becomes:

$\rm = \sqrt{ \dfrac{[1 - \sin(x)]^{2}}{\cos^{2} (x)}}$

$\rm = \dfrac{1 - \sin(x)}{\cos(x)}$

$\rm = \dfrac{1}{\cos(x)} - \dfrac{ \sin(x) }{ \cos(x) }$

$\rm = \sec(x) - \tan(x)$

7 0

2 years ago

Read 2 more answers

Trevor solved the system of equations below. What mistake did he make in his work?

storchak [24]

The answer is He subtracted 10 from the right side instead of adding 10 to the right side

Let's solve it:
2x + y = 5
x − 2y = 10
________
Rearrange first equation to get y:
y = 5 - 2x
________
Substitute y into the second equation:
x - 2(5 - 2x) = 10
________
Multiply the terms:
x - 10 + 4x = 10
________
Combine the terms:
5x - 10 = 10
________
Add 10 on the both sides of the equation:
5x = 10 + 10
5x = 20
x = 4

3 0

2 years ago

Noah wants to buy a 5 year annuity that pays $1000 at the end of each year, starting one year from now. It earns interest at 6.2

pav-90 [236]

Answer:

cost is $4183.87

Step-by-step explanation:

given data

time t = 5 year

amount A = $1000

rate r = 6.25 % = 0.0625

to find out

how much it will cost

solution

we will apply here formula for present value of annuity that is express as

present value = amount × $\frac{1-(1+r)^{-t}}{r}$ ....................1

put here all these value we get cost we will pay

present value = amount × $\frac{1-(1+r)^{-t}}{r}$

present value = 1000 × $\frac{1-(1+0.0625)^{-5}}{0.0625}$

present value = 4183.869221

so cost is $4183.87

5 0

3 years ago

Help me of i die so pls help me

nekit [7.7K]

Answer:

100

1000

Step-by-step explanation:

I had a quiz on that the other day got 100%

7 0

2 years ago

Evaluate the integral x^3 (x 4 −8)^44 dx by making the substitution u = x^4 - 8

Eduardwww [97]

Answer:

(x^4-8)^45 /180 +c

Step-by-step explanation:

If u=x^4-8, then du=(4x^3-0)dx or du=4x^3 dx by power and constant rule.

If du=4x^3 dx, then du/4=x^3 dx. I just divided both sides by 4.

Now we are ready to make substitutions into our integral.

Int(x^3 (x^4-8)^44 dx)

Int(((x^4-8)^44 x^3 dx)

Int(u^44 du/4)

1/4 Int(u^44 dul

1/4 × (u^45 / 45 )+c

Put back in terms of x:

1/4 × (x^4-8)^45/45 +c

We could multiply those fractions

(x^4-8)^45 /180 +c

5 0

2 years ago