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
arlik [135]
2 years ago
12

If a= -2, y = -3 and z = 4, find the values of the following algebraic expressions. -3az

Mathematics
1 answer:
kipiarov [429]2 years ago
5 0

Answer:

24

Step-by-step explanation:

substitute the given values for a and z into the expression

- 3az

= - 3(- 2)(4) = 6 × 4 = 24

You might be interested in
What similarity statement can you write relating the three triangles in the diagram?
murzikaleks [220]

Answer:

d

Step-by-step explanation:

8 0
3 years ago
Pls help and find the area
Zepler [3.9K]

Answer:

I don’t know the area but here’s a hint to help you (hint: length x with x height)

Step-by-step explanation:

5 0
2 years ago
The common ratio of a geometric series is \dfrac14 4 1 ​ start fraction, 1, divided by, 4, end fraction and the sum of the first
myrzilka [38]

Answer:

The common ratio of a geometric series is \dfrac14

4

1 ​

start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

r =  \frac{1}{4}

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

s_n=\frac{a_1(1-r^n)}{1-r}

common ratio, n=4 and equate to 170.

\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170

\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4}  \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2}  \\\\\frac{1}{256} a_1 = \frac{1}{2}  \\\\ a_1 = \frac{1}{2}   \times 256\\\\a_1 = \frac{1}{2}   \times 256 \\\\= 128

8 0
3 years ago
2. (15 points) Find the volume of the solid generated by revolving the region bounded by the curves x=
dangina [55]

Step-by-step explanation:

First, graph the region.  The first equation is x = 3y² − 2, which has a vertex at (-2,0).  The second equation is x = y², which has a vertex at (0, 0).  The two curves meet at the point (1, 1).  The region should look kind of like a shark fin.

(a) Rotate the region about y = -1.  Make vertical cuts and divide the volume into a stack of hollow disks (washers).

Between x=-2 and x=0, the outside radius of each washer is y₁ + 1, and the inside radius is 1.  Between x=0 and x=1, the outside radius of each washer is y₁ + 1, and the inside radius is y₂ + 1.

The thickness of each washer is dx.

Solve for y in each equation:

y₁ = √(⅓(x + 2))

y₂ = √x

The volume is therefore:

∫₋₂⁰ {π[√(⅓(x+2)) + 1]² − π 1²} dx + ∫₀¹ {π[√(⅓(x+2)) + 1]² − π[√x + 1]²} dx

∫₋₂⁰ π[⅓(x+2) + 2√(⅓(x+2))] dx + ∫₀¹ π[⅓(x+2) + 2√(⅓(x+2)) − x − 2√x] dx

∫₋₂¹ π[⅓(x+2) + 2√(⅓(x+2))] dx − ∫₀¹ π(x + 2√x) dx

π[⅙(x+2)² + 4 (⅓(x+2))^(3/2)] |₋₂¹ − π[½x² + 4/3 x^(3/2)] |₀¹

π(3/2 + 4) − π(½ + 4/3)

11π/3

(b) This time, instead of slicing vertically, we'll divide the volume into concentric shells.  The radius of each shell y + 1.  The width of each shell is x₂ − x₁.

The thickness of each shell is dy.

The volume is therefore:

∫₀¹ 2π (y + 1) (x₂ − x₁) dy

∫₀¹ 2π (y + 1) (y² − (3y² − 2)) dy

∫₀¹ 2π (y + 1) (2 − 2y²) dy

4π ∫₀¹ (y + 1) (1 − y²) dy

4π ∫₀¹ (y − y³ + 1 − y²) dy

4π (½y² − ¼y⁴ + y − ⅓y³) |₀¹

4π (½ − ¼ + 1 − ⅓)

11π/3

As you can see, when given x = f(y) and a rotation axis of y = -1, it's easier to use shell method.

(c) Since we're given x = f(y), and the rotation axis is x = -4, we should use washer method.

Make horizontal slices and divide the volume into a stack of washers.  The inside radius is 4 + x₁, and the outside radius is 4 + x₂.

The thickness of each washer is dy.

The volume is therefore:

∫₀¹ π [(4 + x₂)² − (4 + x₁)²] dy

∫₀¹ π [(4 + y²)² − (3y² + 2)²] dy

∫₀¹ π [(y⁴ + 8y² + 16) − (9y⁴ + 12y² + 4)] dy

∫₀¹ π (-8y⁴ − 4y² + 12) dy

-4π ∫₀¹ (2y⁴ + y² − 3) dy

-4π (⅖y⁵ + ⅓y³ − 3y) |₀¹

-4π (⅖ + ⅓ − 3)

136π/15

5 0
2 years ago
Explain how to use a graph of the function f(x) to<br> find f(3).
Lady bird [3.3K]
Look at the graph at which x=3, then look and see what value y is and that will give you f(3).
4 0
3 years ago
Read 2 more answers
Other questions:
  • Transform the equation to isolate x: ax = bx + 1. How is
    9·2 answers
  • Straight and vertical angles
    11·1 answer
  • X + y = 10<br> x - y = 2
    13·2 answers
  • If you follow the steps necessary to prove that square root 7 is irrational (use a proof by contradiction) to prove that square
    12·1 answer
  • A recipe calls for 3/4 ounces of vanilla to each muffin. How many ounces of vanilla will you need to make 7 muffin?
    6·1 answer
  • How do we find the slope of a line that is given in slope-intercept form?
    7·1 answer
  • Graph the opposite of the opposite of 10 on the number line. Click on the number line to
    9·1 answer
  • sarah simplify each of the Expressions what is the difference between the values of the two expressions 3 * 12 - 9 + 10 * 3 (12
    14·1 answer
  • Pls help 30 points 7th grade math
    15·1 answer
  • Expand the following:<br> c) 4(2x +1)
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!