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3 years ago

I need help with this word problem please

Mathematics

1 answer:

nika2105 [10]3 years ago

7 0

Answer:

786.9 feet to the nearest tenth.

Step-by-step explanation:

In the triangle formed between the boat, base of the lighthouse and the top of the lighthouse, the opposite side to angle 21 49' is the height of the lighthouse and the distance (d) of the boat is the adjacent side.

So we have:

tan 21 49 = 315 / d

d = 315/ tan21 49

= 786.89 ft.

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3/4 of $530.40 show work

Minchanka [31]

Multiply $530.40 by 3/4. You get the equation
$\frac{530.40 * 3}{4}$
If you simplify this, you get the solution of $397.80

$397.80

4 0

3 years ago

HELP Question below in the photo linked

lora16 [44]

Answer:

D. x = 10, m<TRS = 60°

Step-by-step explanation:

m<QRS = 122° (given)

m<QRT = (7x - 8)° (given)

m<TRS = (6x)° (given)

m<QRT + m<TRS = m<QRS (angle addition postulate)

(7x - 8)° + (6x)° = 122° (substitution)

Solve for x

7x - 8 + 6x = 122

Add like terms

13x - 8 = 122

13x = 122 + 8

13x = 130

x = 130/13

x = 10

✔️m<TRS = (6x)°

Plug in the value of x

m<TRS = (6*10)° = 60°

6 0

3 years ago

Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

Yuri [45]

Let the curve C be the intersection of the cylinder

$16x^2+y^2=16$

and the plane

$x+y+z=1$

The projection of C on to the x-y plane is the ellipse

$16x^2+y^2=16$

To see clearly that this is an ellipse, le us divide through by 16, to get

$\frac{x^2}{1}+ \frac{y^2}{16}=1$

$\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1$ ,

We can write the following parametric equations,

$x=cos(t), y=4sin(t)$

for

$0\le t \le 2\pi$

Since C lies on the plane,

$x+y+z=1$

it must satisfy its equation.

Let us make z the subject first,

$z=1-x-y$

This implies that,

$z=1-sin(t)-4cos(t)$

We can now write the vector equation of C, to obtain,

$r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))$

The length of the curve of the intersection of the cylinder and the plane is now given by,

$\int\limits^{2\pi}_0 {|r'(t)|} \, dt$

But

$r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))$

$|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}$

$\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184$

Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0

3 years ago

Sarah is 6 years older than Amy.

Umnica [9.8K]

Answer:

Step-by-step explanation:

The problem has got to be addition.

The sentence "Sarah is 6 years older than Amy." does not include any hint of subtracting, or multiplying.

A hint of multiplying in a expression would be the word 'times', like "Brandon is 6 times the age of Emily" which eliminates D.

A hint of subtraction in an expression would be the word 'less', like "Brandon is 6 less the age of Emily." which eliminates A and C.

The word 'older' indicates addition, or adding, and if it would have been subtraction, the keyword would be 'younger' because you are subtracting their age, like 19 - 11. The same goes with B, but adding.

Finally, we now know that it is B because there is no other addition choice.

I hope this helped. Please correct me if I am wrong.

8 0

3 years ago

You are painting the outside of a 28

Artemon [7]

Answer:

you have done 1/4 ... ....

8 0

3 years ago

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