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Marat540 [252]
3 years ago
12

In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.

Mathematics
1 answer:
Sergio039 [100]3 years ago
5 0

Answer:

182 ft

Step-by-step explanation:

BDC is a right angle triangle.

With respect to angle C, CD is the adjacent length and BC is the hypotenuse.

cos(C) = adjacent/hypotenuse

cos(77) = 41/BC

BC = 41/cos(77)

BC = 182.261870786

BC = 182

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3. Rectangle ABCD is shown on the coordinate grid below.
VMariaS [17]

Answer:

A. 8 units

Step-by-step explanation:

Coordinates of A = (-2, -2)

Coordinates of C = (5, 2)

Use distance formula, d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} to calculate the length of diagonal \overline{AC}.

Let,

A(-2, -2) = (x_1, y_1)

C(5, 2) = (x_2, y_2)

d = \sqrt{(5 -(-2))^2 + (2 -(-2))^2}

d = \sqrt{(7)^2 + (4)^2}

d = \sqrt{49 + 16} = \sqrt{65}

d = 8.1 (nearest tenth)

Therefore, the closest to the length of diagonal \overline{AC} = 8 units

4 0
3 years ago
If Julie invests $9,250 at a rate of 7%, compounded weekly, find the value of the investment after 5 years. $13,455.78
STatiana [176]
What is that $13,455.78? Something? I did this and got $13,122.76.  Here's how I did it:
Use this formula
A=P(1+ \frac{r}{n} ) ^{(n)(t)} where A is the ending amount, P is the starting amount, n is the number of times it compounds a year, and t is the number of years.  We have all we need to set it up:
A=9,250(1+ \frac{.07}{52} ) ^{(52)(5)}
First divide and add inside the parenthesis:
A=9,250(1.001346) ^{(52)(5)}
then multiply the exponents:
A=9,250(1.001346) ^{260}
raise the value inside the parenthesis to the power of 260:
A=9,250(1.418676)
and finally multiply to get A = $13,122.76
6 0
3 years ago
The rate of change (dP/dt), of the number of people on an ocean beach is modeled by a logistic differential equation. The maximu
Kazeer [188]

Answer:

\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})

Step-by-step explanation:

The logistic differential equation is as follows:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

In this problem, we have that:

K = 1200, which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.

At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.

This means that \frac{dP}{dt} = 400 when P = 200. With this, we can find r, that is, the growth rate,

So

\frac{dP}{dt} = rP(1 - \frac{P}{K})

400 = 200r(1 - \frac{200}{1200})

166.67r = 400

r = 2.4

So the differential equation is:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})

3 0
3 years ago
Find (f ° g)(0). *
atroni [7]

Answer:

B

Step-by-step explanation:

Remark

I have to represent f(x) as plus +f(x)

I like to show this situation as +f(g(x)) which I think is much clearer.

+f(x) = 5x - 4    

Solution

+f(g(x)) = 5(g(x)) - 4  What has happened is that wherever you see an x on the right you put in g(x).

Now on the right, you put whatever g(x) is equal  to.

+f(g(x)) = 5(x^2 - 1)  - 4    

Remove the brackets.

+f(g(x)) = 5x^2 - 5 - 4

And make x = 0

+f(g(0)) = 5*0 - 5 - 4

+f(g(0)) = - 9

8 0
3 years ago
Find the lines slope and a point on the line.
sesenic [268]

Answer:

The slope is  3/4 and a point on the line is (-5,2)

Step-by-step explanation:

This is given in point slope form

y - y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-2 = 3/4(x +5)

y-2 = 3/4(x - -5)

The slope is  3/4 and a point on the line is (-5,2)

7 0
3 years ago
Read 2 more answers
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