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
hammer [34]
3 years ago
8

1. Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is

16.5 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height? Show your work please.
Mathematics
1 answer:
yan [13]3 years ago
3 0

Answer:

NO, the ladder is too steep.

Step-by-step explanation:

Length of ladder = 17 feet.  This is the hypotenuse.  

 Side a of a right triangle = 16.6    

To answer this, you need one of the trigonometric functions.      Opposite = 16.5    

hypotenuse = 17    

The function you need is the sine function.    

Sin(theta) = opposite / hypotenuse    

sin(theta) = 16.5 / 17    

Sin(theta) = 0.97059    

theta = sin-1(0.07059)    

theta = 76.07  

No the ladder is too steep.

You might be interested in
What are the solutions of the quadratic equation -x2 + 2x + 8?
nevsk [136]

-x2+2x+8 is 8 can you help me with bio

7 0
3 years ago
Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4​
jok3333 [9.3K]

Answer:

\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10

General Formulas and Concepts:
<u>Calculus</u>

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:                                                           \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Rule [Fundamental Theorem of Calculus 1]:                                 \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Integration Property [Multiplied Constant]:                                                     \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Integration Property [Addition/Subtraction]:                                                   \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

Area of a Region Formula:                                                                               \displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify.</em>

y = 2x + 3

<em>x</em>-interval [3, 4]

<em>x</em>-axis

<em>See attachment for graph.</em>

<u>Step 2: Find Area</u>

  1. Substitute in variables [Area of a Region Formula]:                               \displaystyle A = \int\limits^4_3 {2x + 3} \, dx
  2. [Integral] Rewrite [Integration Property - Addition/Subtraction]:           \displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx
  3. [Integrals] Rewrite [Integration Property - Multiplied Constant]:           \displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx
  4. [Integrals] Integrate [Integration Rule - Reverse Power Rule]:               \displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3
  5. [Integrals] Integrate [Integration Rule - FTC 1]:                                       \displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)
  6. Simplify:                                                                                                     \displaystyle A = 10

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

---

Learn more about integration: brainly.com/question/26401241

Learn more about calculus: brainly.com/question/20197752

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

3 0
2 years ago
The cylinder’s diameter and height are both 39.2 millimeters. What is the surface area of this cylinder?
Dominik [7]

Answer:

A = 7,241.2454026112  square mm.

or exact : A = 2,304.96‬*π  sq mm

Step-by-step explanation:

Cylinder formula:   A = π* r^2 +  2 *π * r* h  +  π*r^2

is the surface area.

d = 2r = 39.2 mm

h = 39.2 mm

r = 19.6 mm

A = π* r^2 +  2 *π * r* h  +  π*r^2

A = 2* π* (19.6)^2  + 2π (19.6)*(39.2)  

A = 2,413.748467537 +  4,827.496935

A = 7,241.2454026112  square mm.

or

A =  2*pi* (768.32‬ + 384.16)

A = 2*1,152.48‬* pi

A = 2,304.96‬*π  sq mm

8 0
3 years ago
A number from 0 to 9 is randomly selected and then a letter from A to D is randomly selected. What is the probability that the n
maw [93]

Answer:

3/20

Step-by-step explanation:

First we must get the total amount of possibilities.

We have ten numbers(0 included) and 4 letters. 10 * 4 = 40, so 40 total possibilities.

Now, let's see how many possibilities we can have for this.

Consonants in the 4 letters are B, C, D. This means we have 3 possibilities, but we ACTUALLy have 6 since it could b then 3, or 3 then b for all the letters.

So, we end up having 6/40 which simplifies in to 3/20

7 0
3 years ago
I NEED AN ANSWER ASAP!! IM MARKING THE FIRST ANSWER BRAINLIEST!
Rom4ik [11]
The tennis balls will not go the same distance

Hope this helps :D

(Sometimes i don’t know what the question is asking so pls tell me if I’m wrong)
3 0
3 years ago
Other questions:
  • The table shows the relationship between the number of members in a group and the minuted each member speaks during the presenta
    10·1 answer
  • Maureen cut a 20-cm ribbion into exactly three pieces. The first piece is 3cm shorter than the second piece. The third piece is
    10·1 answer
  • Find the height of a parallelogram with a base 6.75 meter and an area of 218.7 sqaure meters
    6·2 answers
  • There are 26 students at Williams math class the mean height of the student is 160 cm and the median height is 156 cm to inch aq
    6·1 answer
  • What is a example of information management
    7·1 answer
  • Nine times the sum of a number and 2 is 189. I need to make it to an equation.
    7·1 answer
  • Who ever gets this right correctly I’ll mark as the BRAINLY <br> I need this ASAP <br> X*2-10
    5·1 answer
  • Please answer this question
    8·2 answers
  • HELP PLEASE QUICK! its 7-grade math
    9·2 answers
  • Hi I'm the mom I would like some help with this
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!