Patty is 50 mi. due north of Todd. Emma is due east of Todd. The angle between the direction of the shortest distance from Emma and Patty and due east is 40°. To the nearest mile, how far is Emma from each person?

Answers

Answer 1

Answer: For this it would be helpful if you draw a diagram of the situation. You will see that a right triangle can be formed from the problem. We use trigonometric functions to solve. We do as follows:

sin 40 = 50/y
tan 40 = 50/x

Solving we obtain,
x = 60 mi
y = 78 mi

Hope this answers the question. Have a nice day.

Answer 2

Answer:

Answer:

Hence, the distance between Todd and Emma is:41.955 mi.

and the distance between Patty and Emma is:32.14 mi.

Step-by-step explanation:

We will see that we will get a right angled triangle based on our information(The graph is attached to the answer)

Now let x denotes the distance between Emma and Todd.

and y denotes the distance between Emma and Patty.

Now as the triangle is right angled so we can use the trignometric identities to find the distance.

$\tan40\degree=(50)/(x)$

this means $x=\tan40\degree * 50$

Now as $\tan40\degree=0.8391$

Hence, $x=41.955 \text{mi.}$

Similarly,

$\sin40\degree=(50)/(y)$

Hence $y=32.14 \text{mi.}$

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Convert the number below from exponential to standard notation.6(104) + 4(103) + 8(102) + 1(101) + 7(100)

6,481,700
648.17
648,170
64,817

Answers

$6(10^4) + 4(10^3) + 8(10^2) + 1(10^1) + 7(10^0)\n\n = 6(10,000) + 4(1,000) + 8(100) + 1(10) + 7(1)\n\n=60,000 + 4,000 + 800 + 10 + 7\n\n = \boxed{\bf{64,817}}$

Your answer is D.

Multiply. start fraction k plus 3 over 4 k minus 2 end fraction dot left parenthesis 12 k squared plus 2 k minus 4 right parenthesis

Answers

Answer:

$\therefore ((k+3))/((4k-2)).(12k^2+2k-4)=3k^2+11k+6$

Step-by-step explanation:

Factorization of a Quadratic polynomial:

In order to factorize $ax^2+bx+c$ we have to find out the numbers p and q such that, p+q = b and pq=ac.

Finding the two integers p and q, we rewrite the middle term of the quadratic as px+qx. Then by grouping of the terms we can get desired factors.

Multiplication of two binomial:

(a+b)(c+d)

=a(c+d)+b(c+d)

=(ac+ad)+(bc+bd)

=ac+ad+bc+bd

Given that,

$((k+3))/((4k-2)).(12k^2+2k-4)$

$=((k+3))/(2(2k-1)).2(6k^2+k-2)$ [ taking common 2]

$=((k+3))/((2k-1)).(6k^2+k-2)$ [ cancel 2]

$=((k+3))/((2k-1)).(6k^2+4k-3k-2)$

$=((k+3))/((2k-1)).\{2k(3k+2)-1(3k+2)\}$

$=((k+3))/((2k-1)).(3k+2)(2k-1)$

$=(k+3).(3k+2)$

$=3k^2+9k+2k+6$

$=3k^2+11k+6$

$\therefore ((k+3))/((4k-2)).(12k^2+2k-4)=3k^2+11k+6$

"I am thinking of a number 3
_
4

Of my number is 12
Work out 5 times my number. You must show your working "

Answers

The number is 16.

I know this cause 4 can go into 16 four times. I now do 4 x 3 which is 12

12/3=4 And 4 times 4 equals 16. Therefore, your number is 16. And 16 multiplied by five equals 80.

3
16
*
5
__

80

A cone has a circular base with a diameter of 18 inches. the height of the cone is 40 inches. what is the approximate lateral area of the cone? use 3.14 for π and round to the nearest whole number. 565 square inches 580 square inches 1,131 square inches 1,159 square inches

Answers

The lateral area of a cone is expressed as:

Lateral surface area of a cone: L = πrs = πr√(r^2 + h^2)
L = π(9)√(9^2 + 40^2)
L = 1159.248

Therefore, the correct answer is the last option. Hope this answers the question. Have a nice day.

To solve this problem, we have to use the formula of lateral surface area of a cone and substituting the values into the formula and then solve.

The lateral surface area of this cone is 2260.8in^2