1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Evgen [1.6K]
3 years ago
8

Find the angle represented by x (rounded to the nearest tenth of a degree).

Mathematics
1 answer:
koban [17]3 years ago
3 0

Answer:

Option (D)

Step-by-step explanation:

By applying sine rule in the triangle shown,

Since, \text{sin}\theta=\frac{\text{Opposite side}}{\text{Hypotenuse}}

By this rule,

\text{sinx}=\frac{\text{5000}}{8000}

x = \text{sin}^{-1}(\frac{5}{8})

x = \text{sin}^{-1}(0.625)

x = 38.682°

  ≈ 38.7°

Therefore, Option (D) is the correct option.

You might be interested in
14 minus 48 plus 93 divided by -95​
ankoles [38]

Answer:

The answer would be -35.

Step-by-step explanation: (14-48) + (93 DIVIDED BY (-95))= -34.9789473684 WHICH ROUNDS OUT TO BE -35.

7 0
3 years ago
Irina has 6 tubs of yogurt she wants to scoop it all into bowls each bowl holds 1/4 tub of yogurt which division equation can be
elena55 [62]
In order to find the answer, you can use-

1/4x=6

In order to get the answer, you multiply 6 by the denominator. 

6x4=24

Then, you'd divide the solution of that part by the numerator.

24 divided by 1 equals 24.


Therefore, the final answer would be 24.


7 0
3 years ago
Read 2 more answers
7400 dollars is placed in an account with an annual interest
Anastasy [175]

Answer:

17

Step-by-step explanation:

We have the following equation for compounding annual interest

AV=PV(1+i)ⁿ

We have

19200=7400(1+.06)ⁿ

Solve for n

divide both sides by 7400

2.594=(1.06)ⁿ

then use the following rule for exponents

x^y=z\\log_xz=y

which means that

log_{1.06}2.594=n

Solve and get

16.362

which rounds to 17

6 0
3 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 6x2 − 15x + 4 (a) Find the interval on which
kozerog [31]

Answer:

a) The function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Written in interval form

(-∞, -1.45) and (3.45, ∞)

- The function, f(x) is decreasing at the interval (-1.45 < x < 3.45)

(-1.45, 3.45)

b) Local minimum value of f(x) = -78.1, occurring at x = 3.45

Local maximum value of f(x) = 10.1, occurring at x = -1.45

c) Inflection point = (x, y) = (1, -16)

Interval where the function is concave up

= (x > 1), written in interval form, (1, ∞)

Interval where the function is concave down

= (x < 1), written in interval form, (-∞, 1)

Step-by-step explanation:

f(x) = x³ - 6x² - 15x + 4

a) Find the interval on which f is increasing.

A function is said to be increasing in any interval where f'(x) > 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

the function is increasing at the points where

f'(x) = 3x² - 6x - 15 > 0

x² - 2x - 5 > 0

(x - 3.45)(x + 1.45) > 0

we then do the inequality check to see which intervals where f'(x) is greater than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

So, the function (x - 3.45)(x + 1.45) is positive (+ve) at the intervals (x < -1.45) and (x > 3.45).

Hence, the function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Find the interval on which f is decreasing.

At the interval where f(x) is decreasing, f'(x) < 0

from above,

f'(x) = 3x² - 6x - 15

the function is decreasing at the points where

f'(x) = 3x² - 6x - 15 < 0

x² - 2x - 5 < 0

(x - 3.45)(x + 1.45) < 0

With the similar inequality check for where f'(x) is less than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

Hence, the function, f(x) is decreasing at the intervals (-1.45 < x < 3.45)

b) Find the local minimum and maximum values of f.

For the local maximum and minimum points,

f'(x) = 0

but f"(x) < 0 for a local maximum

And f"(x) > 0 for a local minimum

From (a) above

f'(x) = 3x² - 6x - 15

f'(x) = 3x² - 6x - 15 = 0

(x - 3.45)(x + 1.45) = 0

x = 3.45 or x = -1.45

To now investigate the points that corresponds to a minimum and a maximum point, we need f"(x)

f"(x) = 6x - 6

At x = -1.45,

f"(x) = (6×-1.45) - 6 = -14.7 < 0

Hence, x = -1.45 corresponds to a maximum point

At x = 3.45

f"(x) = (6×3.45) - 6 = 14.7 > 0

Hence, x = 3.45 corresponds to a minimum point.

So, at minimum point, x = 3.45

f(x) = x³ - 6x² - 15x + 4

f(3.45) = 3.45³ - 6(3.45²) - 15(3.45) + 4

= -78.101375 = -78.1

At maximum point, x = -1.45

f(x) = x³ - 6x² - 15x + 4

f(-1.45) = (-1.45)³ - 6(-1.45)² - 15(-1.45) + 4

= 10.086375 = 10.1

c) Find the inflection point.

The inflection point is the point where the curve changes from concave up to concave down and vice versa.

This occurs at the point f"(x) = 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

f"(x) = 6x - 6

At inflection point, f"(x) = 0

f"(x) = 6x - 6 = 0

6x = 6

x = 1

At this point where x = 1, f(x) will be

f(x) = x³ - 6x² - 15x + 4

f(1) = 1³ - 6(1²) - 15(1) + 4 = -16

Hence, the inflection point is at (x, y) = (1, -16)

- Find the interval on which f is concave up.

The curve is said to be concave up when on a given interval, the graph of the function always lies above its tangent lines on that interval. In other words, if you draw a tangent line at any given point, then the graph seems to curve upwards, away from the line.

At the interval where the curve is concave up, f"(x) > 0

f"(x) = 6x - 6 > 0

6x > 6

x > 1

- Find the interval on which f is concave down.

A curve/function is said to be concave down on an interval if, on that interval, the graph of the function always lies below its tangent lines on that interval. That is the graph seems to curve downwards, away from its tangent line at any given point.

At the interval where the curve is concave down, f"(x) < 0

f"(x) = 6x - 6 < 0

6x < 6

x < 1

Hope this Helps!!!

5 0
3 years ago
What is the slope of (10,150) and (1,-75)
valentina_108 [34]

Answer:

25

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • I'm still giving away prizes i have 5 more left in announcing sometime this week but I need help,
    7·1 answer
  • Bryant just drank a cup of coffee to help him stay awake. The coffee had 52 milligrams of caffeine in it. If his body processes
    9·1 answer
  • What is 35.99 as a mixed number in simplest form
    12·2 answers
  • Brenda has $43 in the bank. Each month the bank deducts $5 from her account for a service fee. Which equation represents the dol
    7·1 answer
  • Can someone help me find the radius? Thanks! :D
    11·1 answer
  • Liam solved the equation 72 = 8. b. His work is shown.<br> What error did Liam make?
    13·1 answer
  • The transitive property holds true for similar figures.<br><br> Always<br> Sometimes<br> Never
    7·2 answers
  • Help i'll give brainlesttt
    10·2 answers
  • Find the area of the triangle with vertices A(-3,2), B(1,-2), and c(1,3)
    15·1 answer
  • The following is a conversion table for hours and minutes. Which numbers belong in the hours column?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!